diff options
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/matrix.spad.pamphlet | 60 | ||||
| -rw-r--r-- | src/interp/database.boot | 23 | ||||
| -rw-r--r-- | src/interp/i-analy.boot | 26 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2010 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 5798 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1971 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9532 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 32216 |
9 files changed, 24843 insertions, 26798 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 6d17d7b4..60e28147 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,8 @@ +2008-09-26 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/matrix.spad.pamphlet (new$Matrix): New. + Remove uses of pretend. Define Rep. + 2008-09-25 Gabriel Dos Reis <gdr@cs.tamu.edu> * include/cfuns.h (oa_copy_file): Declare. diff --git a/src/algebra/matrix.spad.pamphlet b/src/algebra/matrix.spad.pamphlet index a5c173dc..9e4318b6 100644 --- a/src/algebra/matrix.spad.pamphlet +++ b/src/algebra/matrix.spad.pamphlet @@ -368,15 +368,16 @@ SquareMatrix(ndim,R): Exports == Implementation where Exports ==> Join(SquareMatrixCategory(ndim,R,Row,Col),_ CoercibleTo Matrix R) with - + + new: R -> % + ++ \spad{new(c)} constructs a new \spadtype{SquareMatrix} + ++ object of dimension \spad{ndim} with initial entries equal + ++ to \spad{c}. transpose: $ -> $ ++ \spad{transpose(m)} returns the transpose of the matrix m. squareMatrix: Matrix R -> $ ++ \spad{squareMatrix(m)} converts a matrix of type \spadtype{Matrix} ++ to a matrix of type \spadtype{SquareMatrix}. - coerce: $ -> Matrix R - ++ \spad{coerce(m)} converts a matrix of type \spadtype{SquareMatrix} - ++ to a matrix of type \spadtype{Matrix}. -- symdecomp : $ -> Record(sym:$,antisym:$) -- ++ \spad{symdecomp(m)} decomposes the matrix m as a sum of a symmetric -- ++ matrix \spad{m1} and an antisymmetric matrix \spad{m2}. The object @@ -394,6 +395,7 @@ SquareMatrix(ndim,R): Exports == Implementation where if R has ConvertibleTo InputForm then ConvertibleTo InputForm Implementation ==> Matrix R add + Rep == Matrix R minr ==> minRowIndex maxr ==> maxRowIndex minc ==> minColIndex @@ -407,78 +409,80 @@ SquareMatrix(ndim,R): Exports == Implementation where 1 == ONE characteristic() == characteristic()$R + + new c == per new(ndim,ndim,c)$Rep matrix(l: List List R) == -- error check: this is a top level function #l ~= ndim => error "matrix: wrong number of rows" for ll in l repeat #ll ~= ndim => error "matrix: wrong number of columns" - ans : Matrix R := new(ndim,ndim,0) + ans := new(ndim,ndim,0)$Rep for i in minr(ans)..maxr(ans) for ll in l repeat for j in minc(ans)..maxc(ans) for r in ll repeat - qsetelt_!(ans,i,j,r) - ans pretend $ + qsetelt!(ans,i,j,r) + per ans - row(x,i) == directProduct row(x pretend Matrix(R),i) - column(x,j) == directProduct column(x pretend Matrix(R),j) - coerce(x:$):OutputForm == coerce(x pretend Matrix R)$Matrix(R) + row(x,i) == directProduct row(rep x,i) + column(x,j) == directProduct column(rep x,j) + coerce(x:$):OutputForm == rep(x)::OutputForm - scalarMatrix r == scalarMatrix(ndim,r)$Matrix(R) pretend $ + scalarMatrix r == per scalarMatrix(ndim,r)$Matrix(R) diagonalMatrix l == #l ~= ndim => error "diagonalMatrix: wrong number of entries in list" - diagonalMatrix(l)$Matrix(R) pretend $ + per diagonalMatrix(l)$Matrix(R) - coerce(x:$):Matrix(R) == copy(x pretend Matrix(R)) + coerce(x: %): Matrix(R) == copy rep x squareMatrix x == (nrows(x) ~= ndim) or (ncols(x) ~= ndim) => error "squareMatrix: matrix of bad dimensions" - copy(x) pretend $ + per copy x - x:$ * v:Col == - directProduct((x pretend Matrix(R)) * (v :: Vector(R))) + x:% * v:Col == + directProduct(rep(x) * (v :: Vector(R))) v:Row * x:$ == - directProduct((v :: Vector(R)) * (x pretend Matrix(R))) + directProduct((v :: Vector(R)) * rep(x)) x:$ ** n:NonNegativeInteger == - ((x pretend Matrix(R)) ** n) pretend $ + per(rep(x) ** n) if R has commutative("*") then - determinant x == determinant(x pretend Matrix(R)) - minordet x == minordet(x pretend Matrix(R)) + determinant x == determinant rep x + minordet x == minordet rep x if R has EuclideanDomain then - rowEchelon x == rowEchelon(x pretend Matrix(R)) pretend $ + rowEchelon x == per rowEchelon rep x if R has IntegralDomain then - rank x == rank(x pretend Matrix(R)) - nullity x == nullity(x pretend Matrix(R)) + rank x == rank rep x + nullity x == nullity rep x nullSpace x == - [directProduct c for c in nullSpace(x pretend Matrix(R))] + [directProduct c for c in nullSpace rep x] if R has Field then dimension() == (m * n) :: CardinalNumber inverse x == - (u := inverse(x pretend Matrix(R))) case "failed" => "failed" - (u :: Matrix(R)) pretend $ + (u := inverse rep x) case "failed" => "failed" + per(u :: Matrix(R)) x:$ ** n:Integer == - ((x pretend Matrix(R)) ** n) pretend $ + per(rep(x) ** n) recip x == inverse x if R has ConvertibleTo InputForm then convert(x:$):InputForm == convert [convert("squareMatrix"::Symbol)@InputForm, - convert(x::Matrix(R))]$List(InputForm) + convert(rep x)@InputForm]$List(InputForm) @ diff --git a/src/interp/database.boot b/src/interp/database.boot index 48e5d1e7..06422176 100644 --- a/src/interp/database.boot +++ b/src/interp/database.boot @@ -491,15 +491,26 @@ replaceVars(x,oldvars,newvars) == x := substitute(new,old,x) x +++ Return the list of qualifying predicates of the system modemap `mm'. +getConditionListFromMm mm == + [., cond] := mm + if cond is ["partial", :c] then cond := c + cond is ["AND", :cl] => cl + cond is ["OR", ["AND", :cl],:.] => cl --all cl's should give same info + [cond] + + +++ Returns the domain of computation of the modemap `mm'. This is not +++ to be confused with `getDomainFromMm' below, which can also return +++ a category. +getDCFromSystemModemap mm == + for cond in getConditionListFromMm mm repeat + cond is ["isDomain","*1",dom] => return dom + getDomainFromMm mm == -- Returns the Domain (or package or category) of origin from a pattern -- modemap - [., cond] := mm - if cond is ['partial, :c] then cond := c - condList := - cond is ['AND, :cl] => cl - cond is ['OR, ['AND, :cl],:.] => cl --all cl's should give same info - [cond] + condList := getConditionListFromMm mm val := for condition in condList repeat condition is ['isDomain, "*1", dom] => return opOf dom diff --git a/src/interp/i-analy.boot b/src/interp/i-analy.boot index 26a1309d..45623e50 100644 --- a/src/interp/i-analy.boot +++ b/src/interp/i-analy.boot @@ -342,8 +342,34 @@ bottomUpIdentifier(t,id) == (isMapExpr expr and [objMode(u)]) or keyedSystemError("S2GE0016", ['"bottomUpIdentifier",'"cannot evaluate identifier"]) + m := namedConstant(id,t) => [m] bottomUpDefault(t,id,defaultType,getTarget t) +getConstantObject(id,dc,sig) == + mode := substitute(dc,"$",first sig) + $genValue => + objNewWrap(SPADCALL compiledLookupCheck(id,sig,evalDomain dc),mode) + objNew(["SPADCALL",["compiledLookupCheck",id,sig,["evalDomain",dc]]],mode) + +namedConstant(id,t) == + -- for the time being, ignore the case where the target type is imposed. + getTarget(t) ^= nil => nil + sysmms := getModemapsFromDatabase(id,0) or return nil + -- ignore polymorphic constants are not supported yet. + doms := [getDCFromSystemModemap sysmm for sysmm in sysmms] + candidates := nil + for dc in doms | niladicConstructorFromDB first dc repeat + LASSOC(id,getOperationAlistFromLisplib first dc) is [[sig,.,.,"CONST"]] => + candidates := [[dc,sig],:candidates] + null candidates => nil + #candidates = 1 => + [[dc,sig]] := candidates + val := getConstantObject(id,dc,sig) + putValue(t,val) + putMode(t,objMode val) + + -- error for ambiguity. + bottomUpDefault(t,id,defaultMode,target) == if $genValue then bottomUpDefaultEval(t,id,defaultMode,target,nil) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 2da45484..bd487162 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2266112 . 3431185328) +(2264448 . 3431436953) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL NIL (-19 S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4333 . T) (-4331 . T) (-4330 . T) ((-4338 "*") . T) (-4329 . T) (-4334 . T) (-4328 . T) (-2623 . T)) +((-4333 . T) (-4331 . T) (-4330 . T) ((-4338 "*") . T) (-4329 . T) (-4334 . T) (-4328 . T) (-2359 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,17 +56,17 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1421) +(-32 R -3416) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) +((|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL ((|HasAttribute| |#1| (QUOTE -4336))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2623 . T)) +((-2359 . T)) NIL (-35) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4336 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4337 . T) (-2359 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -88,14 +88,14 @@ 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 -1421 UP UPUP -2968) +(-40 -3416 UP UPUP -2931) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4329 |has| (-400 |#2|) (-356)) (-4334 |has| (-400 |#2|) (-356)) (-4328 |has| (-400 |#2|) (-356)) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-342))) (-1536 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-1536 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (-1536 (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-342))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1536 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356))))) -(-41 R -1421) +((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-343))) (-3874 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-343)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-3874 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-343)))) (-3874 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-343))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-3874 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356))))) +(-41 R -3416) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -414) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,24 +106,24 @@ NIL ((|HasCategory| |#1| (QUOTE (-300)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4333 |has| |#1| (-541)) (-4331 . T) (-4330 . T)) -((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) +((-4333 |has| |#1| (-542)) (-4331 . T) (-4330 . T)) +((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4336 . T) (-4337 . T)) -((-1536 (-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|))))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-823)))) (-12 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067))))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-3874 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-823))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067))) (-3874 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (-12 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356)))) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-549))))) +((|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-535))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL @@ -132,19 +132,19 @@ NIL ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) ((-4333 . T)) NIL -(-51 S) -((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) +(-51) +((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) NIL NIL -(-52) -((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) +(-52 S) +((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) NIL NIL (-53 R M P) ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1421) +(-54 |Base| R -3416) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -154,133 +154,133 @@ NIL NIL (-56 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4336 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4337 . T) (-2359 . T)) NIL -(-57 A B) +(-57 S) +((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) +((-4337 . T) (-4336 . T)) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) NIL NIL -(-58 S) -((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (-59 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) -(-60 -2480) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-60 -3888) +((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +NIL +NIL +(-61 -3888) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-61 -2480) +(-62 -3888) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-62 -2480) +(-63 -3888) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-63 -2480) -((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) -NIL -NIL -(-64 -2480) +(-64 -3888) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-65 -2480) +(-65 -3888) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-66 -2480) +(-66 -3888) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -2480) +(-67 -3888) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2480) +(-68 -3888) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-69 -2480) +(-69 -3888) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-70 -2480) +(-70 -3888) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-71 -2480) +(-71 -3888) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-72 -2480) +(-72 -3888) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-73 -2480) +(-73 -3888) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-74 |nameOne| |nameTwo| |nameThree|) -((|constructor| (NIL "\\spadtype{Asp41} produces Fortran for Type 41 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE FCN(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=Y(2) F(2)=Y(3) F(3)=(-1.0D0*Y(1)*Y(3))+2.0D0*EPS*Y(2)**2+(-2.0D0*EPS) RETURN END SUBROUTINE JACOBF(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N,N),X,Y(N) INTEGER N F(1,1)=0.0D0 F(1,2)=1.0D0 F(1,3)=0.0D0 F(2,1)=0.0D0 F(2,2)=0.0D0 F(2,3)=1.0D0 F(3,1)=-1.0D0*Y(3) F(3,2)=4.0D0*EPS*Y(2) F(3,3)=-1.0D0*Y(1) RETURN END SUBROUTINE JACEPS(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=0.0D0 F(2)=0.0D0 F(3)=2.0D0*Y(2)**2-2.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-74 -3888) +((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL (-75 |nameOne| |nameTwo| |nameThree|) -((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +((|constructor| (NIL "\\spadtype{Asp41} produces Fortran for Type 41 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE FCN(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=Y(2) F(2)=Y(3) F(3)=(-1.0D0*Y(1)*Y(3))+2.0D0*EPS*Y(2)**2+(-2.0D0*EPS) RETURN END SUBROUTINE JACOBF(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N,N),X,Y(N) INTEGER N F(1,1)=0.0D0 F(1,2)=1.0D0 F(1,3)=0.0D0 F(2,1)=0.0D0 F(2,2)=0.0D0 F(2,3)=1.0D0 F(3,1)=-1.0D0*Y(3) F(3,2)=4.0D0*EPS*Y(2) F(3,3)=-1.0D0*Y(1) RETURN END SUBROUTINE JACEPS(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=0.0D0 F(2)=0.0D0 F(3)=2.0D0*Y(2)**2-2.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-76 -2480) -((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +(-76 |nameOne| |nameTwo| |nameThree|) +((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2480) -((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +(-77 -3888) +((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2480) +(-78 -3888) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -2480) +(-79 -3888) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2480) +(-80 -3888) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2480) +(-81 -3888) +((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +NIL +NIL +(-82 -3888) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -2480) +(-83 -3888) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2480) +(-84 -3888) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2480) +(-85 -3888) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2480) -((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-86 -3888) +((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-86 -2480) +(-87 -3888) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2480) -((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) -NIL -NIL -(-88 -2480) +(-88 -3888) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -291,7 +291,7 @@ NIL (-90 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-91 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -339,7 +339,7 @@ NIL (-102 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-103 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -354,12 +354,12 @@ NIL NIL (-106 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4337 . T) (-2623 . T)) +((-4337 . T) (-2359 . T)) NIL (-107) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-549) (QUOTE (-880))) (|HasCategory| (-549) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-549) (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-145))) (|HasCategory| (-549) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-549) (QUOTE (-993))) (|HasCategory| (-549) (QUOTE (-796))) (-1536 (|HasCategory| (-549) (QUOTE (-796))) (|HasCategory| (-549) (QUOTE (-823)))) (|HasCategory| (-549) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| (-549) (QUOTE (-1117))) (|HasCategory| (-549) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| (-549) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| (-549) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| (-549) (QUOTE (-227))) (|HasCategory| (-549) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-549) (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -302) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -279) (QUOTE (-549)) (QUOTE (-549)))) (|HasCategory| (-549) (QUOTE (-300))) (|HasCategory| (-549) (QUOTE (-534))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-549) (LIST (QUOTE -617) (QUOTE (-549)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-880)))) (|HasCategory| (-549) (QUOTE (-143))))) +((|HasCategory| (-535) (QUOTE (-881))) (|HasCategory| (-535) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-535) (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-145))) (|HasCategory| (-535) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-535) (QUOTE (-991))) (|HasCategory| (-535) (QUOTE (-796))) (-3874 (|HasCategory| (-535) (QUOTE (-796))) (|HasCategory| (-535) (QUOTE (-823)))) (|HasCategory| (-535) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-535) (QUOTE (-1117))) (|HasCategory| (-535) (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-535) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-535) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-535) (QUOTE (-227))) (|HasCategory| (-535) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-535) (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -302) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -279) (QUOTE (-535)) (QUOTE (-535)))) (|HasCategory| (-535) (QUOTE (-300))) (|HasCategory| (-535) (QUOTE (-534))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-535) (LIST (QUOTE -617) (QUOTE (-535)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-881)))) (-3874 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-881)))) (|HasCategory| (-535) (QUOTE (-143))))) (-108) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -371,7 +371,7 @@ NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1066))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-112) (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-112) (QUOTE (-1066))) (|HasCategory| (-112) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-112) (QUOTE (-1067))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-112) (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-112) (QUOTE (-1067))) (|HasCategory| (-112) (LIST (QUOTE -593) (QUOTE (-835))))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) ((-4331 . T) (-4330 . T)) @@ -380,15 +380,15 @@ NIL ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-113 A) -((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise."))) -NIL -((|HasCategory| |#1| (QUOTE (-823)))) -(-114) +(-113) ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -1421 UP) +(-114 A) +((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise."))) +NIL +((|HasCategory| |#1| (QUOTE (-823)))) +(-115 -3416 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -399,14 +399,14 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-880))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-116 |#1|) (QUOTE (-993))) (|HasCategory| (-116 |#1|) (QUOTE (-796))) (-1536 (|HasCategory| (-116 |#1|) (QUOTE (-796))) (|HasCategory| (-116 |#1|) (QUOTE (-823)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| (-116 |#1|) (QUOTE (-1117))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| (-116 |#1|) (QUOTE (-227))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -505) (QUOTE (-1142)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-300))) (|HasCategory| (-116 |#1|) (QUOTE (-534))) (|HasCategory| (-116 |#1|) (QUOTE (-823))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-880)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))))) +((|HasCategory| (-116 |#1|) (QUOTE (-881))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-116 |#1|) (QUOTE (-991))) (|HasCategory| (-116 |#1|) (QUOTE (-796))) (-3874 (|HasCategory| (-116 |#1|) (QUOTE (-796))) (|HasCategory| (-116 |#1|) (QUOTE (-823)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-116 |#1|) (QUOTE (-1117))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| (-116 |#1|) (QUOTE (-227))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -505) (QUOTE (-1142)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-300))) (|HasCategory| (-116 |#1|) (QUOTE (-534))) (|HasCategory| (-116 |#1|) (QUOTE (-823))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-881)))) (-3874 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-881)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4337))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) -((-2623 . T)) +((-2359 . T)) NIL (-120 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) @@ -415,14 +415,14 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,24 +430,24 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4336 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4337 . T) (-2359 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-128) -((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) -((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| (-129) (QUOTE (-823))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1066))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129)))))) (-1536 (-12 (|HasCategory| (-129) (QUOTE (-1066))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-129) (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| (-129) (QUOTE (-823))) (|HasCategory| (-129) (QUOTE (-1066)))) (|HasCategory| (-129) (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-129) (QUOTE (-1066))) (-12 (|HasCategory| (-129) (QUOTE (-1066))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -593) (QUOTE (-834))))) -(-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL NIL +(-129) +((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) +((-4337 . T) (-4336 . T)) +((-3874 (-12 (|HasCategory| (-128) (QUOTE (-823))) (|HasCategory| (-128) (LIST (QUOTE -302) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1067))) (|HasCategory| (-128) (LIST (QUOTE -302) (QUOTE (-128)))))) (-3874 (-12 (|HasCategory| (-128) (QUOTE (-1067))) (|HasCategory| (-128) (LIST (QUOTE -302) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| (-128) (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| (-128) (QUOTE (-823))) (|HasCategory| (-128) (QUOTE (-1067)))) (|HasCategory| (-128) (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-128) (QUOTE (-1067))) (-12 (|HasCategory| (-128) (QUOTE (-1067))) (|HasCategory| (-128) (LIST (QUOTE -302) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -593) (QUOTE (-835))))) (-130) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL @@ -464,12 +464,12 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4338 "*") . T)) NIL -(-134 |minix| -2727 S T$) -((|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}."))) +(-134 |minix| -2938 R) +((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-135 |minix| -2727 R) -((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) +(-135 |minix| -2938 S T$) +((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL (-136) @@ -487,7 +487,7 @@ NIL (-139) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4336 . T) (-4326 . T) (-4337 . T)) -((-1536 (-12 (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1066))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-142) (QUOTE (-1066))) (-12 (|HasCategory| (-142) (QUOTE (-1066))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1067))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-142) (QUOTE (-1067))) (-12 (|HasCategory| (-142) (QUOTE (-1067))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -593) (QUOTE (-835))))) (-140 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -512,7 +512,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4333 . T)) NIL -(-146 -1421 UP UPUP) +(-146 -3416 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) NIL NIL @@ -523,10 +523,10 @@ NIL (-148 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasAttribute| |#1| (QUOTE -4336))) +((|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasAttribute| |#1| (QUOTE -4336))) (-149 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-2623 . T)) +((-2359 . T)) NIL (-150 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) @@ -552,7 +552,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-156 R -1421) +(-156 R -3416) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -565,11 +565,11 @@ NIL NIL NIL (-159) -((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'."))) +((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) NIL NIL (-160) -((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) +((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'."))) NIL NIL (-161) @@ -583,23 +583,23 @@ NIL (-163 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-880))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-1164))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-993))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasAttribute| |#2| (QUOTE -4332)) (|HasAttribute| |#2| (QUOTE -4335)) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-823)))) +((|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-1164))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasAttribute| |#2| (QUOTE -4332)) (|HasAttribute| |#2| (QUOTE -4335)) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-823)))) (-164 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4329 -1536 (|has| |#1| (-541)) (-12 (|has| |#1| (-300)) (|has| |#1| (-880)))) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4332 |has| |#1| (-6 -4332)) (-4335 |has| |#1| (-6 -4335)) (-3409 . T) (-2623 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-4329 -3874 (|has| |#1| (-542)) (-12 (|has| |#1| (-300)) (|has| |#1| (-881)))) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4332 |has| |#1| (-6 -4332)) (-4335 |has| |#1| (-6 -4335)) (-1420 . T) (-2359 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-165 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) NIL NIL -(-166 R S) +(-166 R) +((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) +((-4329 -3874 (|has| |#1| (-542)) (-12 (|has| |#1| (-300)) (|has| |#1| (-881)))) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4332 |has| |#1| (-6 -4332)) (-4335 |has| |#1| (-6 -4335)) (-1420 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-343))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-1164)))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) 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(|HasCategory| |#1| (QUOTE (-881)))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-881))))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1164)))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-542)))) (-3874 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-797))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1164)))) (|HasCategory| |#1| (QUOTE (-534))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-881))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-356)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-227))) (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasAttribute| |#1| (QUOTE -4332)) (|HasAttribute| |#1| (QUOTE -4335)) (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-343))))) +(-167 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,{}u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL NIL -(-167 R) -((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4329 -1536 (|has| |#1| (-541)) (-12 (|has| |#1| (-300)) (|has| |#1| (-880)))) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4332 |has| |#1| (-6 -4332)) (-4335 |has| |#1| (-6 -4335)) (-3409 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-342))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-227))) (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-361)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-804)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-993)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-1164)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-880))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-880)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-880)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-880))))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1164)))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#1| (QUOTE (-1027))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1164)))) (|HasCategory| |#1| (QUOTE (-534))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-880))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-356)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-227))) (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasAttribute| |#1| (QUOTE -4332)) (|HasAttribute| |#1| (QUOTE -4335)) (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-342))))) (-168 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -635,7 +635,7 @@ NIL (-176 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-923 |#2|) (LIST (QUOTE -857) (|devaluate| |#1|)))) +((|HasCategory| (-917 |#2|) (LIST (QUOTE -857) (|devaluate| |#1|)))) (-177 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) NIL @@ -656,7 +656,7 @@ NIL ((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-182 R -1421) +(-182 R -3416) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -764,28 +764,28 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-209 -1421 UP UPUP R) +(-209 -3416 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-210 -1421 FP) +(-210 -3416 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-211) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-549) (QUOTE (-880))) (|HasCategory| (-549) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-549) (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-145))) (|HasCategory| (-549) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-549) (QUOTE (-993))) (|HasCategory| (-549) (QUOTE (-796))) (-1536 (|HasCategory| (-549) (QUOTE (-796))) (|HasCategory| (-549) (QUOTE (-823)))) (|HasCategory| (-549) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| (-549) (QUOTE (-1117))) (|HasCategory| (-549) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| (-549) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| (-549) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| (-549) (QUOTE (-227))) (|HasCategory| (-549) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-549) (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -302) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -279) (QUOTE (-549)) (QUOTE (-549)))) (|HasCategory| (-549) (QUOTE (-300))) (|HasCategory| (-549) (QUOTE (-534))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-549) (LIST (QUOTE -617) (QUOTE (-549)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-880)))) (|HasCategory| (-549) (QUOTE (-143))))) +((|HasCategory| (-535) (QUOTE (-881))) (|HasCategory| (-535) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-535) (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-145))) (|HasCategory| (-535) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-535) (QUOTE (-991))) (|HasCategory| (-535) (QUOTE (-796))) (-3874 (|HasCategory| (-535) (QUOTE (-796))) (|HasCategory| (-535) (QUOTE (-823)))) (|HasCategory| (-535) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-535) (QUOTE (-1117))) (|HasCategory| (-535) (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-535) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-535) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-535) (QUOTE (-227))) (|HasCategory| (-535) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-535) (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -302) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -279) (QUOTE (-535)) (QUOTE (-535)))) (|HasCategory| (-535) (QUOTE (-300))) (|HasCategory| (-535) (QUOTE (-534))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-535) (LIST (QUOTE -617) (QUOTE (-535)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-881)))) (-3874 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-881)))) (|HasCategory| (-535) (QUOTE (-143))))) (-212) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-213 R -1421) -((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) +(-213 R -3416) +((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL (-214 R) -((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) +((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL (-215 R1 R2) @@ -795,18 +795,18 @@ NIL (-216 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-217 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4333 . T)) NIL -(-218 R -1421) +(-218 R -3416) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-219) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2660 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-4112 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-220) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -815,14 +815,14 @@ NIL (-221 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-541))) (|HasAttribute| |#1| (QUOTE (-4338 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))) (|HasAttribute| |#1| (QUOTE (-4338 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-222 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-223 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4337 . T) (-2623 . T)) +((-4337 . T) (-2359 . T)) NIL (-224 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -846,28 +846,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4336))) (-229 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4337 . T) (-2623 . T)) +((-4337 . T) (-2359 . T)) NIL (-230) ((|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 -(-231 S -2727 R) +(-231 S -2938 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-769))) (|HasCategory| |#3| (QUOTE (-821))) (|HasAttribute| |#3| (QUOTE -4333)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (QUOTE (-703))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (QUOTE (-1066)))) -(-232 -2727 R) +((|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-769))) (|HasCategory| |#3| (QUOTE (-821))) (|HasAttribute| |#3| (QUOTE -4333)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (QUOTE (-703))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (QUOTE (-1067)))) +(-232 -2938 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4330 |has| |#2| (-1018)) (-4331 |has| |#2| (-1018)) (-4333 |has| |#2| (-6 -4333)) ((-4338 "*") |has| |#2| (-170)) (-4336 . T) (-2623 . T)) +((-4330 |has| |#2| (-1018)) (-4331 |has| |#2| (-1018)) (-4333 |has| |#2| (-6 -4333)) ((-4338 "*") |has| |#2| (-170)) (-4336 . T) (-2359 . T)) NIL -(-233 -2727 A B) +(-233 -2938 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."))) +((-4330 |has| |#2| (-1018)) (-4331 |has| |#2| (-1018)) (-4333 |has| |#2| (-6 -4333)) ((-4338 "*") |has| |#2| (-170)) (-4336 . 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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}."))) 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(QUOTE (-549)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-1066)))) (|HasAttribute| |#2| (QUOTE -4333)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (-235) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 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(|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) -((-2623 . T)) +((-2359 . T)) NIL (-239 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) ((-4337 . T) (-4336 . 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(|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-241 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(QUOTE (-703))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (QUOTE (-769))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (QUOTE (-821))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535)))))) (|HasCategory| (-535) (QUOTE (-823))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1018)))) (-3874 (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1018)))) (|HasCategory| |#3| (QUOTE (-703)))) (-3874 (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (|HasCategory| |#3| (QUOTE (-1018)))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (-3874 (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -617) (QUOTE (-535))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142))))) (|HasAttribute| |#3| (QUOTE -4333)) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1018))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-835))))) (-245 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-227)))) (-246 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) NIL (-247 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4336 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4337 . T) (-2359 . T)) +NIL +(-248 |Ex|) +((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) +NIL NIL -(-248) +(-249) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL NIL -(-249 R |Ex|) +(-250 R |Ex|) ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y) = g(x,{}y),{}x,{}y,{}l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) NIL NIL -(-250) +(-251) ((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,{}rRange,{}iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f,{} -2..2,{} -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,{}rRange,{}iRange,{}arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f,{} 0.3..3,{} 0..2*\\%\\spad{pi},{} false)}} Parameter descriptions: \\indented{2}{\\spad{f:}\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) NIL NIL -(-251 R) +(-252 R) ((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) NIL NIL -(-252 |Ex|) -((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) -NIL -NIL (-253) ((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}lz,{}l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly,{}lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,{}l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) NIL NIL (-254) -((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,{}u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,{}r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,{}ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) +((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) NIL NIL -(-255 S) -((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,{}s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) +(-255) +((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,{}u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,{}r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,{}ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) NIL NIL -(-256) -((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) +(-256 S) +((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,{}s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) NIL NIL (-257 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . 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T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-881))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| |#3| (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#3| (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| |#3| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#3| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#3| (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) (-258 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1004,11 +1004,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-269 R -1421) +(-269 R -3416) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-270 R -1421) +(-270 R -3416) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1027,10 +1027,10 @@ NIL (-274 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066)))) +((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1067)))) (-275 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4337 . T) (-2623 . T)) +((-4337 . T) (-2359 . T)) NIL (-276 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1056,7 +1056,7 @@ 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 -(-282 S R |Mod| -1998 -1586 |exactQuo|) +(-282 S R |Mod| -2145 -3855 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL @@ -1072,58 +1072,58 @@ NIL ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,{}m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,{}m,{}k,{}g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,{}m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) NIL NIL -(-286 S R) +(-286 S) +((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) +((-4333 -3874 (|has| |#1| (-1018)) (|has| |#1| (-465))) (-4330 |has| |#1| (-1018)) (-4331 |has| |#1| (-1018))) +((|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1018)))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (-3874 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-3874 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-3874 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-3874 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-703)))) (|HasCategory| |#1| (QUOTE (-465))) (-3874 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-3874 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-291))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465)))) (-3874 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-703)))) (-3874 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) +(-287 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,{}eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL -(-287 S) -((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4333 -1536 (|has| |#1| (-1018)) (|has| |#1| (-465))) (-4330 |has| |#1| (-1018)) (-4331 |has| |#1| (-1018))) -((|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-703)))) (|HasCategory| |#1| (QUOTE (-465))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-1066)))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-295))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465)))) (-1536 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-703)))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) (-288 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1067))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835))))) (-289) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-290 -1421 S) -((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) +(-290 S) +((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) +NIL +((|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-1018)))) +(-291) +((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-291 E -1421) -((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) +(-292 -3416 S) +((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-292 A B) -((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) +(-293 E -3416) +((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL NIL -(-293) +(-294) ((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) NIL NIL -(-294 S) -((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) +(-295 A B) +((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1018)))) -(-295) -((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) +NIL +(-296) +((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) NIL NIL -(-296 R1) +(-297 R1) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage1} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}"))) NIL NIL -(-297 R1 R2) +(-298 R1 R2) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage2} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,{}m)} applies a mapping f:R1 \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}"))) NIL NIL -(-298) -((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) -NIL -NIL (-299 S) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) NIL @@ -1140,35 +1140,35 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-303 -1421) +(-303 -3416) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL (-304) -((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) +((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) NIL NIL (-305) -((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) +((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) NIL NIL (-306 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-880))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-993))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-796))) (-1536 (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-796))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-823)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-1117))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-227))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -505) (QUOTE (-1142)) (LIST (QUOTE -1211) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -302) (LIST (QUOTE -1211) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -279) (LIST (QUOTE -1211) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1211) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-300))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-534))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-823))) (-12 (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-880))) (|HasCategory| $ (QUOTE (-143)))) (-1536 (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (-12 (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-880))) (|HasCategory| $ (QUOTE (-143)))))) -(-307 R S) +((|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-881))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-991))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-796))) (-3874 (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-796))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-823)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-1117))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-227))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -505) (QUOTE (-1142)) (LIST (QUOTE -1211) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -302) (LIST (QUOTE -1211) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (LIST (QUOTE -279) (LIST (QUOTE -1211) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1211) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-300))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-534))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-823))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-881)))) (-3874 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-881)))) (|HasCategory| (-1211 |#1| |#2| |#3| |#4|) (QUOTE (-143))))) +(-307 R) +((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) +((-4333 -3874 (-3179 (|has| |#1| (-1018)) (|has| |#1| (-617 (-535)))) (-12 (|has| |#1| (-542)) (-3874 (-3179 (|has| |#1| (-1018)) (|has| |#1| (-617 (-535)))) (|has| |#1| (-1018)) (|has| |#1| (-465)))) (|has| |#1| (-1018)) (|has| |#1| (-465))) (-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) ((-4338 "*") |has| |#1| (-542)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-542)) (-4328 |has| |#1| (-542))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasCategory| |#1| (QUOTE (-542))) (-3874 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (-3874 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (-3874 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (-3874 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (-3874 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542)))) (-3874 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-542)))) (-3874 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (-3874 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-1078)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-21)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1078)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-25)))) (-3874 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1018)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-535))))) +(-308 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL NIL -(-308 R FE) +(-309 R FE) ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,{}x = a,{}n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,{}x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,{}n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}x = a,{}n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,{}x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,{}x = a,{}n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,{}x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,{}n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,{}n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-309 R) -((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4333 -1536 (-1820 (|has| |#1| (-1018)) (|has| |#1| (-617 (-549)))) (-12 (|has| |#1| (-541)) (-1536 (-1820 (|has| |#1| (-1018)) (|has| |#1| (-617 (-549)))) (|has| |#1| (-1018)) (|has| |#1| (-465)))) (|has| |#1| (-1018)) (|has| |#1| (-465))) (-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) ((-4338 "*") |has| |#1| (-541)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-541)) (-4328 |has| |#1| (-541))) -((-1536 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549))))) (-1536 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1078)))) (-1536 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))))) (-1536 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1078)))) (-1536 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))))) (-1536 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-549))))) -(-310 R -1421) +(-310 R -3416) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1178,8 +1178,8 @@ NIL NIL (-312 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."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -1531) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-535)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasSignature| |#1| (LIST (QUOTE -4300) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535)))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-931))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasSignature| |#1| (LIST (QUOTE -4155) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (LIST (QUOTE -618) (QUOTE (-1142))) (|devaluate| |#1|))))))) (-313 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1191,7 +1191,7 @@ NIL (-315 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) ((-4331 . T) (-4330 . T)) -((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-768)))) +((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-768)))) (-316 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1203,20 +1203,20 @@ NIL (-318 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-170)))) +((|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170)))) (-319 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-320 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) -(-321 S -1421) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-321 S -3416) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-361)))) -(-322 -1421) +(-322 -3416) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL @@ -1232,22 +1232,22 @@ NIL ((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and,{} where appropriate,{} naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables I1,{} I2,{} and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,{}p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,{}p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,{}b,{}d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,{}p,{}q)} uses loop variables in the Fortran,{} I1 and I2")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,{}p)} \\undocumented{}"))) NIL NIL -(-326 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +(-326 -3416 UP UPUP R) +((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) +NIL +NIL +(-327 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-327 S -1421 UP UPUP R) +(-328 S -3416 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-328 -1421 UP UPUP R) +(-329 -3416 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-329 -1421 UP UPUP R) -((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) -NIL -NIL (-330 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL @@ -1259,87 +1259,87 @@ NIL (-332 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) ((-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-372)))) (|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-549))))) -(-333 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) -((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) -NIL -NIL -(-334 S -1421 UP UPUP) +((|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-371)))) (|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-535))))) +(-333 |p| |n|) +((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) +((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-3874 (|HasCategory| (-877 |#1|) (QUOTE (-143))) (|HasCategory| (-877 |#1|) (QUOTE (-361)))) (|HasCategory| (-877 |#1|) (QUOTE (-145))) (|HasCategory| (-877 |#1|) (QUOTE (-361))) (|HasCategory| (-877 |#1|) (QUOTE (-143)))) +(-334 S -3416 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-356)))) -(-335 -1421 UP UPUP) +(-335 -3416 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4329 |has| (-400 |#2|) (-356)) (-4334 |has| (-400 |#2|) (-356)) (-4328 |has| (-400 |#2|) (-356)) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-336 |p| |extdeg|) +(-336 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) +NIL +NIL +(-337 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| (-881 |#1|) (QUOTE (-143))) (|HasCategory| (-881 |#1|) (QUOTE (-361)))) (|HasCategory| (-881 |#1|) (QUOTE (-145))) (|HasCategory| (-881 |#1|) (QUOTE (-361))) (|HasCategory| (-881 |#1|) (QUOTE (-143)))) -(-337 GF |defpol|) +((-3874 (|HasCategory| (-877 |#1|) (QUOTE (-143))) (|HasCategory| (-877 |#1|) (QUOTE (-361)))) (|HasCategory| (-877 |#1|) (QUOTE (-145))) (|HasCategory| (-877 |#1|) (QUOTE (-361))) (|HasCategory| (-877 |#1|) (QUOTE (-143)))) +(-338 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) -(-338 GF |extdeg|) +((-3874 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) +(-339 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) -(-339 GF) +((-3874 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) +(-340 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL NIL -(-340 F1 GF F2) +(-341 F1 GF F2) ((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}\\spad{GF},{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn\\spad{'t} divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn\\spad{'t} divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) NIL NIL -(-341 S) +(-342 S) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) NIL NIL -(-342) +(-343) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-343 R UP -1421) +(-344 R UP -3416) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL -(-344 |p| |extdeg|) +(-345 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| (-881 |#1|) (QUOTE (-143))) (|HasCategory| (-881 |#1|) (QUOTE (-361)))) (|HasCategory| (-881 |#1|) (QUOTE (-145))) (|HasCategory| (-881 |#1|) (QUOTE (-361))) (|HasCategory| (-881 |#1|) (QUOTE (-143)))) -(-345 GF |uni|) +((-3874 (|HasCategory| (-877 |#1|) (QUOTE (-143))) (|HasCategory| (-877 |#1|) (QUOTE (-361)))) (|HasCategory| (-877 |#1|) (QUOTE (-145))) (|HasCategory| (-877 |#1|) (QUOTE (-361))) (|HasCategory| (-877 |#1|) (QUOTE (-143)))) +(-346 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) -(-346 GF |extdeg|) +((-3874 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) +(-347 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) -(-347 |p| |n|) -((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| (-881 |#1|) (QUOTE (-143))) (|HasCategory| (-881 |#1|) (QUOTE (-361)))) (|HasCategory| (-881 |#1|) (QUOTE (-145))) (|HasCategory| (-881 |#1|) (QUOTE (-361))) (|HasCategory| (-881 |#1|) (QUOTE (-143)))) +((-3874 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) (-348 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) -(-349 -1421 GF) -((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) +((-3874 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) +(-349 GF) +((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-350 GF) -((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) +(-350 -3416 GF) +((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-351 -1421 FP FPP) +(-351 -3416 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-352 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) +((-3874 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143)))) (-353 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1356,21 +1356,21 @@ NIL ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-357 |Name| S) -((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) +(-357 S) +((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL -(-358 S) -((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) +(-358 |Name| S) +((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) NIL NIL (-359 S R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-541)))) +((|HasCategory| |#2| (QUOTE (-542)))) (-360 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4333 |has| |#1| (-541)) (-4331 . T) (-4330 . T)) +((-4333 |has| |#1| (-542)) (-4331 . T) (-4330 . T)) NIL (-361) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1384,17 +1384,17 @@ NIL ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) ((-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-364 S A R B) -((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) -NIL -NIL -(-365 A S) +(-364 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4337)) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066)))) -(-366 S) +((|HasAttribute| |#1| (QUOTE -4337)) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1067)))) +(-365 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4336 . T) (-2623 . T)) +((-4336 . T) (-2359 . T)) +NIL +(-366 S A R B) +((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) +NIL NIL (-367 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) @@ -1407,43 +1407,43 @@ NIL (-369 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) +((|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535))))) (-370 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) ((-4333 . T)) NIL -(-371 |Par|) -((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) +(-371) +((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) +((-4319 . T) (-4327 . T) (-4112 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL +(-372 |Par|) +((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) NIL -(-372) -((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4319 . T) (-4327 . T) (-2660 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-373 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) NIL NIL (-374 R S) -((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) +((|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."))) ((-4331 . T) (-4330 . T)) ((|HasCategory| |#1| (QUOTE (-170)))) -(-375 R |Basis|) -((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) +(-375 R S) +((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) ((-4331 . T) (-4330 . T)) -NIL +((|HasCategory| |#1| (QUOTE (-170)))) (-376) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2623 . T)) +((-2359 . T)) +NIL +(-377 R |Basis|) +((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) +((-4331 . T) (-4330 . T)) NIL -(-377) +(-378) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2623 . T)) +((-2359 . T)) NIL -(-378 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."))) -((-4331 . T) (-4330 . T)) -((|HasCategory| |#1| (QUOTE (-170)))) (-379 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{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 @@ -1468,41 +1468,41 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-385 -1421 UP UPUP R) +(-385 -3416 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL -(-386 S) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) +(-386) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format."))) NIL NIL -(-387) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format."))) +(-387 S) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) NIL NIL (-388) -((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-2623 . T)) +((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) +NIL NIL (-389) -((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2623 . T)) +((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) +((-2359 . T)) NIL (-390) -((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) -NIL +((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) +((-2359 . T)) NIL -(-391 -2480 |returnType| -2871 |symbols|) +(-391 -3888 |returnType| -1463 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-392 -1421 UP) +(-392 -3416 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-393 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2623 . T)) +((-2359 . T)) NIL (-394 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1518,121 +1518,121 @@ NIL ((|HasAttribute| |#1| (QUOTE -4319)) (|HasAttribute| |#1| (QUOTE -4327))) (-397) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2660 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-4112 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-398 R S) +(-398 R) +((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) +((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -302) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -279) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (QUOTE (-1183))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-444)))) +(-399 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL -(-399 A B) -((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) -NIL -NIL (-400 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4323 -12 (|has| |#1| (-6 -4334)) (|has| |#1| (-444)) (|has| |#1| (-6 -4323))) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-804)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (QUOTE (-796))) (-1536 (|HasCategory| |#1| (QUOTE (-796))) (|HasCategory| |#1| (QUOTE (-823)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-804)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1117))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-804)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-804))))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-804))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-804)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-534))) (-12 (|HasAttribute| |#1| (QUOTE -4334)) (|HasAttribute| |#1| (QUOTE -4323)) (|HasCategory| |#1| (QUOTE (-444)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143))))) -(-401 S R UP) +((|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-797)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (QUOTE (-796))) (-3874 (|HasCategory| |#1| (QUOTE (-796))) (|HasCategory| |#1| (QUOTE (-823)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-797)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-1117))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-797)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-797)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-797)))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-534))) (-12 (|HasAttribute| |#1| (QUOTE -4323)) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) +(-401 A B) +((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) +NIL +NIL +(-402 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL -(-402 R UP) +(-403 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) ((-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-403 A S) +(-404 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549))))) -(-404 S) +((|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535))))) +(-405 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-405 R1 F1 U1 A1 R2 F2 U2 A2) -((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) -NIL -NIL -(-406 R -1421 UP A) +(-406 R -3416 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) ((-4333 . T)) NIL -(-407 R -1421 UP A |ibasis|) +(-407 R1 F1 U1 A1 R2 F2 U2 A2) +((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) +NIL +NIL +(-408 R -3416 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1009) (|devaluate| |#2|)))) -(-408 AR R AS S) +(-409 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL NIL -(-409 S R) +(-410 S R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#2| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL ((|HasCategory| |#2| (QUOTE (-356)))) -(-410 R) +(-411 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4333 |has| |#1| (-541)) (-4331 . T) (-4330 . T)) +((-4333 |has| |#1| (-542)) (-4331 . T) (-4330 . T)) NIL -(-411 R) -((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -302) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -279) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-1183))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-993))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-444)))) (-412 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL NIL -(-413 R FE |x| |cen|) -((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) +(-413 S R) +((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL +((|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524))))) +(-414 R) +((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) +((-4333 -3874 (|has| |#1| (-1018)) (|has| |#1| (-465))) (-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) ((-4338 "*") |has| |#1| (-542)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-542)) (-4328 |has| |#1| (-542)) (-2359 . T)) NIL -(-414 R A S B) +(-415 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) NIL NIL -(-415 R FE |Expon| UPS TRAN |x|) -((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'"))) +(-416 R FE |x| |cen|) +((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) NIL NIL -(-416 S A R B) -((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) +(-417 R FE |Expon| UPS TRAN |x|) +((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'"))) NIL NIL -(-417 A S) +(-418 A S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) NIL ((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-361)))) -(-418 S) +(-419 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4336 . T) (-4326 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4326 . T) (-4337 . T) (-2359 . T)) NIL -(-419 R -1421) +(-420 S A R B) +((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) +NIL +NIL +(-421 R -3416) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL -(-420 R E) +(-422 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4323 -12 (|has| |#1| (-6 -4323)) (|has| |#2| (-6 -4323))) (-4330 . T) (-4331 . T) (-4333 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4323)) (|HasAttribute| |#2| (QUOTE -4323)))) -(-421 R -1421) +(-423 R -3416) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL -(-422 S R) -((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -NIL -((|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525))))) -(-423 R) -((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4333 -1536 (|has| |#1| (-1018)) (|has| |#1| (-465))) (-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) ((-4338 "*") |has| |#1| (-541)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-541)) (-4328 |has| |#1| (-541)) (-2623 . T)) -NIL -(-424 R -1421) +(-424 R -3416) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-425 R -1421) +(-425 R -3416) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-426 R -1421) +(-426 R -3416) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1640,16 +1640,16 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-428 R -1421 UP) +(-428 R -3416 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-48))))) (-429) -((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) +((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}"))) NIL NIL (-430) -((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}"))) +((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) NIL NIL (-431 |f|) @@ -1658,17 +1658,17 @@ NIL NIL (-432) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2623 . T)) +((-2359 . T)) NIL (-433) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2623 . T)) +((-2359 . T)) NIL (-434 UP) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-435 R UP -1421) +(-435 R UP -3416) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1685,21 +1685,21 @@ NIL NIL NIL (-439 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) -NIL +((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) NIL +((|HasCategory| |#1| (QUOTE (-356)))) (-440 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions,{} info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,{}info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) +((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) NIL NIL (-441 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) +((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions,{} info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,{}info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) NIL NIL (-442 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) +((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) +NIL NIL -((|HasCategory| |#1| (QUOTE (-356)))) (-443 S) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) NIL @@ -1710,12 +1710,12 @@ NIL NIL (-445 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4333 |has| (-400 (-923 |#1|)) (-541)) (-4331 . T) (-4330 . T)) -((|HasCategory| (-400 (-923 |#1|)) (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| (-400 (-923 |#1|)) (QUOTE (-541)))) +((-4333 |has| (-400 (-917 |#1|)) (-542)) (-4331 . T) (-4330 . T)) +((|HasCategory| (-400 (-917 |#1|)) (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| (-400 (-917 |#1|)) (QUOTE (-542)))) (-446 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4338 "*") |has| |#2| (-170)) (-4329 |has| |#2| (-541)) (-4334 |has| |#2| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . 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T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#2| (QUOTE (-881))) (-3874 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-881)))) (-3874 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-881)))) (-3874 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-881)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (-3874 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-542)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-356))) (-3874 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#2| (QUOTE -4334)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143))))) (-447 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1751,7 +1751,7 @@ NIL (-455 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-835))))) (-456 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1780,7 +1780,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-463 |lv| -1421 R) +(-463 |lv| -3416 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1794,16 +1794,16 @@ NIL NIL (-466 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . 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T)) -((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-823))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-823))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835))))) (-468 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-835))))) (-469) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) @@ -1815,19 +1815,19 @@ NIL (-471 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4336 . T) (-4337 . 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Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. 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(|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1835,8 +1835,8 @@ NIL (-476 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) -(-477 -1421 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-477 -3416 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1847,14 +1847,14 @@ NIL (-479) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . 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In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4336)) (|HasAttribute| |#1| (QUOTE -4337)) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) +((|HasAttribute| |#1| (QUOTE -4336)) (|HasAttribute| |#1| (QUOTE -4337)) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835))))) (-481 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2623 . T)) +((-2359 . T)) NIL (-482) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) @@ -1868,34 +1868,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-485 -1421 UP |AlExt| |AlPol|) +(-485 -3416 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-486) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-549))))) +((|HasCategory| $ (QUOTE (-1018))) (|HasCategory| $ (LIST (QUOTE -1009) (QUOTE (-535))))) (-487 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-488 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-489 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-490 R UP -1421) +(-490 R UP -3416) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-491 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1066))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-112) (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-112) (QUOTE (-1066))) (|HasCategory| (-112) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-112) (QUOTE (-1067))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-112) (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-112) (QUOTE (-1067))) (|HasCategory| (-112) (LIST (QUOTE -593) (QUOTE (-835))))) (-492 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1908,7 +1908,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-495 -1421 |Expon| |VarSet| |DPoly|) +(-495 -3416 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -594) (QUOTE (-1142))))) @@ -1933,15 +1933,15 @@ NIL NIL NIL (-501 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL NIL (-502 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL NIL (-503 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL NIL (-504 S A B) @@ -1959,7 +1959,7 @@ NIL (-507 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-508) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -1967,15 +1967,15 @@ NIL (-509 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((-1536 (|HasCategory| (-563 |#1|) (QUOTE (-143))) (|HasCategory| (-563 |#1|) (QUOTE (-361)))) (|HasCategory| (-563 |#1|) (QUOTE (-145))) (|HasCategory| (-563 |#1|) (QUOTE (-361))) (|HasCategory| (-563 |#1|) (QUOTE (-143)))) +((-3874 (|HasCategory| (-563 |#1|) (QUOTE (-143))) (|HasCategory| (-563 |#1|) (QUOTE (-361)))) (|HasCategory| (-563 |#1|) (QUOTE (-145))) (|HasCategory| (-563 |#1|) (QUOTE (-361))) (|HasCategory| (-563 |#1|) (QUOTE (-143)))) (-510 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-511 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-512 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -1987,7 +1987,7 @@ NIL (-514 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-541))) (|HasAttribute| |#1| (QUOTE (-4338 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))) (|HasAttribute| |#1| (QUOTE (-4338 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-515) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2016,7 +2016,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-522 K -1421 |Par|) +(-522 K -3416 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2024,19 +2024,19 @@ NIL ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) NIL NIL -(-524 R) -((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) +(-524) +((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) NIL NIL -(-525) -((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) +(-525 R) +((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) NIL NIL (-526 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-527 K -1421 |Par|) +(-527 K -3416 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2057,7 +2057,7 @@ NIL NIL NIL (-532 R UP) -((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented"))) +((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented"))) NIL NIL (-533 S) @@ -2068,79 +2068,79 @@ NIL ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) ((-4334 . T) (-4335 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-535 |Key| |Entry| |addDom|) +(-535) +((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) +((-4318 . T) (-4324 . T) (-4328 . T) (-4323 . T) (-4334 . T) (-4335 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +NIL +(-536 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) -(-536 R -1421) +((-12 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1067))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835))))) +(-537 R -3416) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-537 R0 -1421 UP UPUP R) +(-538 R0 -3416 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL -(-538) +(-539) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,{}m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,{}m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) NIL NIL -(-539 R) +(-540 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2660 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-4112 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-540 S) +(-541 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) NIL NIL -(-541) +(-542) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-542 R -1421) -((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) +(-543 R -3416) +((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL -(-543 I) +(-544 I) ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra\\spad{'s} eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-544) -((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) +(-545) +((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-545 R -1421 L) -((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) +(-546 R -3416 L) +((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -632) (|devaluate| |#2|)))) -(-546) +((|HasCategory| |#3| (LIST (QUOTE -634) (|devaluate| |#2|)))) +(-547) ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-547 -1421 UP UPUP R) +(-548 -3416 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-548 -1421 UP) +(-549 -3416 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} D)} returns \\spad{[g,{} h,{} s,{} p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL -(-549) -((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4318 . T) (-4324 . T) (-4328 . T) (-4323 . T) (-4334 . T) (-4335 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -NIL (-550) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-551 R -1421 L) -((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) +(-551 R -3416 L) +((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -632) (|devaluate| |#2|)))) -(-552 R -1421) +((|HasCategory| |#3| (LIST (QUOTE -634) (|devaluate| |#2|)))) +(-552 R -3416) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1105)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-607))))) -(-553 -1421 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1105)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-608))))) +(-553 -3416 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2148,27 +2148,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-555 -1421) +(-555 -3416) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-556 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2660 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-4112 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-557) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-558 R -1421) +(-558 R -3416) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-277))) (|HasCategory| |#2| (QUOTE (-607))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142))))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-277)))) (|HasCategory| |#1| (QUOTE (-541)))) -(-559 -1421 UP) -((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) +((-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-277))) (|HasCategory| |#2| (QUOTE (-608))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142))))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-277)))) (|HasCategory| |#1| (QUOTE (-542)))) +(-559 -3416 UP) +((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-560 R -1421) +(-560 R -3416) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2188,18 +2188,18 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-565 R -1421) -((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) +(-565 -3416) +((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) +((-4331 . T) (-4330 . T)) +((|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-1142))))) +(-566 E -3416) +((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) NIL NIL -(-566 E -1421) -((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) +(-567 R -3416) +((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-567 -1421) -((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4331 . T) (-4330 . T)) -((|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-1142))))) (-568 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL @@ -2227,19 +2227,19 @@ NIL (-574 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1066))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (-1536 (|HasCategory| (-142) (LIST (QUOTE -593) (QUOTE (-834)))) (-12 (|HasCategory| (-142) (QUOTE (-1066))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-142) (QUOTE (-1066)))) (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-142) (QUOTE (-1066))) (-12 (|HasCategory| (-142) (QUOTE (-1066))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1067))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (-3874 (-12 (|HasCategory| (-142) (QUOTE (-1067))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| (-142) (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-142) (QUOTE (-1067)))) (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-142) (QUOTE (-1067))) (-12 (|HasCategory| (-142) (QUOTE (-1067))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -593) (QUOTE (-835))))) (-575 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-576 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-549)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-549)) (|devaluate| |#1|)))) (|HasCategory| (-549) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-549)))))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-542))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-535)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-535)) (|devaluate| |#1|)))) (|HasCategory| (-535) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-535))))) (|HasSignature| |#1| (LIST (QUOTE -4300) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-535)))))) (-577 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4331 |has| |#1| (-541)) (-4330 |has| |#1| (-541)) ((-4338 "*") |has| |#1| (-541)) (-4329 |has| |#1| (-541)) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-541)))) +((-4331 |has| |#1| (-542)) (-4330 |has| |#1| (-542)) ((-4338 "*") |has| |#1| (-542)) (-4329 |has| |#1| (-542)) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-542)))) (-578 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL @@ -2248,7 +2248,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-580 R -1421 FG) +(-580 R -3416 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2259,14 +2259,14 @@ NIL (-582 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-583 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4337)) (|HasCategory| |#2| (QUOTE (-823))) (|HasAttribute| |#1| (QUOTE -4336)) (|HasCategory| |#3| (QUOTE (-1066)))) +((|HasAttribute| |#1| (QUOTE -4337)) (|HasCategory| |#2| (QUOTE (-823))) (|HasAttribute| |#1| (QUOTE -4336)) (|HasCategory| |#3| (QUOTE (-1067)))) (-584 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2623 . T)) +((-2359 . T)) NIL (-585) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2278,28 +2278,28 @@ NIL NIL (-587 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4333 -1536 (-1820 (|has| |#2| (-360 |#1|)) (|has| |#1| (-541))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-541)))) (-4331 . T) (-4330 . T)) -((-1536 (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) +((-4333 -3874 (-3179 (|has| |#2| (-360 |#1|)) (|has| |#1| (-542))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-542)))) (-4331 . T) (-4330 . T)) +((-3874 (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-588 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| (-1124) (QUOTE (-823))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| (-1124) (QUOTE (-823))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (LIST (QUOTE -593) (QUOTE (-835))))) (-589 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL (-590 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4337 . T) (-2623 . T)) +((-4337 . T) (-2359 . T)) NIL -(-591 R S) -((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) +(-591 S) +((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) NIL +((|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) +(-592 R S) +((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) NIL -(-592 S) -((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-593 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL @@ -2308,7 +2308,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-595 -1421 UP) +(-595 -3416 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2316,26 +2316,26 @@ NIL ((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of \\spad{`x'} is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of \\spad{`x'} is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of \\spad{`x'} is `false'")) (|true| (($) "the definite truth value")) (|unknown| (($) "the indefinite `unknown'")) (|false| (($) "the definite falsehood value"))) NIL NIL -(-597 S R) +(-597 A R S) +((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) +((-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-821)))) +(-598 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-598 R) +(-599 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) ((-4333 . T)) NIL -(-599 A R S) -((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-821)))) -(-600 R -1421) +(-600 R -3416) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f,{} t,{} s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t),{} t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f,{} t,{} s)} if it cannot compute the transform."))) NIL NIL (-601 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) ((-4331 . T) (-4330 . T) ((-4338 "*") . T) (-4329 . T) (-4333 . T)) -((|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) +((|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (-602 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL @@ -2356,66 +2356,66 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) NIL NIL -(-607) -((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) +(-607 R -3416) +((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-608 R -1421) -((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) +(-608) +((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-609 |lv| -1421) +(-609 |lv| -3416) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-610) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4337 . 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Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) 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Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL NIL (-615 R) -((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) +((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) 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T)) NIL -(-618 A B) -((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) -NIL -NIL +(-618 S) +((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) +((-4337 . T) (-4336 . T)) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-797))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-619 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) NIL NIL -(-620 A B C) +(-620 A B) +((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) +NIL +NIL +(-621 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL -(-621 S) -((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (-622 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2423,7 +2423,7 @@ NIL (-623 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-624 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2438,52 +2438,52 @@ NIL ((|HasAttribute| |#1| (QUOTE -4337))) (-627 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) -((-2623 . T)) +((-2359 . T)) NIL -(-628 R -1421 L) +(-628 M R S) +((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) +((-4331 . T) (-4330 . T)) +((|HasCategory| |#1| (QUOTE (-767)))) +(-629 R -3416 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL -(-629 A) +(-630 A -2739) +((|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}}"))) +((-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) +(-631 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) -(-630 A M) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) +(-632 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) ((-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) -(-631 S A) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) +(-633 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-356)))) -(-632 A) +(-634 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-633 -1421 UP) +(-635 -3416 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-634 A -3399) -((|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}}"))) -((-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) -(-635 A L) +(-636 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-636 S) +(-637 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-637) +(-638) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-638 M R S) -((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4331 . T) (-4330 . T)) -((|HasCategory| |#1| (QUOTE (-767)))) (-639 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) NIL @@ -2498,14 +2498,14 @@ NIL NIL (-642 S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL -(-643 -1421) -((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) +(-643 -3416 |Row| |Col| M) +((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-644 -1421 |Row| |Col| M) -((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) +(-644 -3416) +((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL (-645 R E OV P) @@ -2515,7 +2515,7 @@ NIL (-646 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4333 . T) (-4336 . T) (-4330 . T) (-4331 . T)) -((|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4338 "*"))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (-1536 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-541))) (-1536 (|HasAttribute| |#2| (QUOTE (-4338 "*"))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-170)))) +((|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4338 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (-3874 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-542))) (-3874 (|HasAttribute| |#2| (QUOTE (-4338 #1#))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-170)))) (-647) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2530,12 +2530,12 @@ NIL NIL (-650 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) -((-2623 . T)) +((-2359 . T)) NIL (-651 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-652) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2572,26 +2572,26 @@ NIL ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}"))) NIL NIL -(-661 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) -((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) -NIL -NIL -(-662 S R |Row| |Col|) +(-661 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4338 "*"))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-541)))) -(-663 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-4338 "*"))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-542)))) +(-662 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4336 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4337 . T) (-2359 . T)) +NIL +(-663 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) +NIL NIL (-664 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) NIL -((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-541)))) +((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542)))) (-665 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4336 . T) (-4337 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-541))) (|HasAttribute| |#1| (QUOTE (-4338 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))) (|HasAttribute| |#1| (QUOTE (-4338 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-666 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2600,7 +2600,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}."))) NIL NIL -(-668 S -1421 FLAF FLAS) +(-668 S -3416 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2610,27 +2610,27 @@ NIL NIL (-670) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4329 . T) (-4334 |has| (-675) (-356)) (-4328 |has| (-675) (-356)) (-3409 . T) (-4335 |has| (-675) (-6 -4335)) (-4332 |has| (-675) (-6 -4332)) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . 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T)) +((|HasCategory| (-675) (QUOTE (-145))) (|HasCategory| (-675) (QUOTE (-143))) (|HasCategory| (-675) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-675) (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| (-675) (QUOTE (-361))) (|HasCategory| (-675) (QUOTE (-356))) (|HasCategory| (-675) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-675) (QUOTE (-227))) (-3874 (|HasCategory| (-675) (QUOTE (-356))) (|HasCategory| (-675) (QUOTE (-343)))) (|HasCategory| (-675) (QUOTE (-343))) (|HasCategory| (-675) (LIST (QUOTE -279) (QUOTE (-675)) (QUOTE (-675)))) (|HasCategory| (-675) (LIST (QUOTE -302) (QUOTE (-675)))) (|HasCategory| (-675) (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE (-675)))) (|HasCategory| (-675) (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-675) (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-675) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-675) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (-3874 (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-356))) (|HasCategory| (-675) (QUOTE (-343)))) (|HasCategory| (-675) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-675) (QUOTE (-991))) (|HasCategory| (-675) (QUOTE (-1164))) (-12 (|HasCategory| (-675) (QUOTE (-973))) (|HasCategory| (-675) (QUOTE (-1164)))) (-3874 (-12 (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-881)))) (-12 (|HasCategory| (-675) (QUOTE (-343))) (|HasCategory| (-675) (QUOTE (-881)))) (|HasCategory| (-675) (QUOTE (-356)))) (-3874 (-12 (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-881)))) (-12 (|HasCategory| (-675) (QUOTE (-356))) (|HasCategory| (-675) (QUOTE (-881)))) (-12 (|HasCategory| (-675) (QUOTE (-343))) (|HasCategory| (-675) (QUOTE (-881))))) (|HasCategory| (-675) (QUOTE (-534))) (-12 (|HasCategory| (-675) (QUOTE (-1027))) (|HasCategory| (-675) (QUOTE (-1164)))) (|HasCategory| (-675) (QUOTE (-1027))) (-3874 (|HasCategory| (-675) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-675) (QUOTE (-356)))) (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-881))) (-3874 (-12 (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-881)))) (|HasCategory| (-675) (QUOTE (-356)))) (-3874 (-12 (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-881)))) (|HasCategory| (-675) (QUOTE (-542)))) (-12 (|HasCategory| (-675) (QUOTE (-227))) (|HasCategory| (-675) (QUOTE (-356)))) (-12 (|HasCategory| (-675) (QUOTE (-356))) (|HasCategory| (-675) (LIST (QUOTE -871) (QUOTE (-1142))))) (|HasCategory| (-675) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-675) (QUOTE (-823))) (|HasCategory| (-675) (QUOTE (-542))) (|HasAttribute| (-675) (QUOTE -4335)) (|HasAttribute| (-675) (QUOTE -4332)) (-12 (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-881)))) (-3874 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-881)))) (|HasCategory| (-675) (QUOTE (-143)))) (-3874 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-675) (QUOTE (-300))) (|HasCategory| (-675) (QUOTE (-881)))) (|HasCategory| (-675) (QUOTE (-343))))) (-671 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4337 . T) (-2623 . T)) +((-4337 . T) (-2359 . T)) NIL (-672 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) NIL NIL (-673) -((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) +((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-674 OV E -1421 PG) +(-674 OV E -3416 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-675) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-2660 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-4112 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-676 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2660,7 +2660,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-683 S -1700 I) +(-683 S -2990 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2680,14 +2680,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-688 R |Mod| -1998 -1586 |exactQuo|) +(-688 R |Mod| -2145 -3855 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-689 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4332 |has| |#1| (-356)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372)))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-342))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4332 |has| |#1| (-356)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-1048) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-343))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) (-690 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2696,7 +2696,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) (-4333 . T)) ((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145)))) -(-692 R |Mod| -1998 -1586 |exactQuo|) +(-692 R |Mod| -2145 -3855 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4333 . T)) NIL @@ -2708,7 +2708,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4331 . T) (-4330 . T)) NIL -(-695 -1421) +(-695 -3416) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) ((-4333 . T)) NIL @@ -2731,7 +2731,7 @@ NIL (-700 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL -((|HasCategory| |#2| (QUOTE (-342))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-361)))) +((|HasCategory| |#2| (QUOTE (-343))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-361)))) (-701 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) ((-4329 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) @@ -2744,7 +2744,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-704 -1421 UP) +(-704 -3416 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2762,8 +2762,8 @@ NIL NIL (-708 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) -(((-4338 "*") |has| |#2| (-170)) (-4329 |has| |#2| (-541)) (-4334 |has| |#2| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#2| (QUOTE (-880))) (-1536 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-880)))) (-1536 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-880)))) (-1536 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-170))) (-1536 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-541)))) (-12 (|HasCategory| (-836 |#1|) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| (-836 |#1|) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372)))))) (-12 (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-12 (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-356))) (-1536 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasAttribute| |#2| (QUOTE -4334)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-143))))) +(((-4338 "*") |has| |#2| (-170)) (-4329 |has| |#2| (-542)) (-4334 |has| |#2| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#2| (QUOTE (-881))) (-3874 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-881)))) (-3874 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-881)))) (-3874 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-881)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (-3874 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-542)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-836 |#1|) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-356))) (-3874 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#2| (QUOTE -4334)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143))))) (-709 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2781,13 +2781,13 @@ NIL ((-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) (-4333 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-823)))) (-713 S) -((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4326 . T) (-4337 . T) (-2623 . T)) -NIL -(-714 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) ((-4336 . T) (-4326 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-714 S) +((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) +((-4326 . T) (-4337 . T) (-2359 . T)) +NIL (-715) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL @@ -2798,7 +2798,7 @@ NIL NIL (-717 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,{}x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|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}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,{}x,{}n)} returns \\spad{min(n,{}order(f,{}x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,{}x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,{}x,{}n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4331 . T) (-4330 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4331 . T) (-4330 . T) (-4333 . T)) NIL (-718 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2896,15 +2896,15 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-742 -1421) +(-742 -3416) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-743 P -1421) +(-743 P -3416) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL -(-744 UP -1421) +(-744 UP -3416) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -2920,16 +2920,16 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4338 "*") . T)) NIL -(-748 R -1421) +(-748 R -3416) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL -(-749 S) -((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) +(-749) +((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-750) -((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) +(-750 S) +((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL (-751 R |PolR| E |PolE|) @@ -2940,7 +2940,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-753 -1421 |ExtF| |SUEx| |ExtP| |n|) +(-753 -3416 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -2954,28 +2954,28 @@ NIL NIL (-756 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . 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(|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4332 |has| |#1| (-356)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-1048) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) +(-758 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-758 R) -((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4332 |has| |#1| (-356)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372)))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143))))) (-759 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535)))))) (-760 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL (-761 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-170)))) +((-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-170)))) (-762) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL @@ -3012,43 +3012,43 @@ NIL ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-771) -((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) -NIL -NIL -(-772 S R) +(-771 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-361)))) -(-773 R) +((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-361)))) +(-772 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-774 -1536 R OS S) -((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) +(-773) +((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-775 R) +(-774 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (-1536 (|HasCategory| (-970 |#1|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (|HasCategory| (-970 |#1|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-970 |#1|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-970 |#1|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (-3874 (|HasCategory| (-967 |#1|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-967 |#1|) (LIST (QUOTE -1009) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-534))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-967 |#1|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-967 |#1|) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) +(-775 -3874 R OS S) +((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) +NIL +NIL (-776) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-777 R -1421 L) +(-777 R -3416 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-778 R -1421) -((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) +(-778 R -3416) +((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL (-779) ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-780 R -1421) +(-780 R -3416) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3056,11 +3056,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-782 -1421 UP UPUP R) +(-782 -3416 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-783 -1421 UP L LQ) +(-783 -3416 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3068,38 +3068,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-785 -1421 UP L LQ) +(-785 -3416 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-786 -1421 UP) -((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) +(-786 -3416 UP) +((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-787 -1421 L UP A LO) +(-787 -3416 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-788 -1421 UP) +(-788 -3416 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-789 -1421 LO) +(-789 -3416 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-790 -1421 LODO) +(-790 -3416 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-791 -2727 S |f|) +(-791 -2938 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4330 |has| |#2| (-1018)) (-4331 |has| |#2| (-1018)) (-4333 |has| |#2| (-6 -4333)) ((-4338 "*") |has| |#2| (-170)) (-4336 . 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coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-880))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| (-794 (-1142)) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| (-794 (-1142)) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| (-794 (-1142)) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372)))))) (-12 (|HasCategory| (-794 (-1142)) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-12 (|HasCategory| (-794 (-1142)) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-881))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-794 (-1142)) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-794 (-1142)) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-794 (-1142)) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-794 (-1142)) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-794 (-1142)) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) (-793 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) (((-4338 "*") |has| |#2| (-356)) (-4329 |has| |#2| (-356)) (-4334 |has| |#2| (-356)) (-4328 |has| |#2| (-356)) (-4333 . T) (-4331 . T) (-4330 . T)) @@ -3117,57 +3117,57 @@ NIL ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-797) -((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) +((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) NIL NIL (-798) -((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) +((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) NIL NIL (-799) -((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) +((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) NIL NIL (-800) -((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) +((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) NIL NIL (-801) ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-802 R) +(-802) +((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) +NIL +NIL +(-803 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-803 P R) +(-804 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) ((-4330 . T) (-4331 . T) (-4333 . T)) ((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-227)))) -(-804) -((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) -NIL -NIL (-805) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,{}cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,{}cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) NIL NIL (-806 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4336 . T) (-4326 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4326 . T) (-4337 . T) (-2359 . T)) NIL (-807) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) NIL NIL -(-808 R S) +(-808 R) +((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) +((-4333 |has| |#1| (-821))) +((|HasCategory| |#1| (QUOTE (-821))) (-3874 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-534))) (-3874 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-21)))) +(-809 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-809 R) -((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) -((-4333 |has| |#1| (-821))) -((|HasCategory| |#1| (QUOTE (-821))) (-1536 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-534))) (-1536 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-21)))) (-810 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4331 |has| |#1| (-170)) (-4330 |has| |#1| (-170)) (-4333 . T)) @@ -3188,19 +3188,19 @@ NIL ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-815 R S) +(-815 R) +((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) +((-4333 |has| |#1| (-821))) +((|HasCategory| |#1| (QUOTE (-821))) (-3874 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-534))) (-3874 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-21)))) +(-816 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-816 R) -((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4333 |has| |#1| (-821))) -((|HasCategory| |#1| (QUOTE (-821))) (-1536 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-534))) (-1536 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-21)))) (-817) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-818 -2727 S) +(-818 -2938 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3227,7 +3227,7 @@ NIL (-824 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-170)))) +((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170)))) (-825 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) ((-4330 . T) (-4331 . T) (-4333 . T)) @@ -3235,19 +3235,19 @@ NIL (-826 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL -((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) -(-827 R |sigma| -2656) +((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) +(-827 R |sigma| -3578) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) -(-828 |x| R |sigma| -2656) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356)))) +(-828 |x| R |sigma| -3578) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) ((-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-356)))) +((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-356)))) (-829 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535)))))) (-830) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL @@ -3256,20 +3256,20 @@ NIL ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-832 S) -((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) +(-832) +((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-833) +(-833 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) NIL NIL (-834) -((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) +((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) NIL NIL (-835) -((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) +((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL (-836 |VariableList|) @@ -3289,25 +3289,25 @@ NIL NIL NIL (-840 |p|) -((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) +((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-841 |p|) -((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) +((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-842 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-841 |#1|) (QUOTE (-880))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-841 |#1|) (QUOTE (-143))) (|HasCategory| (-841 |#1|) (QUOTE (-145))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-841 |#1|) (QUOTE (-993))) (|HasCategory| (-841 |#1|) (QUOTE (-796))) (-1536 (|HasCategory| (-841 |#1|) (QUOTE (-796))) (|HasCategory| (-841 |#1|) (QUOTE (-823)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| (-841 |#1|) (QUOTE (-1117))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| (-841 |#1|) (QUOTE (-227))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -505) (QUOTE (-1142)) (LIST (QUOTE -841) (|devaluate| |#1|)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -841) (|devaluate| |#1|)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -841) (|devaluate| |#1|)) (LIST (QUOTE -841) (|devaluate| |#1|)))) (|HasCategory| (-841 |#1|) (QUOTE (-300))) (|HasCategory| (-841 |#1|) (QUOTE (-534))) (|HasCategory| (-841 |#1|) (QUOTE (-823))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-841 |#1|) (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-841 |#1|) (QUOTE (-880)))) (|HasCategory| (-841 |#1|) (QUOTE (-143))))) +((|HasCategory| (-840 |#1|) (QUOTE (-881))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-840 |#1|) (QUOTE (-143))) (|HasCategory| (-840 |#1|) (QUOTE (-145))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-840 |#1|) (QUOTE (-991))) (|HasCategory| (-840 |#1|) (QUOTE (-796))) (-3874 (|HasCategory| (-840 |#1|) (QUOTE (-796))) (|HasCategory| (-840 |#1|) (QUOTE (-823)))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-840 |#1|) (QUOTE (-1117))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| (-840 |#1|) (QUOTE (-227))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -505) (QUOTE (-1142)) (LIST (QUOTE -840) (|devaluate| |#1|)))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -840) (|devaluate| |#1|)))) (|HasCategory| (-840 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -840) (|devaluate| |#1|)) (LIST (QUOTE -840) (|devaluate| |#1|)))) (|HasCategory| (-840 |#1|) (QUOTE (-300))) (|HasCategory| (-840 |#1|) (QUOTE (-534))) (|HasCategory| (-840 |#1|) (QUOTE (-823))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-840 |#1|) (QUOTE (-881)))) (-3874 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-840 |#1|) (QUOTE (-881)))) (|HasCategory| (-840 |#1|) (QUOTE (-143))))) (-843 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#2| (QUOTE (-880))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-993))) (|HasCategory| |#2| (QUOTE (-796))) (-1536 (|HasCategory| |#2| (QUOTE (-796))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -279) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-823))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-143))))) +((|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-796))) (-3874 (|HasCategory| |#2| (QUOTE (-796))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -279) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-823))) (-12 (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143))))) (-844 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-1067)))) (-3874 (-12 (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835))))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-1067))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))))) (-845) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3363,27 +3363,27 @@ NIL (-858 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-4007 (|HasCategory| |#2| (QUOTE (-1018)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142)))))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142)))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142))))) -(-859 R A B) +((-12 (-3659 (|HasCategory| |#2| (QUOTE (-1018)))) (-3659 (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142)))))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (-3659 (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142)))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142))))) +(-859 R S) +((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) +NIL +NIL +(-860 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-860 R S) -((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) +(-861 R) +((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-861 R -1700) +(-862 R -2990) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL -(-862 R S) +(-863 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-863 R) -((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) -NIL -NIL (-864 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL @@ -3396,7 +3396,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-867 UP -1421) +(-867 UP -3416) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3419,44 +3419,44 @@ NIL (-872 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) -(-873 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-873 S) +((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) +((-4333 . T)) +((-3874 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-823)))) +(-874 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL -(-874 S) +(-875 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) ((-4333 . T)) NIL -(-875 S) +(-876 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-876 S) -((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4333 . T)) -((-1536 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-823)))) -(-877 R E |VarSet| S) +(-877 |p|) +((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) +((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-361)))) +(-878 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-878 R S) +(-879 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-879 S) +(-880 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-143)))) -(-880) +(-881) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-881 |p|) -((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-361)))) -(-882 R0 -1421 UP UPUP R) +(-882 R0 -3416 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3484,63 +3484,63 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-889 -1421) +(-889 -3416) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL -(-890 R) +(-890) +((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) +(((-4338 "*") . T)) +NIL +(-891 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-891) +(-892) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-892) -((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4338 "*") . T)) -NIL -(-893 -1421 P) -((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) +(-893 |xx| -3416) +((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) NIL NIL -(-894 |xx| -1421) -((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) +(-894 -3416 P) +((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL (-895 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-896 S) -((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) +(-896) +((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) NIL NIL -(-897) -((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) +(-897 S) +((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL (-898) -((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) +((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL (-899) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-900 R -1421) -((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) +(-900) +((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-901) -((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) +(-901 R -3416) +((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL (-902 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-903 S R -1421) +(-903 S R -3416) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3560,12 +3560,12 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -857) (|devaluate| |#1|)))) -(-908 R -1421 -1700) -((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) +(-908 -2990) +((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-909 -1700) -((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) +(-909 R -3416 -2990) +((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL (-910 S R Q) @@ -3587,7 +3587,7 @@ NIL (-914 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-915 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3596,35 +3596,35 @@ NIL ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL ((|HasCategory| |#1| (QUOTE (-821)))) -(-917 R S) +(-917 R) +((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-881))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-1142) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-1142) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-1142) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-1142) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-1142) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) +(-918 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-918 |x| R) +(-919 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-919 S R E |VarSet|) +(-920 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-880))) (|HasAttribute| |#2| (QUOTE -4334)) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#4| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#4| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#4| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-823)))) -(-920 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-881))) (|HasAttribute| |#2| (QUOTE -4334)) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| |#4| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#4| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| |#4| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (QUOTE (-823)))) +(-921 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) NIL -(-921 E V R P -1421) +(-922 E V R P -3416) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-922 E |Vars| R P S) +(-923 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-923 R) -((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-880))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| (-1142) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| (-1142) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| (-1142) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372)))))) (-12 (|HasCategory| (-1142) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-12 (|HasCategory| (-1142) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143))))) -(-924 E V R P -1421) +(-924 E V R P -3416) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-444)))) @@ -3636,42 +3636,42 @@ NIL ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-927 R L) +(-927 R E) +((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-542))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-130)))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#1| (QUOTE -4334))) +(-928 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) NIL NIL -(-928 A B) -((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) -NIL -NIL (-929 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) -(-930) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-930 A B) +((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) +NIL +NIL +(-931) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-931 -1421) +(-932 -3416) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL -(-932 I) +(-933 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-933) +(-934) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-934 R E) -((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-130)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasAttribute| |#1| (QUOTE -4334))) (-935 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) ((-4333 -12 (|has| |#2| (-465)) (|has| |#1| (-465)))) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769)))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-823))))) (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769))))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-465)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-465)))) (-12 (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-703))))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-361)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-465)))) (-12 (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-703)))) (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769))))) (-12 (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-703)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-823))))) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769)))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-823))))) (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-465)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-465)))) (-12 (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-703))))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-361)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#2| (QUOTE (-769)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-465)))) (-12 (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-703))))) (-12 (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-703)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-823))))) (-936) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3686,7 +3686,7 @@ NIL NIL (-939 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4336 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4337 . T) (-2359 . T)) NIL (-940 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3706,7 +3706,7 @@ NIL NIL (-944 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-945) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3715,10 +3715,10 @@ NIL (-946 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL -((|HasCategory| |#2| (QUOTE (-541)))) +((|HasCategory| |#2| (QUOTE (-542)))) (-947 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4336 . T) (-2623 . T)) +((-4336 . T) (-2359 . T)) NIL (-948 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3734,7 +3734,7 @@ NIL NIL (-951 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL (-952 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3752,18 +3752,18 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-956 K R UP -1421) +(-956 K R UP -3416) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL -(-957 |vl| |nv|) -((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) +(-957 R |Var| |Expon| |Dpoly|) +((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL +((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-300))))) +(-958 |vl| |nv|) +((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL -(-958 R |Var| |Expon| |Dpoly|) -((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-300))))) (-959 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL @@ -3772,17 +3772,17 @@ NIL ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation."))) NIL NIL -(-961 A B R S) -((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) -NIL -NIL -(-962 A S) +(-961 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-880))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-993))) (|HasCategory| |#2| (QUOTE (-796))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1117)))) -(-963 S) +((|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-796))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1117)))) +(-962 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-2623 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-2359 . T) (-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +NIL +(-963 A B R S) +((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) +NIL NIL (-964 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3794,28 +3794,28 @@ NIL NIL (-966 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4336 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4337 . T) (-2359 . T)) NIL -(-967 S R) +(-967 R) +((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) +((-4329 |has| |#1| (-283)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-534))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))))) +(-968 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-283)))) -(-968 R) +((|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-283)))) +(-969 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) ((-4329 |has| |#1| (-283)) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-969 QR R QS S) +(-970 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-970 R) -((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) -((-4329 |has| |#1| (-283)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1142)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-534))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-356))))) (-971 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-972 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3824,14 +3824,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-974 -1421 UP UPUP |radicnd| |n|) +(-974 -3416 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4329 |has| (-400 |#2|) (-356)) (-4334 |has| (-400 |#2|) (-356)) (-4328 |has| (-400 |#2|) (-356)) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-342))) (-1536 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-1536 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (-1536 (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-342))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1536 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356))))) +((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-343))) (-3874 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-343)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-3874 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-343)))) (-3874 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-343))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-3874 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356))))) (-975 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-549) (QUOTE (-880))) (|HasCategory| (-549) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-549) (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-145))) (|HasCategory| (-549) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-549) (QUOTE (-993))) (|HasCategory| (-549) (QUOTE (-796))) (-1536 (|HasCategory| (-549) (QUOTE (-796))) (|HasCategory| (-549) (QUOTE (-823)))) (|HasCategory| (-549) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| (-549) (QUOTE (-1117))) (|HasCategory| (-549) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| (-549) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| (-549) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| (-549) (QUOTE (-227))) (|HasCategory| (-549) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-549) (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -302) (QUOTE (-549)))) (|HasCategory| (-549) (LIST (QUOTE -279) (QUOTE (-549)) (QUOTE (-549)))) (|HasCategory| (-549) (QUOTE (-300))) (|HasCategory| (-549) (QUOTE (-534))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-549) (LIST (QUOTE -617) (QUOTE (-549)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-549) (QUOTE (-880)))) (|HasCategory| (-549) (QUOTE (-143))))) +((|HasCategory| (-535) (QUOTE (-881))) (|HasCategory| (-535) (LIST (QUOTE -1009) (QUOTE (-1142)))) (|HasCategory| (-535) (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-145))) (|HasCategory| (-535) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-535) (QUOTE (-991))) (|HasCategory| (-535) (QUOTE (-796))) (-3874 (|HasCategory| (-535) (QUOTE (-796))) (|HasCategory| (-535) (QUOTE (-823)))) (|HasCategory| (-535) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-535) (QUOTE (-1117))) (|HasCategory| (-535) (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-535) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-535) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-535) (QUOTE (-227))) (|HasCategory| (-535) (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| (-535) (LIST (QUOTE -505) (QUOTE (-1142)) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -302) (QUOTE (-535)))) (|HasCategory| (-535) (LIST (QUOTE -279) (QUOTE (-535)) (QUOTE (-535)))) (|HasCategory| (-535) (QUOTE (-300))) (|HasCategory| (-535) (QUOTE (-534))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-535) (LIST (QUOTE -617) (QUOTE (-535)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-881)))) (-3874 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-535) (QUOTE (-881)))) (|HasCategory| (-535) (QUOTE (-143))))) (-976) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3851,10 +3851,10 @@ NIL (-980 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4337)) (|HasCategory| |#2| (QUOTE (-1066)))) +((|HasAttribute| |#1| (QUOTE -4337)) (|HasCategory| |#2| (QUOTE (-1067)))) (-981 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) -((-2623 . T)) +((-2359 . T)) NIL (-982 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3864,19 +3864,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4329 . T) (-4334 . T) (-4328 . T) (-4331 . T) (-4330 . T) ((-4338 "*") . T) (-4333 . T)) NIL -(-984 R -1421) +(-984 R -3416) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-985 R -1421) +(-985 R -3416) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-986 -1421 UP) +(-986 -3416 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-987 -1421 UP) +(-987 -3416 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -3892,16 +3892,16 @@ NIL ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-991 |Pol|) -((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) +(-991) +((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL (-992 |Pol|) -((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) +((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-993) -((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) +(-993 |Pol|) +((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL (-994) @@ -3911,35 +3911,35 @@ NIL (-995 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4329 . T) (-4334 . T) (-4328 . T) (-4331 . T) (-4330 . T) ((-4338 "*") . T) (-4333 . T)) -((-1536 (|HasCategory| (-400 (-549)) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| (-400 (-549)) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-400 (-549)) (LIST (QUOTE -1009) (QUOTE (-549))))) -(-996 -1421 L) +((-3874 (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-400 (-535)) (LIST (QUOTE -1009) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-400 (-535)) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-400 (-535)) (LIST (QUOTE -1009) (QUOTE (-535))))) +(-996 -3416 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL (-997 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1066)))) +((|HasCategory| |#1| (QUOTE (-1067)))) (-998 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-834))))) -(-999 R) +((-12 (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-835))))) +(-999) +((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) +NIL +NIL +(-1000 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL ((|HasAttribute| |#1| (QUOTE (-4338 "*")))) -(-1000 R) +(-1001 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-300)))) -(-1001 S) +(-1002 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-1002) -((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) -NIL -NIL (-1003 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL @@ -3948,14 +3948,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1005 -1421 |Expon| |VarSet| |FPol| |LFPol|) +(-1005 -3416 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-1006) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1142))) (LIST (QUOTE |:|) (QUOTE -1792) (QUOTE (-52))))))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-52) (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-1142) (QUOTE (-823))) (|HasCategory| (-52) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (QUOTE (-1142))) (LIST (QUOTE |:|) (QUOTE -2184) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (QUOTE (-1067)))) (-3874 (|HasCategory| (-51) (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-51) (QUOTE (-1067))) (|HasCategory| (-51) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| (-51) (QUOTE (-1067))) (|HasCategory| (-51) (LIST (QUOTE -302) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (QUOTE (-1067))) (|HasCategory| (-1142) (QUOTE (-823))) (|HasCategory| (-51) (QUOTE (-1067))) (-3874 (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-51) (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| (-51) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -593) (QUOTE (-835))))) (-1007) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -3972,26 +3972,26 @@ NIL ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-1011) -((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) +(-1011 R) +((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-1012 UP) -((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) +(-1012) +((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-1013 R) -((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) +(-1013 UP) +((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL (-1014 R) -((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) +((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL (-1015 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| (-756 |#1| (-836 |#2|)) (QUOTE (-1066))) (|HasCategory| (-756 |#1| (-836 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -756) (|devaluate| |#1|) (LIST (QUOTE -836) (|devaluate| |#2|)))))) (|HasCategory| (-756 |#1| (-836 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-756 |#1| (-836 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| (-836 |#2|) (QUOTE (-361))) (|HasCategory| (-756 |#1| (-836 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-756 |#1| (-836 |#2|)) (QUOTE (-1067))) (|HasCategory| (-756 |#1| (-836 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -756) (|devaluate| |#1|) (LIST (QUOTE -836) (|devaluate| |#2|)))))) (|HasCategory| (-756 |#1| (-836 |#2|)) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-756 |#1| (-836 |#2|)) (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| (-836 |#2|) (QUOTE (-361))) (|HasCategory| (-756 |#1| (-836 |#2|)) (LIST (QUOTE -593) (QUOTE (-835))))) (-1016) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL @@ -4004,22 +4004,22 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4333 . T)) NIL -(-1019 |xx| -1421) +(-1019 |xx| -3416) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL (-1020 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL -((|HasCategory| |#4| (QUOTE (-300))) (|HasCategory| |#4| (QUOTE (-356))) (|HasCategory| |#4| (QUOTE (-541))) (|HasCategory| |#4| (QUOTE (-170)))) +((|HasCategory| |#4| (QUOTE (-300))) (|HasCategory| |#4| (QUOTE (-356))) (|HasCategory| |#4| (QUOTE (-542))) (|HasCategory| |#4| (QUOTE (-170)))) (-1021 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4336 . T) (-2623 . T) (-4331 . T) (-4330 . T)) +((-4336 . T) (-2359 . T) (-4331 . T) (-4330 . T)) NIL (-1022 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4336 . T) (-4331 . T) (-4330 . T)) -((-1536 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356)))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (QUOTE (-300))) (|HasCategory| |#3| (QUOTE (-541))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-834)))) (-12 (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))))) +((-3874 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356)))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (QUOTE (-300))) (|HasCategory| |#3| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-835)))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))))) (-1023 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4051,14 +4051,14 @@ NIL (-1030) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1142))) (LIST (QUOTE |:|) (QUOTE -1792) (QUOTE (-52))))))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-52) (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| (-52) (QUOTE (-1066))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (QUOTE (-1066))) (|HasCategory| (-1142) (QUOTE (-823))) (|HasCategory| (-52) (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-52) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 (-1142)) (|:| -1792 (-52))) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (QUOTE (-1142))) (LIST (QUOTE |:|) (QUOTE -2184) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (QUOTE (-1067)))) (-3874 (|HasCategory| (-51) (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-51) (QUOTE (-1067))) (|HasCategory| (-51) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| (-51) (QUOTE (-1067))) (|HasCategory| (-51) (LIST (QUOTE -302) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (QUOTE (-1067))) (|HasCategory| (-1142) (QUOTE (-823))) (|HasCategory| (-51) (QUOTE (-1067))) (-3874 (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-51) (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| (-51) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 (-1142)) (|:| -2184 (-51))) (LIST (QUOTE -593) (QUOTE (-835))))) (-1031 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -963) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-1142))))) +((|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-534))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-1142))))) (-1032 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) NIL (-1033) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -4082,7 +4082,7 @@ NIL NIL (-1038 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL (-1039 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -4092,15 +4092,15 @@ NIL ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1041 |f|) -((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) +(-1041 |Base| R -3416) +((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1042 |Base| R -1421) -((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) +(-1042 |f|) +((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1043 |Base| R -1421) +(-1043 |Base| R -3416) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) NIL NIL @@ -4108,14 +4108,14 @@ NIL ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1045 UP SAE UPA) +(-1045 R UP M) +((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) +((-4329 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-343))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-343)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356))))) +(-1046 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1046 R UP M) -((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) -((-4329 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-342))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-342)))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142))))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356))))) (-1047 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4142,74 +4142,74 @@ NIL NIL (-1053 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-880))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372)))))) (-12 (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-12 (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-881))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-1054 (-1142)) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1054 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1055 R S) +(-1055 S) +((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) +NIL +((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1067)))) +(-1056 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL ((|HasCategory| |#1| (QUOTE (-821)))) -(-1056) +(-1057) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1057 R S) -((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) -NIL -NIL (-1058 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1066)))) -(-1059 S) -((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-2623 . T)) +((|HasCategory| |#1| (QUOTE (-1067)))) +(-1059 R S) +((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) +NIL NIL (-1060 S) -((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) +((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) +((-2359 . T)) NIL -((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1066)))) (-1061 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2623 . T)) +((-2359 . T)) NIL (-1062) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1063 A S) +(-1063 S) +((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) +((-4336 . T) (-4326 . T) (-4337 . T)) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-823))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-1064 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1064 S) +(-1065 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4326 . T) (-2623 . T)) +((-4326 . T) (-2359 . T)) NIL -(-1065 S) +(-1066 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1066) +(-1067) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1067 |m| |n|) -((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) +(-1068 |m| |n|) +((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1068 S) -((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) -((-4336 . T) (-4326 . T) (-4337 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) -(-1069 |Str| |Sym| |Int| |Flt| |Expr|) -((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) +(-1069) +((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1070) -((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) +(-1070 |Str| |Sym| |Int| |Flt| |Expr|) +((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL (-1071 |Str| |Sym| |Int| |Flt| |Expr|) @@ -4230,7 +4230,7 @@ NIL NIL (-1075 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL (-1076) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4247,25 +4247,25 @@ NIL (-1079 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1018)))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (-3874 (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -1009) (QUOTE (-535))))) (|HasCategory| |#3| (QUOTE (-1018)))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#3| (QUOTE -4333)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1067))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -593) (QUOTE (-835))))) (-1080 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-444)))) (-1081) -((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) +((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) NIL NIL -(-1082 R -1421) -((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) +(-1082) +((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1083 R) -((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) +(-1083 R -3416) +((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1084) -((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) +(-1084 R) +((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL (-1085) @@ -4278,7 +4278,7 @@ NIL NIL (-1087 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4336 . T) (-4337 . T) (-2623 . T)) +((-4336 . T) (-4337 . T) (-2359 . T)) NIL (-1088 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) @@ -4286,7 +4286,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-356))) (|HasAttribute| |#3| (QUOTE (-4338 "*"))) (|HasCategory| |#3| (QUOTE (-170)))) (-1089 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-2623 . T) (-4336 . T) (-4330 . T) (-4331 . T) (-4333 . T)) +((-2359 . T) (-4336 . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-1090 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4294,17 +4294,17 @@ NIL NIL (-1091 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-880))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-881))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1092 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-356)))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-356)))) (-1093 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL -(-1094 UP -1421) +(-1094 UP -3416) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4342,7 +4342,7 @@ NIL NIL (-1103) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) -((-2623 . T)) +((-2359 . T)) NIL (-1104) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) @@ -4359,18 +4359,18 @@ NIL (-1107 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| (-1106 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1106) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1106 |#1| |#2|) (QUOTE (-1066)))) (|HasCategory| (-1106 |#1| |#2|) (QUOTE (-1066))) (-1536 (|HasCategory| (-1106 |#1| |#2|) (LIST (QUOTE -593) (QUOTE (-834)))) (-12 (|HasCategory| (-1106 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1106) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1106 |#1| |#2|) (QUOTE (-1066))))) (|HasCategory| (-1106 |#1| |#2|) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-1106 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1106) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1106 |#1| |#2|) (QUOTE (-1067)))) (|HasCategory| (-1106 |#1| |#2|) (QUOTE (-1067))) (-3874 (-12 (|HasCategory| (-1106 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1106) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1106 |#1| |#2|) (QUOTE (-1067)))) (|HasCategory| (-1106 |#1| |#2|) (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| (-1106 |#1| |#2|) (LIST (QUOTE -593) (QUOTE (-835))))) (-1108 |ndim| R) -((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}."))) +((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4333 . T) (-4325 |has| |#2| (-6 (-4338 "*"))) (-4336 . T) (-4330 . T) (-4331 . T)) -((|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4338 "*"))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-549)))) (-1536 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-356))) (-1536 (|HasAttribute| |#2| (QUOTE (-4338 "*"))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-170)))) +((|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4338 "*"))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (-3874 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))))) (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-356))) (-3874 (|HasAttribute| |#2| (QUOTE (-4338 "*"))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142))))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-170)))) (-1109 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1110) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL (-1111 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4379,23 +4379,23 @@ NIL (-1112 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-835))))) (-1113 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-1114 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL (-1115 S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) -((-2623 . T)) +((-2359 . T)) NIL (-1116 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4337 . T)) -((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-823))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-823))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835))))) (-1117) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4405,43 +4405,43 @@ NIL NIL NIL (-1119 S) +((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) +((-4337 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-1120 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}."))) NIL NIL -(-1120 A B) +(-1121 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL NIL -(-1121 A B C) +(-1122 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}."))) NIL NIL -(-1122 S) -((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4337 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (-1123) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL (-1124) NIL ((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1066))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| (-142) (QUOTE (-1066))) (-12 (|HasCategory| (-142) (QUOTE (-1066))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -593) (QUOTE (-834))))) +((-3874 (-12 (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1067))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-142) (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| (-142) (QUOTE (-1067))) (-12 (|HasCategory| (-142) (QUOTE (-1067))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -593) (QUOTE (-835))))) (-1125 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#1|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (QUOTE (-1066))) (|HasCategory| (-1124) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 (-1124)) (|:| -1792 |#1|)) (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (QUOTE (-1124))) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (QUOTE (-1067)))) (-3874 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (QUOTE (-1067))) (|HasCategory| (-1124) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 (-1124)) (|:| -2184 |#1|)) (LIST (QUOTE -593) (QUOTE (-835))))) (-1126 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL -((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) +((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535)))))) (-1127 |Coef|) -((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) +((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL (-1128 |Coef|) -((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) +((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL (-1129 R UP) @@ -4462,9 +4462,9 @@ NIL NIL (-1133 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4338 "*") -1536 (-1820 (|has| |#1| (-356)) (|has| (-1140 |#1| |#2| |#3|) (-796))) (|has| |#1| (-170)) (-1820 (|has| |#1| (-356)) (|has| (-1140 |#1| |#2| |#3|) (-880)))) (-4329 -1536 (-1820 (|has| |#1| (-356)) (|has| (-1140 |#1| |#2| |#3|) (-796))) (|has| |#1| (-541)) (-1820 (|has| |#1| (-356)) (|has| (-1140 |#1| |#2| |#3|) (-880)))) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . 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(((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) NIL NIL -(-1136 R S) +(-1136 R) +((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4332 |has| |#1| (-356)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-1048) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-881)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-881)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) +(-1137 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1137 E OV R P) +(-1138 E OV R P) ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) NIL NIL -(-1138 R) -((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4332 |has| |#1| (-356)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-372))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -857) (QUOTE (-549))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-372)))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (QUOTE (-549)))))) (-12 (|HasCategory| (-1048) (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -617) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4334)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (-1536 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1139 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -1531) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-535)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasSignature| |#1| (LIST (QUOTE -4300) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535)))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-931))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasSignature| |#1| (LIST (QUOTE -4155) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (LIST (QUOTE -618) (QUOTE (-1142))) (|devaluate| |#1|))))))) (-1140 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-542))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|)))) (|HasCategory| (-747) (QUOTE (-1078))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasSignature| |#1| (LIST (QUOTE -4300) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-931))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasSignature| |#1| (LIST (QUOTE -4155) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (LIST (QUOTE -618) (QUOTE (-1142))) (|devaluate| |#1|))))))) (-1141) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4506,10 +4506,10 @@ NIL NIL (-1144 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-6 -4334)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| (-942) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasAttribute| |#1| (QUOTE -4334))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-6 -4334)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-542))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| (-942) (QUOTE (-130)))) (-3874 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasAttribute| |#1| (QUOTE -4334))) (-1145) -((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) +((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL (-1146) @@ -4532,14 +4532,14 @@ NIL ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1151 S) +(-1151 |Key| |Entry|) +((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) +((-4336 . T) (-4337 . T)) +((-12 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4203) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2184) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -594) (QUOTE (-524)))) (-12 (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1067))) (-3874 (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-835)))) (|HasCategory| (-2 (|:| -4203 |#1|) (|:| -2184 |#2|)) (LIST (QUOTE -593) (QUOTE (-835))))) +(-1152 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1152 |Key| |Entry|) -((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4336 . T) (-4337 . T)) -((-12 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3337) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1792) (|devaluate| |#2|)))))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1066)))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -594) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1066))) (-1536 (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#2| (LIST (QUOTE -593) (QUOTE (-834)))) (|HasCategory| (-2 (|:| -3337 |#1|) (|:| -1792 |#2|)) (LIST (QUOTE -593) (QUOTE (-834))))) (-1153 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4550,7 +4550,7 @@ NIL NIL (-1155 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4337 . T) (-2623 . T)) +((-4337 . T) (-2359 . T)) NIL (-1156 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4560,12 +4560,12 @@ NIL ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1158 S) -((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) +(-1158) +((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) NIL NIL -(-1159) -((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) +(-1159 S) +((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL (-1160) @@ -4591,7 +4591,7 @@ NIL (-1165 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1066))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1067))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (-1166 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4600,7 +4600,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1168 R -1421) +(-1168 R -3416) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4608,22 +4608,22 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1170 R -1421) +(-1170 R -3416) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -857) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -857) (|devaluate| |#1|))))) -(-1171 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -594) (LIST (QUOTE -861) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -857) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -857) (|devaluate| |#1|))))) +(-1171 |Coef|) +((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-356)))) +(-1172 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-361)))) -(-1172 R E V P) +(-1173 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL -(-1173 |Coef|) -((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-356)))) (-1174 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4635,18 +4635,18 @@ NIL (-1176 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) NIL -((|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) -(-1177 -1421) +((|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-1177 -3416) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL (-1178) -((|constructor| (NIL "This domain represents a type AST."))) -NIL +((|constructor| (NIL "The fundamental Type."))) +((-2359 . T)) NIL (-1179) -((|constructor| (NIL "The fundamental Type."))) -((-2623 . T)) +((|constructor| (NIL "This domain represents a type AST."))) +NIL NIL (-1180 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) @@ -4664,153 +4664,153 @@ NIL ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) ((-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-1184 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1184 |Coef| |var| |cen|) +((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) +(((-4338 "*") -3874 (-3179 (|has| |#1| (-356)) (|has| (-1214 |#1| |#2| |#3|) (-796))) (|has| |#1| (-170)) (-3179 (|has| |#1| (-356)) (|has| (-1214 |#1| |#2| |#3|) (-881)))) (-4329 -3874 (-3179 (|has| |#1| (-356)) (|has| (-1214 |#1| |#2| |#3|) (-796))) (|has| |#1| (-542)) (-3179 (|has| |#1| (-356)) (|has| (-1214 |#1| |#2| |#3|) (-881)))) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . 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((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 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(|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-356)))) -(-1187 |Coef| UTS) +(-1188 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) 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(|HasSignature| |#1| (LIST (QUOTE -4300) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-535))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-931))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasSignature| |#1| (LIST (QUOTE -4155) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (LIST (QUOTE -618) (QUOTE (-1142))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-881))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-300)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-143)))))) (-1190 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1191 R S) +(-1191 S) +((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) +NIL +((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1067)))) +(-1192 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-821)))) -(-1192 S) -((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) -NIL -((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1066)))) -(-1193 |x| R |y| S) +(-1193 |x| R) +((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) +(((-4338 "*") |has| |#2| (-170)) (-4329 |has| |#2| (-542)) (-4332 |has| |#2| (-356)) (-4334 |has| |#2| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +((|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (-3874 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-542)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-371)))) (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-371))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -857) (QUOTE (-535)))) (|HasCategory| (-1048) (LIST (QUOTE -857) (QUOTE (-535))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371))))) (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-371)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535))))) (|HasCategory| (-1048) (LIST (QUOTE -594) (LIST (QUOTE -861) (QUOTE (-535)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| (-1048) (LIST (QUOTE -594) (QUOTE (-524))))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (LIST (QUOTE -617) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (-3874 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-881)))) (-3874 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-881)))) (-3874 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-881)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (-3874 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE -4334)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (-3874 (-12 (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143))))) +(-1194 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1194 R Q UP) +(-1195 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1195 R UP) +(-1196 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1196 R UP) +(-1197 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1197 R U) +(-1198 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1198 |x| R) -((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) -(((-4338 "*") |has| |#2| (-170)) (-4329 |has| |#2| (-541)) (-4332 |has| |#2| (-356)) (-4334 |has| |#2| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) -NIL -NIL -(-1200 S R) +(-1199 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-541))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1117)))) -(-1201 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1117)))) +(-1200 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4332 |has| |#1| (-356)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4332 |has| |#1| (-356)) (-4334 |has| |#1| (-6 -4334)) (-4331 . T) (-4330 . T) (-4333 . T)) +NIL +(-1201 R PR S PS) +((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) +NIL NIL (-1202 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1078))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3845) (LIST (|devaluate| |#2|) (QUOTE (-1142)))))) +((|HasCategory| |#2| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1078))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4300) (LIST (|devaluate| |#2|) (QUOTE (-1142)))))) (-1203 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4330 . T) (-4331 . T) (-4333 . T)) NIL (-1204 RC P) -((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) +((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1205 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1205 |Coef| |var| |cen|) +((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-535)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasSignature| |#1| (LIST (QUOTE -4300) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535)))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-931))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasSignature| |#1| (LIST (QUOTE -4155) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (LIST (QUOTE -618) (QUOTE (-1142))) (|devaluate| |#1|))))))) +(-1206 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1206 |Coef|) +(-1207 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux 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),{}var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,{}r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,{}st)} creates a series from a common denomiator and 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 and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-1207 S |Coef| ULS) +(-1208 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1208 |Coef| ULS) +(-1209 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-1209 |Coef| ULS) +(-1210 |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)}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -1531) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) -(-1210 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#1| (QUOTE (-170))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-549)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-1536 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-541)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-549)))))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -1531) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4334 |has| |#1| (-356)) (-4328 |has| |#1| (-356)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-535)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-3874 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasSignature| |#1| (LIST (QUOTE -4300) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-535)))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-931))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasSignature| |#1| (LIST (QUOTE -4155) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (LIST (QUOTE -618) (QUOTE (-1142))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535)))))) (-1211 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))}."))) -(((-4338 "*") |has| (-1210 |#2| |#3| |#4|) (-170)) (-4329 |has| (-1210 |#2| |#3| |#4|) (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -1009) (QUOTE (-549)))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-356))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-444))) (-1536 (|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-549)))))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-541)))) +(((-4338 "*") |has| (-1205 |#2| |#3| |#4|) (-170)) (-4329 |has| (-1205 |#2| |#3| |#4|) (-542)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| (-1205 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-1205 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1205 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1205 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1205 |#2| |#3| |#4|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-1205 |#2| |#3| |#4|) (LIST (QUOTE -1009) (QUOTE (-535)))) (|HasCategory| (-1205 |#2| |#3| |#4|) (QUOTE (-356))) (|HasCategory| (-1205 |#2| |#3| |#4|) (QUOTE (-444))) (-3874 (|HasCategory| (-1205 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| (-1205 |#2| |#3| |#4|) (LIST (QUOTE -1009) (LIST (QUOTE -400) (QUOTE (-535)))))) (|HasCategory| (-1205 |#2| |#3| |#4|) (QUOTE (-542)))) (-1212 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4337))) (-1213 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2623 . T)) +((-2359 . T)) NIL -(-1214 |Coef1| |Coef2| UTS1 UTS2) +(-1214 |Coef| |var| |cen|) +((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4330 . T) (-4331 . T) (-4333 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-542))) (-3874 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|)))) (|HasCategory| (-747) (QUOTE (-1078))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasSignature| |#1| (LIST (QUOTE -4300) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasCategory| |#1| (QUOTE (-356))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-931))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasSignature| |#1| (LIST (QUOTE -4155) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -3405) (LIST (LIST (QUOTE -618) (QUOTE (-1142))) (|devaluate| |#1|))))))) +(-1215 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1215 S |Coef|) +(-1216 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 (-549)))) (|HasCategory| |#2| (QUOTE (-930))) (|HasCategory| |#2| (QUOTE (-1164))) (|HasSignature| |#2| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1531) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1142))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#2| (QUOTE (-356)))) -(-1216 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-931))) (|HasCategory| |#2| (QUOTE (-1164))) (|HasSignature| |#2| (LIST (QUOTE -3405) (LIST (LIST (QUOTE -618) (QUOTE (-1142))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4155) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1142))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-356)))) +(-1217 |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."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) +(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-542)) (-4330 . T) (-4331 . T) (-4333 . T)) NIL -(-1217 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4338 "*") |has| |#1| (-170)) (-4329 |has| |#1| (-541)) (-4330 . T) (-4331 . T) (-4333 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-541))) (-1536 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -871) (QUOTE (-1142)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-747)) (|devaluate| |#1|)))) (|HasCategory| (-747) (QUOTE (-1078))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasSignature| |#1| (LIST (QUOTE -3845) (LIST (|devaluate| |#1|) (QUOTE (-1142)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-747))))) (|HasCategory| |#1| (QUOTE (-356))) (-1536 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1164))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasSignature| |#1| (LIST (QUOTE -1531) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1142))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (LIST (QUOTE -621) (QUOTE (-1142))) (|devaluate| |#1|))))))) (-1218 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1219 -1421 UP L UTS) +(-1219 -3416 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL -((|HasCategory| |#1| (QUOTE (-541)))) +((|HasCategory| |#1| (QUOTE (-542)))) (-1220) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) -((-2623 . T)) +((-2359 . T)) NIL (-1221 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4822,30 +4822,30 @@ NIL ((|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-703))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1223 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4337 . T) (-4336 . T) (-2623 . T)) +((-4337 . T) (-4336 . T) (-2359 . T)) NIL -(-1224 A B) +(-1224 R) +((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) +((-4337 . T) (-4336 . T)) +((-3874 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3874 (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-524)))) (-3874 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-535) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-835))))) +(-1225 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1225 R) -((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4337 . T) (-4336 . T)) -((-1536 (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1536 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (|HasCategory| |#1| (LIST (QUOTE -594) (QUOTE (-525)))) (-1536 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-549) (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-703))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -593) (QUOTE (-834))))) (-1226) -((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) +((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL (-1227) -((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) +((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL (-1228) -((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) +((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL (-1229) -((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) +((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL (-1230) @@ -4864,7 +4864,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1234 K R UP -1421) +(-1234 K R UP -3416) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -4883,7 +4883,7 @@ NIL (-1238 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) ((-4337 . T) (-4336 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-541))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-834))))) +((-12 (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -594) (QUOTE (-524)))) (|HasCategory| |#4| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -593) (QUOTE (-835))))) (-1239 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) ((-4330 . T) (-4331 . T) (-4333 . T)) @@ -4896,30 +4896,30 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1242 |vl| R) -((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4329 |has| |#2| (-6 -4329)) (-4331 . T) (-4330 . T) (-4333 . T)) -NIL -(-1243 S -1421) +(-1242 S -3416) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145)))) -(-1244 -1421) +(-1243 -3416) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4328 . T) (-4334 . T) (-4329 . T) ((-4338 "*") . T) (-4330 . T) (-4331 . T) (-4333 . T)) NIL +(-1244 |vl| R) +((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) +((-4329 |has| |#2| (-6 -4329)) (-4331 . T) (-4330 . T) (-4333 . T)) +NIL (-1245 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) ((-4329 |has| |#2| (-6 -4329)) (-4331 . T) (-4330 . T) (-4333 . T)) -((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -694) (LIST (QUOTE -400) (QUOTE (-549))))) (|HasAttribute| |#2| (QUOTE -4329))) -(-1246 |vl| R) -((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4329 |has| |#2| (-6 -4329)) (-4331 . T) (-4330 . T) (-4333 . T)) -NIL -(-1247 R) +((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -694) (LIST (QUOTE -400) (QUOTE (-535))))) (|HasAttribute| |#2| (QUOTE -4329))) +(-1246 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) ((-4329 |has| |#1| (-6 -4329)) (-4331 . T) (-4330 . T) (-4333 . T)) ((|HasCategory| |#1| (QUOTE (-170))) (|HasAttribute| |#1| (QUOTE -4329))) +(-1247 |vl| R) +((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) +((-4329 |has| |#2| (-6 -4329)) (-4331 . T) (-4330 . T) (-4333 . T)) +NIL (-1248 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) ((-4333 . T) (-4334 |has| |#1| (-6 -4334)) (-4329 |has| |#1| (-6 -4329)) (-4331 . T) (-4330 . T)) @@ -4960,4 +4960,4 @@ NIL NIL NIL NIL -((-3 NIL 2266092 2266097 2266102 2266107) (-2 NIL 2266072 2266077 2266082 2266087) (-1 NIL 2266052 2266057 2266062 2266067) (0 NIL 2266032 2266037 2266042 2266047) (-1253 "ZMOD.spad" 2265841 2265854 2265970 2266027) (-1252 "ZLINDEP.spad" 2264885 2264896 2265831 2265836) (-1251 "ZDSOLVE.spad" 2254734 2254756 2264875 2264880) (-1250 "YSTREAM.spad" 2254227 2254238 2254724 2254729) (-1249 "XRPOLY.spad" 2253447 2253467 2254083 2254152) (-1248 "XPR.spad" 2251176 2251189 2253165 2253264) (-1247 "XPOLY.spad" 2250731 2250742 2251032 2251101) (-1246 "XPOLYC.spad" 2250048 2250064 2250657 2250726) (-1245 "XPBWPOLY.spad" 2248485 2248505 2249828 2249897) (-1244 "XF.spad" 2246946 2246961 2248387 2248480) (-1243 "XF.spad" 2245387 2245404 2246830 2246835) (-1242 "XFALG.spad" 2242411 2242427 2245313 2245382) (-1241 "XEXPPKG.spad" 2241662 2241688 2242401 2242406) (-1240 "XDPOLY.spad" 2241276 2241292 2241518 2241587) (-1239 "XALG.spad" 2240874 2240885 2241232 2241271) (-1238 "WUTSET.spad" 2236713 2236730 2240520 2240547) (-1237 "WP.spad" 2235727 2235771 2236571 2236638) (-1236 "WHILEAST.spad" 2235525 2235534 2235717 2235722) (-1235 "WHEREAST.spad" 2235196 2235205 2235515 2235520) (-1234 "WFFINTBS.spad" 2232759 2232781 2235186 2235191) (-1233 "WEIER.spad" 2230973 2230984 2232749 2232754) (-1232 "VSPACE.spad" 2230646 2230657 2230941 2230968) (-1231 "VSPACE.spad" 2230339 2230352 2230636 2230641) (-1230 "VOID.spad" 2229929 2229938 2230329 2230334) (-1229 "VIEW.spad" 2227551 2227560 2229919 2229924) (-1228 "VIEWDEF.spad" 2222748 2222757 2227541 2227546) (-1227 "VIEW3D.spad" 2206583 2206592 2222738 2222743) (-1226 "VIEW2D.spad" 2194320 2194329 2206573 2206578) (-1225 "VECTOR.spad" 2192995 2193006 2193246 2193273) (-1224 "VECTOR2.spad" 2191622 2191635 2192985 2192990) (-1223 "VECTCAT.spad" 2189510 2189521 2191578 2191617) (-1222 "VECTCAT.spad" 2187218 2187231 2189288 2189293) (-1221 "VARIABLE.spad" 2186998 2187013 2187208 2187213) (-1220 "UTYPE.spad" 2186632 2186641 2186978 2186993) (-1219 "UTSODETL.spad" 2185925 2185949 2186588 2186593) (-1218 "UTSODE.spad" 2184113 2184133 2185915 2185920) (-1217 "UTS.spad" 2178902 2178930 2182580 2182677) (-1216 "UTSCAT.spad" 2176353 2176369 2178800 2178897) (-1215 "UTSCAT.spad" 2173448 2173466 2175897 2175902) (-1214 "UTS2.spad" 2173041 2173076 2173438 2173443) (-1213 "URAGG.spad" 2167663 2167674 2173021 2173036) (-1212 "URAGG.spad" 2162259 2162272 2167619 2167624) (-1211 "UPXSSING.spad" 2159902 2159928 2161340 2161473) (-1210 "UPXS.spad" 2156929 2156957 2158034 2158183) (-1209 "UPXSCONS.spad" 2154686 2154706 2155061 2155210) (-1208 "UPXSCCA.spad" 2153144 2153164 2154532 2154681) (-1207 "UPXSCCA.spad" 2151744 2151766 2153134 2153139) (-1206 "UPXSCAT.spad" 2150325 2150341 2151590 2151739) (-1205 "UPXS2.spad" 2149866 2149919 2150315 2150320) (-1204 "UPSQFREE.spad" 2148278 2148292 2149856 2149861) (-1203 "UPSCAT.spad" 2145871 2145895 2148176 2148273) (-1202 "UPSCAT.spad" 2143170 2143196 2145477 2145482) (-1201 "UPOLYC.spad" 2138148 2138159 2143012 2143165) (-1200 "UPOLYC.spad" 2133018 2133031 2137884 2137889) (-1199 "UPOLYC2.spad" 2132487 2132506 2133008 2133013) (-1198 "UP.spad" 2129529 2129544 2130037 2130190) (-1197 "UPMP.spad" 2128419 2128432 2129519 2129524) (-1196 "UPDIVP.spad" 2127982 2127996 2128409 2128414) (-1195 "UPDECOMP.spad" 2126219 2126233 2127972 2127977) (-1194 "UPCDEN.spad" 2125426 2125442 2126209 2126214) (-1193 "UP2.spad" 2124788 2124809 2125416 2125421) (-1192 "UNISEG.spad" 2124141 2124152 2124707 2124712) (-1191 "UNISEG2.spad" 2123634 2123647 2124097 2124102) (-1190 "UNIFACT.spad" 2122735 2122747 2123624 2123629) (-1189 "ULS.spad" 2113289 2113317 2114382 2114811) (-1188 "ULSCONS.spad" 2107328 2107348 2107700 2107849) (-1187 "ULSCCAT.spad" 2104925 2104945 2107148 2107323) (-1186 "ULSCCAT.spad" 2102656 2102678 2104881 2104886) (-1185 "ULSCAT.spad" 2100872 2100888 2102502 2102651) (-1184 "ULS2.spad" 2100384 2100437 2100862 2100867) (-1183 "UFD.spad" 2099449 2099458 2100310 2100379) (-1182 "UFD.spad" 2098576 2098587 2099439 2099444) (-1181 "UDVO.spad" 2097423 2097432 2098566 2098571) (-1180 "UDPO.spad" 2094850 2094861 2097379 2097384) (-1179 "TYPE.spad" 2094772 2094781 2094830 2094845) (-1178 "TYPEAST.spad" 2094691 2094700 2094762 2094767) (-1177 "TWOFACT.spad" 2093341 2093356 2094681 2094686) (-1176 "TUPLE.spad" 2092727 2092738 2093240 2093245) (-1175 "TUBETOOL.spad" 2089564 2089573 2092717 2092722) (-1174 "TUBE.spad" 2088205 2088222 2089554 2089559) (-1173 "TS.spad" 2086794 2086810 2087770 2087867) (-1172 "TSETCAT.spad" 2073909 2073926 2086750 2086789) (-1171 "TSETCAT.spad" 2061022 2061041 2073865 2073870) (-1170 "TRMANIP.spad" 2055388 2055405 2060728 2060733) (-1169 "TRIMAT.spad" 2054347 2054372 2055378 2055383) (-1168 "TRIGMNIP.spad" 2052864 2052881 2054337 2054342) (-1167 "TRIGCAT.spad" 2052376 2052385 2052854 2052859) (-1166 "TRIGCAT.spad" 2051886 2051897 2052366 2052371) (-1165 "TREE.spad" 2050457 2050468 2051493 2051520) (-1164 "TRANFUN.spad" 2050288 2050297 2050447 2050452) (-1163 "TRANFUN.spad" 2050117 2050128 2050278 2050283) (-1162 "TOPSP.spad" 2049791 2049800 2050107 2050112) (-1161 "TOOLSIGN.spad" 2049454 2049465 2049781 2049786) (-1160 "TEXTFILE.spad" 2048011 2048020 2049444 2049449) (-1159 "TEX.spad" 2045028 2045037 2048001 2048006) (-1158 "TEX1.spad" 2044584 2044595 2045018 2045023) (-1157 "TEMUTL.spad" 2044139 2044148 2044574 2044579) (-1156 "TBCMPPK.spad" 2042232 2042255 2044129 2044134) (-1155 "TBAGG.spad" 2041256 2041279 2042200 2042227) (-1154 "TBAGG.spad" 2040300 2040325 2041246 2041251) (-1153 "TANEXP.spad" 2039676 2039687 2040290 2040295) (-1152 "TABLE.spad" 2038087 2038110 2038357 2038384) (-1151 "TABLEAU.spad" 2037568 2037579 2038077 2038082) (-1150 "TABLBUMP.spad" 2034351 2034362 2037558 2037563) (-1149 "SYSTEM.spad" 2033625 2033634 2034341 2034346) (-1148 "SYSSOLP.spad" 2031098 2031109 2033615 2033620) (-1147 "SYNTAX.spad" 2027290 2027299 2031088 2031093) (-1146 "SYMTAB.spad" 2025346 2025355 2027280 2027285) (-1145 "SYMS.spad" 2021331 2021340 2025336 2025341) (-1144 "SYMPOLY.spad" 2020338 2020349 2020420 2020547) (-1143 "SYMFUNC.spad" 2019813 2019824 2020328 2020333) (-1142 "SYMBOL.spad" 2017149 2017158 2019803 2019808) (-1141 "SWITCH.spad" 2013906 2013915 2017139 2017144) (-1140 "SUTS.spad" 2010805 2010833 2012373 2012470) (-1139 "SUPXS.spad" 2007819 2007847 2008937 2009086) (-1138 "SUP.spad" 2004588 2004599 2005369 2005522) (-1137 "SUPFRACF.spad" 2003693 2003711 2004578 2004583) (-1136 "SUP2.spad" 2003083 2003096 2003683 2003688) (-1135 "SUMRF.spad" 2002049 2002060 2003073 2003078) (-1134 "SUMFS.spad" 2001682 2001699 2002039 2002044) (-1133 "SULS.spad" 1992223 1992251 1993329 1993758) (-1132 "SUCHTAST.spad" 1991992 1992001 1992213 1992218) (-1131 "SUCH.spad" 1991672 1991687 1991982 1991987) (-1130 "SUBSPACE.spad" 1983679 1983694 1991662 1991667) (-1129 "SUBRESP.spad" 1982839 1982853 1983635 1983640) (-1128 "STTF.spad" 1978938 1978954 1982829 1982834) (-1127 "STTFNC.spad" 1975406 1975422 1978928 1978933) (-1126 "STTAYLOR.spad" 1967804 1967815 1975287 1975292) (-1125 "STRTBL.spad" 1966309 1966326 1966458 1966485) (-1124 "STRING.spad" 1965718 1965727 1965732 1965759) (-1123 "STRICAT.spad" 1965494 1965503 1965674 1965713) (-1122 "STREAM.spad" 1962262 1962273 1965019 1965034) (-1121 "STREAM3.spad" 1961807 1961822 1962252 1962257) (-1120 "STREAM2.spad" 1960875 1960888 1961797 1961802) (-1119 "STREAM1.spad" 1960579 1960590 1960865 1960870) (-1118 "STINPROD.spad" 1959485 1959501 1960569 1960574) (-1117 "STEP.spad" 1958686 1958695 1959475 1959480) (-1116 "STBL.spad" 1957212 1957240 1957379 1957394) (-1115 "STAGG.spad" 1956277 1956288 1957192 1957207) (-1114 "STAGG.spad" 1955350 1955363 1956267 1956272) (-1113 "STACK.spad" 1954701 1954712 1954957 1954984) (-1112 "SREGSET.spad" 1952405 1952422 1954347 1954374) (-1111 "SRDCMPK.spad" 1950950 1950970 1952395 1952400) (-1110 "SRAGG.spad" 1946035 1946044 1950906 1950945) (-1109 "SRAGG.spad" 1941152 1941163 1946025 1946030) (-1108 "SQMATRIX.spad" 1938776 1938794 1939684 1939771) (-1107 "SPLTREE.spad" 1933328 1933341 1938212 1938239) (-1106 "SPLNODE.spad" 1929916 1929929 1933318 1933323) (-1105 "SPFCAT.spad" 1928693 1928702 1929906 1929911) (-1104 "SPECOUT.spad" 1927243 1927252 1928683 1928688) (-1103 "SPADXPT.spad" 1919372 1919381 1927223 1927238) (-1102 "spad-parser.spad" 1918837 1918846 1919362 1919367) (-1101 "SPADAST.spad" 1918538 1918547 1918827 1918832) (-1100 "SPACEC.spad" 1902551 1902562 1918528 1918533) (-1099 "SPACE3.spad" 1902327 1902338 1902541 1902546) (-1098 "SORTPAK.spad" 1901872 1901885 1902283 1902288) (-1097 "SOLVETRA.spad" 1899629 1899640 1901862 1901867) (-1096 "SOLVESER.spad" 1898149 1898160 1899619 1899624) (-1095 "SOLVERAD.spad" 1894159 1894170 1898139 1898144) (-1094 "SOLVEFOR.spad" 1892579 1892597 1894149 1894154) (-1093 "SNTSCAT.spad" 1892167 1892184 1892535 1892574) (-1092 "SMTS.spad" 1890427 1890453 1891732 1891829) (-1091 "SMP.spad" 1887866 1887886 1888256 1888383) (-1090 "SMITH.spad" 1886709 1886734 1887856 1887861) (-1089 "SMATCAT.spad" 1884807 1884837 1886641 1886704) (-1088 "SMATCAT.spad" 1882849 1882881 1884685 1884690) (-1087 "SKAGG.spad" 1881798 1881809 1882805 1882844) (-1086 "SINT.spad" 1880106 1880115 1881664 1881793) (-1085 "SIMPAN.spad" 1879834 1879843 1880096 1880101) (-1084 "SIG.spad" 1879162 1879171 1879824 1879829) (-1083 "SIGNRF.spad" 1878270 1878281 1879152 1879157) (-1082 "SIGNEF.spad" 1877539 1877556 1878260 1878265) (-1081 "SIGAST.spad" 1876920 1876929 1877529 1877534) (-1080 "SHP.spad" 1874838 1874853 1876876 1876881) (-1079 "SHDP.spad" 1865823 1865850 1866332 1866463) (-1078 "SGROUP.spad" 1865431 1865440 1865813 1865818) (-1077 "SGROUP.spad" 1865037 1865048 1865421 1865426) (-1076 "SGCF.spad" 1857918 1857927 1865027 1865032) (-1075 "SFRTCAT.spad" 1856834 1856851 1857874 1857913) (-1074 "SFRGCD.spad" 1855897 1855917 1856824 1856829) (-1073 "SFQCMPK.spad" 1850534 1850554 1855887 1855892) (-1072 "SFORT.spad" 1849969 1849983 1850524 1850529) (-1071 "SEXOF.spad" 1849812 1849852 1849959 1849964) (-1070 "SEX.spad" 1849704 1849713 1849802 1849807) (-1069 "SEXCAT.spad" 1846808 1846848 1849694 1849699) (-1068 "SET.spad" 1845108 1845119 1846229 1846268) (-1067 "SETMN.spad" 1843542 1843559 1845098 1845103) (-1066 "SETCAT.spad" 1843027 1843036 1843532 1843537) (-1065 "SETCAT.spad" 1842510 1842521 1843017 1843022) (-1064 "SETAGG.spad" 1839019 1839030 1842478 1842505) (-1063 "SETAGG.spad" 1835548 1835561 1839009 1839014) (-1062 "SEQAST.spad" 1835251 1835260 1835538 1835543) (-1061 "SEGXCAT.spad" 1834363 1834376 1835231 1835246) (-1060 "SEG.spad" 1834176 1834187 1834282 1834287) (-1059 "SEGCAT.spad" 1832995 1833006 1834156 1834171) (-1058 "SEGBIND.spad" 1832067 1832078 1832950 1832955) (-1057 "SEGBIND2.spad" 1831763 1831776 1832057 1832062) (-1056 "SEGAST.spad" 1831477 1831486 1831753 1831758) (-1055 "SEG2.spad" 1830902 1830915 1831433 1831438) (-1054 "SDVAR.spad" 1830178 1830189 1830892 1830897) (-1053 "SDPOL.spad" 1827568 1827579 1827859 1827986) (-1052 "SCPKG.spad" 1825647 1825658 1827558 1827563) (-1051 "SCOPE.spad" 1824792 1824801 1825637 1825642) (-1050 "SCACHE.spad" 1823474 1823485 1824782 1824787) (-1049 "SASTCAT.spad" 1823383 1823392 1823464 1823469) (-1048 "SAOS.spad" 1823255 1823264 1823373 1823378) (-1047 "SAERFFC.spad" 1822968 1822988 1823245 1823250) (-1046 "SAE.spad" 1821143 1821159 1821754 1821889) (-1045 "SAEFACT.spad" 1820844 1820864 1821133 1821138) (-1044 "RURPK.spad" 1818485 1818501 1820834 1820839) (-1043 "RULESET.spad" 1817926 1817950 1818475 1818480) (-1042 "RULE.spad" 1816130 1816154 1817916 1817921) (-1041 "RULECOLD.spad" 1815982 1815995 1816120 1816125) (-1040 "RSTRCAST.spad" 1815699 1815708 1815972 1815977) (-1039 "RSETGCD.spad" 1812077 1812097 1815689 1815694) (-1038 "RSETCAT.spad" 1801849 1801866 1812033 1812072) (-1037 "RSETCAT.spad" 1791653 1791672 1801839 1801844) (-1036 "RSDCMPK.spad" 1790105 1790125 1791643 1791648) (-1035 "RRCC.spad" 1788489 1788519 1790095 1790100) (-1034 "RRCC.spad" 1786871 1786903 1788479 1788484) (-1033 "RPTAST.spad" 1786573 1786582 1786861 1786866) (-1032 "RPOLCAT.spad" 1765933 1765948 1786441 1786568) (-1031 "RPOLCAT.spad" 1745007 1745024 1765517 1765522) (-1030 "ROUTINE.spad" 1740870 1740879 1743654 1743681) (-1029 "ROMAN.spad" 1740102 1740111 1740736 1740865) (-1028 "ROIRC.spad" 1739182 1739214 1740092 1740097) (-1027 "RNS.spad" 1738085 1738094 1739084 1739177) (-1026 "RNS.spad" 1737074 1737085 1738075 1738080) (-1025 "RNG.spad" 1736809 1736818 1737064 1737069) (-1024 "RMODULE.spad" 1736447 1736458 1736799 1736804) (-1023 "RMCAT2.spad" 1735855 1735912 1736437 1736442) (-1022 "RMATRIX.spad" 1734534 1734553 1735022 1735061) (-1021 "RMATCAT.spad" 1730055 1730086 1734478 1734529) (-1020 "RMATCAT.spad" 1725478 1725511 1729903 1729908) (-1019 "RINTERP.spad" 1725366 1725386 1725468 1725473) (-1018 "RING.spad" 1724723 1724732 1725346 1725361) (-1017 "RING.spad" 1724088 1724099 1724713 1724718) (-1016 "RIDIST.spad" 1723472 1723481 1724078 1724083) (-1015 "RGCHAIN.spad" 1722051 1722067 1722957 1722984) (-1014 "RF.spad" 1719665 1719676 1722041 1722046) (-1013 "RFFACTOR.spad" 1719127 1719138 1719655 1719660) (-1012 "RFFACT.spad" 1718862 1718874 1719117 1719122) (-1011 "RFDIST.spad" 1717850 1717859 1718852 1718857) (-1010 "RETSOL.spad" 1717267 1717280 1717840 1717845) (-1009 "RETRACT.spad" 1716616 1716627 1717257 1717262) (-1008 "RETRACT.spad" 1715963 1715976 1716606 1716611) (-1007 "RETAST.spad" 1715775 1715784 1715953 1715958) (-1006 "RESULT.spad" 1713835 1713844 1714422 1714449) (-1005 "RESRING.spad" 1713182 1713229 1713773 1713830) (-1004 "RESLATC.spad" 1712506 1712517 1713172 1713177) (-1003 "REPSQ.spad" 1712235 1712246 1712496 1712501) (-1002 "REP.spad" 1709787 1709796 1712225 1712230) (-1001 "REPDB.spad" 1709492 1709503 1709777 1709782) (-1000 "REP2.spad" 1699064 1699075 1709334 1709339) (-999 "REP1.spad" 1693055 1693065 1699014 1699019) (-998 "REGSET.spad" 1690853 1690869 1692701 1692728) (-997 "REF.spad" 1690183 1690193 1690808 1690813) (-996 "REDORDER.spad" 1689360 1689376 1690173 1690178) (-995 "RECLOS.spad" 1688144 1688163 1688847 1688940) (-994 "REALSOLV.spad" 1687277 1687285 1688134 1688139) (-993 "REAL.spad" 1687150 1687158 1687267 1687272) (-992 "REAL0Q.spad" 1684433 1684447 1687140 1687145) (-991 "REAL0.spad" 1681262 1681276 1684423 1684428) (-990 "RDUCEAST.spad" 1680984 1680992 1681252 1681257) (-989 "RDIV.spad" 1680636 1680660 1680974 1680979) (-988 "RDIST.spad" 1680200 1680210 1680626 1680631) (-987 "RDETRS.spad" 1678997 1679014 1680190 1680195) (-986 "RDETR.spad" 1677105 1677122 1678987 1678992) (-985 "RDEEFS.spad" 1676179 1676195 1677095 1677100) (-984 "RDEEF.spad" 1675176 1675192 1676169 1676174) (-983 "RCFIELD.spad" 1672363 1672371 1675078 1675171) (-982 "RCFIELD.spad" 1669636 1669646 1672353 1672358) (-981 "RCAGG.spad" 1667539 1667549 1669616 1669631) (-980 "RCAGG.spad" 1665379 1665391 1667458 1667463) 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"FILECAT.spad" 573483 573500 574955 574960) (-356 "FIELD.spad" 572889 572897 573385 573478) (-355 "FIELD.spad" 572381 572391 572879 572884) (-354 "FGROUP.spad" 570990 571000 572361 572376) (-353 "FGLMICPK.spad" 569777 569792 570980 570985) (-352 "FFX.spad" 569152 569167 569493 569586) (-351 "FFSLPE.spad" 568641 568662 569142 569147) (-350 "FFPOLY.spad" 559893 559904 568631 568636) (-349 "FFPOLY2.spad" 558953 558970 559883 559888) (-348 "FFP.spad" 558350 558370 558669 558762) (-347 "FF.spad" 557798 557814 558031 558124) (-346 "FFNBX.spad" 556310 556330 557514 557607) (-345 "FFNBP.spad" 554823 554840 556026 556119) (-344 "FFNB.spad" 553288 553309 554504 554597) (-343 "FFINTBAS.spad" 550702 550721 553278 553283) (-342 "FFIELDC.spad" 548277 548285 550604 550697) (-341 "FFIELDC.spad" 545938 545948 548267 548272) (-340 "FFHOM.spad" 544686 544703 545928 545933) (-339 "FFF.spad" 542121 542132 544676 544681) (-338 "FFCGX.spad" 540968 540988 541837 541930) (-337 "FFCGP.spad" 539857 539877 540684 540777) (-336 "FFCG.spad" 538649 538670 539538 539631) (-335 "FFCAT.spad" 531676 531698 538488 538644) (-334 "FFCAT.spad" 524782 524806 531596 531601) (-333 "FFCAT2.spad" 524527 524567 524772 524777) (-332 "FEXPR.spad" 516236 516282 524283 524322) (-331 "FEVALAB.spad" 515942 515952 516226 516231) (-330 "FEVALAB.spad" 515433 515445 515719 515724) (-329 "FDIV.spad" 514875 514899 515423 515428) (-328 "FDIVCAT.spad" 512917 512941 514865 514870) (-327 "FDIVCAT.spad" 510957 510983 512907 512912) (-326 "FDIV2.spad" 510611 510651 510947 510952) (-325 "FCPAK1.spad" 509164 509172 510601 510606) (-324 "FCOMP.spad" 508543 508553 509154 509159) (-323 "FC.spad" 498368 498376 508533 508538) (-322 "FAXF.spad" 491303 491317 498270 498363) (-321 "FAXF.spad" 484290 484306 491259 491264) (-320 "FARRAY.spad" 482436 482446 483473 483500) (-319 "FAMR.spad" 480556 480568 482334 482431) (-318 "FAMR.spad" 478660 478674 480440 480445) (-317 "FAMONOID.spad" 478310 478320 478614 478619) (-316 "FAMONC.spad" 476532 476544 478300 478305) (-315 "FAGROUP.spad" 476138 476148 476428 476455) (-314 "FACUTIL.spad" 474334 474351 476128 476133) (-313 "FACTFUNC.spad" 473510 473520 474324 474329) (-312 "EXPUPXS.spad" 470343 470366 471642 471791) (-311 "EXPRTUBE.spad" 467571 467579 470333 470338) (-310 "EXPRODE.spad" 464443 464459 467561 467566) (-309 "EXPR.spad" 459718 459728 460432 460839) (-308 "EXPR2UPS.spad" 455810 455823 459708 459713) (-307 "EXPR2.spad" 455513 455525 455800 455805) (-306 "EXPEXPAN.spad" 452452 452477 453086 453179) (-305 "EXIT.spad" 452123 452131 452442 452447) (-304 "EXITAST.spad" 451859 451867 452113 452118) (-303 "EVALCYC.spad" 451317 451331 451849 451854) (-302 "EVALAB.spad" 450881 450891 451307 451312) (-301 "EVALAB.spad" 450443 450455 450871 450876) (-300 "EUCDOM.spad" 447985 447993 450369 450438) (-299 "EUCDOM.spad" 445589 445599 447975 447980) (-298 "ESTOOLS.spad" 437429 437437 445579 445584) (-297 "ESTOOLS2.spad" 437030 437044 437419 437424) (-296 "ESTOOLS1.spad" 436715 436726 437020 437025) (-295 "ES.spad" 429262 429270 436705 436710) (-294 "ES.spad" 421715 421725 429160 429165) (-293 "ESCONT.spad" 418488 418496 421705 421710) (-292 "ESCONT1.spad" 418237 418249 418478 418483) (-291 "ES2.spad" 417732 417748 418227 418232) (-290 "ES1.spad" 417298 417314 417722 417727) (-289 "ERROR.spad" 414619 414627 417288 417293) (-288 "EQTBL.spad" 413091 413113 413300 413327) (-287 "EQ.spad" 407965 407975 410764 410876) (-286 "EQ2.spad" 407681 407693 407955 407960) (-285 "EP.spad" 403995 404005 407671 407676) (-284 "ENV.spad" 402697 402705 403985 403990) (-283 "ENTIRER.spad" 402365 402373 402641 402692) (-282 "EMR.spad" 401566 401607 402291 402360) (-281 "ELTAGG.spad" 399806 399825 401556 401561) (-280 "ELTAGG.spad" 398010 398031 399762 399767) (-279 "ELTAB.spad" 397457 397475 398000 398005) (-278 "ELFUTS.spad" 396836 396855 397447 397452) (-277 "ELEMFUN.spad" 396525 396533 396826 396831) (-276 "ELEMFUN.spad" 396212 396222 396515 396520) (-275 "ELAGG.spad" 394143 394153 396180 396207) (-274 "ELAGG.spad" 392023 392035 394062 394067) (-273 "ELABEXPR.spad" 390954 390962 392013 392018) (-272 "EFUPXS.spad" 387730 387760 390910 390915) (-271 "EFULS.spad" 384566 384589 387686 387691) (-270 "EFSTRUC.spad" 382521 382537 384556 384561) (-269 "EF.spad" 377287 377303 382511 382516) (-268 "EAB.spad" 375563 375571 377277 377282) (-267 "E04UCFA.spad" 375099 375107 375553 375558) (-266 "E04NAFA.spad" 374676 374684 375089 375094) (-265 "E04MBFA.spad" 374256 374264 374666 374671) (-264 "E04JAFA.spad" 373792 373800 374246 374251) (-263 "E04GCFA.spad" 373328 373336 373782 373787) (-262 "E04FDFA.spad" 372864 372872 373318 373323) (-261 "E04DGFA.spad" 372400 372408 372854 372859) (-260 "E04AGNT.spad" 368242 368250 372390 372395) (-259 "DVARCAT.spad" 364927 364937 368232 368237) (-258 "DVARCAT.spad" 361610 361622 364917 364922) (-257 "DSMP.spad" 359041 359055 359346 359473) (-256 "DROPT.spad" 352986 352994 359031 359036) (-255 "DROPT1.spad" 352649 352659 352976 352981) (-254 "DROPT0.spad" 347476 347484 352639 352644) (-253 "DRAWPT.spad" 345631 345639 347466 347471) (-252 "DRAW.spad" 338231 338244 345621 345626) (-251 "DRAWHACK.spad" 337539 337549 338221 338226) (-250 "DRAWCX.spad" 334981 334989 337529 337534) (-249 "DRAWCURV.spad" 334518 334533 334971 334976) (-248 "DRAWCFUN.spad" 323690 323698 334508 334513) (-247 "DQAGG.spad" 321846 321856 323646 323685) (-246 "DPOLCAT.spad" 317187 317203 321714 321841) (-245 "DPOLCAT.spad" 312614 312632 317143 317148) (-244 "DPMO.spad" 305917 305933 306055 306356) (-243 "DPMM.spad" 299233 299251 299358 299659) (-242 "DOMAIN.spad" 298504 298512 299223 299228) (-241 "DMP.spad" 295726 295741 296298 296425) (-240 "DLP.spad" 295074 295084 295716 295721) (-239 "DLIST.spad" 293486 293496 294257 294284) (-238 "DLAGG.spad" 291887 291897 293466 293481) (-237 "DIVRING.spad" 291429 291437 291831 291882) (-236 "DIVRING.spad" 291015 291025 291419 291424) (-235 "DISPLAY.spad" 289195 289203 291005 291010) (-234 "DIRPROD.spad" 280049 280065 280689 280820) (-233 "DIRPROD2.spad" 278857 278875 280039 280044) (-232 "DIRPCAT.spad" 277787 277803 278709 278852) (-231 "DIRPCAT.spad" 276458 276476 277382 277387) (-230 "DIOSP.spad" 275283 275291 276448 276453) (-229 "DIOPS.spad" 274255 274265 275251 275278) (-228 "DIOPS.spad" 273213 273225 274211 274216) (-227 "DIFRING.spad" 272505 272513 273193 273208) (-226 "DIFRING.spad" 271805 271815 272495 272500) (-225 "DIFEXT.spad" 270964 270974 271785 271800) (-224 "DIFEXT.spad" 270040 270052 270863 270868) (-223 "DIAGG.spad" 269658 269668 270008 270035) (-222 "DIAGG.spad" 269296 269308 269648 269653) (-221 "DHMATRIX.spad" 267600 267610 268753 268780) (-220 "DFSFUN.spad" 261008 261016 267590 267595) (-219 "DFLOAT.spad" 257611 257619 260898 261003) (-218 "DFINTTLS.spad" 255820 255836 257601 257606) (-217 "DERHAM.spad" 253730 253762 255800 255815) (-216 "DEQUEUE.spad" 253048 253058 253337 253364) (-215 "DEGRED.spad" 252663 252677 253038 253043) (-214 "DEFINTRF.spad" 250188 250198 252653 252658) (-213 "DEFINTEF.spad" 248684 248700 250178 250183) (-212 "DEFAST.spad" 248052 248060 248674 248679) (-211 "DECIMAL.spad" 245934 245942 246520 246613) (-210 "DDFACT.spad" 243733 243750 245924 245929) (-209 "DBLRESP.spad" 243331 243355 243723 243728) (-208 "DBASE.spad" 241903 241913 243321 243326) (-207 "DATABUF.spad" 241391 241404 241893 241898) (-206 "D03FAFA.spad" 241219 241227 241381 241386) (-205 "D03EEFA.spad" 241039 241047 241209 241214) (-204 "D03AGNT.spad" 240119 240127 241029 241034) (-203 "D02EJFA.spad" 239581 239589 240109 240114) (-202 "D02CJFA.spad" 239059 239067 239571 239576) (-201 "D02BHFA.spad" 238549 238557 239049 239054) (-200 "D02BBFA.spad" 238039 238047 238539 238544) (-199 "D02AGNT.spad" 232843 232851 238029 238034) (-198 "D01WGTS.spad" 231162 231170 232833 232838) (-197 "D01TRNS.spad" 231139 231147 231152 231157) (-196 "D01GBFA.spad" 230661 230669 231129 231134) (-195 "D01FCFA.spad" 230183 230191 230651 230656) (-194 "D01ASFA.spad" 229651 229659 230173 230178) (-193 "D01AQFA.spad" 229097 229105 229641 229646) (-192 "D01APFA.spad" 228521 228529 229087 229092) (-191 "D01ANFA.spad" 228015 228023 228511 228516) (-190 "D01AMFA.spad" 227525 227533 228005 228010) (-189 "D01ALFA.spad" 227065 227073 227515 227520) (-188 "D01AKFA.spad" 226591 226599 227055 227060) (-187 "D01AJFA.spad" 226114 226122 226581 226586) (-186 "D01AGNT.spad" 222173 222181 226104 226109) (-185 "CYCLOTOM.spad" 221679 221687 222163 222168) (-184 "CYCLES.spad" 218511 218519 221669 221674) (-183 "CVMP.spad" 217928 217938 218501 218506) (-182 "CTRIGMNP.spad" 216418 216434 217918 217923) (-181 "CTORCALL.spad" 216006 216014 216408 216413) (-180 "CSTTOOLS.spad" 215249 215262 215996 216001) (-179 "CRFP.spad" 208953 208966 215239 215244) (-178 "CRCEAST.spad" 208673 208681 208943 208948) (-177 "CRAPACK.spad" 207716 207726 208663 208668) (-176 "CPMATCH.spad" 207216 207231 207641 207646) (-175 "CPIMA.spad" 206921 206940 207206 207211) (-174 "COORDSYS.spad" 201814 201824 206911 206916) (-173 "CONTOUR.spad" 201216 201224 201804 201809) (-172 "CONTFRAC.spad" 196828 196838 201118 201211) (-171 "CONDUIT.spad" 196586 196594 196818 196823) (-170 "COMRING.spad" 196260 196268 196524 196581) (-169 "COMPPROP.spad" 195774 195782 196250 196255) (-168 "COMPLPAT.spad" 195541 195556 195764 195769) (-167 "COMPLEX.spad" 189567 189577 189811 190072) (-166 "COMPLEX2.spad" 189280 189292 189557 189562) (-165 "COMPFACT.spad" 188882 188896 189270 189275) (-164 "COMPCAT.spad" 186938 186948 188604 188877) (-163 "COMPCAT.spad" 184700 184712 186368 186373) (-162 "COMMUPC.spad" 184446 184464 184690 184695) (-161 "COMMONOP.spad" 183979 183987 184436 184441) (-160 "COMM.spad" 183788 183796 183969 183974) (-159 "COMMAAST.spad" 183551 183559 183778 183783) (-158 "COMBOPC.spad" 182456 182464 183541 183546) (-157 "COMBINAT.spad" 181201 181211 182446 182451) (-156 "COMBF.spad" 178569 178585 181191 181196) (-155 "COLOR.spad" 177406 177414 178559 178564) (-154 "COLONAST.spad" 177072 177080 177396 177401) (-153 "CMPLXRT.spad" 176781 176798 177062 177067) (-152 "CLLCTAST.spad" 176443 176451 176771 176776) (-151 "CLIP.spad" 172535 172543 176433 176438) (-150 "CLIF.spad" 171174 171190 172491 172530) (-149 "CLAGG.spad" 167649 167659 171154 171169) (-148 "CLAGG.spad" 164005 164017 167512 167517) (-147 "CINTSLPE.spad" 163330 163343 163995 164000) (-146 "CHVAR.spad" 161408 161430 163320 163325) (-145 "CHARZ.spad" 161323 161331 161388 161403) (-144 "CHARPOL.spad" 160831 160841 161313 161318) (-143 "CHARNZ.spad" 160584 160592 160811 160826) (-142 "CHAR.spad" 158452 158460 160574 160579) (-141 "CFCAT.spad" 157768 157776 158442 158447) (-140 "CDEN.spad" 156926 156940 157758 157763) (-139 "CCLASS.spad" 155075 155083 156337 156376) (-138 "CATEGORY.spad" 154854 154862 155065 155070) (-137 "CATAST.spad" 154481 154489 154844 154849) (-136 "CASEAST.spad" 154195 154203 154471 154476) (-135 "CARTEN.spad" 149298 149322 154185 154190) (-134 "CARTEN2.spad" 148684 148711 149288 149293) (-133 "CARD.spad" 145973 145981 148658 148679) (-132 "CAPSLAST.spad" 145747 145755 145963 145968) (-131 "CACHSET.spad" 145369 145377 145737 145742) (-130 "CABMON.spad" 144922 144930 145359 145364) (-129 "BYTE.spad" 144316 144324 144912 144917) (-128 "BYTEARY.spad" 143391 143399 143485 143512) (-127 "BTREE.spad" 142460 142470 142998 143025) (-126 "BTOURN.spad" 141463 141473 142067 142094) (-125 "BTCAT.spad" 140839 140849 141419 141458) (-124 "BTCAT.spad" 140247 140259 140829 140834) (-123 "BTAGG.spad" 139357 139365 140203 140242) (-122 "BTAGG.spad" 138499 138509 139347 139352) (-121 "BSTREE.spad" 137234 137244 138106 138133) (-120 "BRILL.spad" 135429 135440 137224 137229) (-119 "BRAGG.spad" 134343 134353 135409 135424) (-118 "BRAGG.spad" 133231 133243 134299 134304) (-117 "BPADICRT.spad" 131213 131225 131468 131561) (-116 "BPADIC.spad" 130877 130889 131139 131208) (-115 "BOUNDZRO.spad" 130533 130550 130867 130872) (-114 "BOP.spad" 125997 126005 130523 130528) (-113 "BOP1.spad" 123383 123393 125953 125958) (-112 "BOOLEAN.spad" 122707 122715 123373 123378) (-111 "BMODULE.spad" 122419 122431 122675 122702) (-110 "BITS.spad" 121838 121846 122055 122082) (-109 "BINFILE.spad" 121181 121189 121828 121833) (-108 "BINDING.spad" 120600 120608 121171 121176) (-107 "BINARY.spad" 118491 118499 119068 119161) (-106 "BGAGG.spad" 117676 117686 118459 118486) (-105 "BGAGG.spad" 116881 116893 117666 117671) (-104 "BFUNCT.spad" 116445 116453 116861 116876) (-103 "BEZOUT.spad" 115579 115606 116395 116400) (-102 "BBTREE.spad" 112398 112408 115186 115213) (-101 "BASTYPE.spad" 112070 112078 112388 112393) (-100 "BASTYPE.spad" 111740 111750 112060 112065) (-99 "BALFACT.spad" 111180 111192 111730 111735) (-98 "AUTOMOR.spad" 110627 110636 111160 111175) (-97 "ATTREG.spad" 107346 107353 110379 110622) (-96 "ATTRBUT.spad" 103369 103376 107326 107341) (-95 "ATTRAST.spad" 103086 103093 103359 103364) (-94 "ATRIG.spad" 102556 102563 103076 103081) (-93 "ATRIG.spad" 102024 102033 102546 102551) (-92 "ASTCAT.spad" 101928 101935 102014 102019) (-91 "ASTCAT.spad" 101830 101839 101918 101923) (-90 "ASTACK.spad" 101163 101172 101437 101464) (-89 "ASSOCEQ.spad" 99963 99974 101119 101124) (-88 "ASP9.spad" 99044 99057 99953 99958) (-87 "ASP8.spad" 98087 98100 99034 99039) (-86 "ASP80.spad" 97409 97422 98077 98082) (-85 "ASP7.spad" 96569 96582 97399 97404) (-84 "ASP78.spad" 96020 96033 96559 96564) (-83 "ASP77.spad" 95389 95402 96010 96015) (-82 "ASP74.spad" 94481 94494 95379 95384) (-81 "ASP73.spad" 93752 93765 94471 94476) (-80 "ASP6.spad" 92384 92397 93742 93747) (-79 "ASP55.spad" 90893 90906 92374 92379) (-78 "ASP50.spad" 88710 88723 90883 90888) (-77 "ASP4.spad" 88005 88018 88700 88705) (-76 "ASP49.spad" 87004 87017 87995 88000) (-75 "ASP42.spad" 85411 85450 86994 86999) (-74 "ASP41.spad" 83990 84029 85401 85406) (-73 "ASP35.spad" 82978 82991 83980 83985) (-72 "ASP34.spad" 82279 82292 82968 82973) (-71 "ASP33.spad" 81839 81852 82269 82274) (-70 "ASP31.spad" 80979 80992 81829 81834) (-69 "ASP30.spad" 79871 79884 80969 80974) (-68 "ASP29.spad" 79337 79350 79861 79866) (-67 "ASP28.spad" 70610 70623 79327 79332) (-66 "ASP27.spad" 69507 69520 70600 70605) (-65 "ASP24.spad" 68594 68607 69497 69502) (-64 "ASP20.spad" 67810 67823 68584 68589) (-63 "ASP1.spad" 67191 67204 67800 67805) (-62 "ASP19.spad" 61877 61890 67181 67186) (-61 "ASP12.spad" 61291 61304 61867 61872) (-60 "ASP10.spad" 60562 60575 61281 61286) (-59 "ARRAY2.spad" 59922 59931 60169 60196) (-58 "ARRAY1.spad" 58757 58766 59105 59132) (-57 "ARRAY12.spad" 57426 57437 58747 58752) (-56 "ARR2CAT.spad" 53076 53097 57382 57421) (-55 "ARR2CAT.spad" 48758 48781 53066 53071) (-54 "APPRULE.spad" 48002 48024 48748 48753) (-53 "APPLYORE.spad" 47617 47630 47992 47997) (-52 "ANY.spad" 45959 45966 47607 47612) (-51 "ANY1.spad" 45030 45039 45949 45954) (-50 "ANTISYM.spad" 43469 43485 45010 45025) (-49 "ANON.spad" 43166 43173 43459 43464) (-48 "AN.spad" 41467 41474 42982 43075) (-47 "AMR.spad" 39646 39657 41365 41462) (-46 "AMR.spad" 37662 37675 39383 39388) (-45 "ALIST.spad" 35074 35095 35424 35451) (-44 "ALGSC.spad" 34197 34223 34946 34999) (-43 "ALGPKG.spad" 29906 29917 34153 34158) (-42 "ALGMFACT.spad" 29095 29109 29896 29901) (-41 "ALGMANIP.spad" 26515 26530 28892 28897) (-40 "ALGFF.spad" 24830 24857 25047 25203) (-39 "ALGFACT.spad" 23951 23961 24820 24825) (-38 "ALGEBRA.spad" 23682 23691 23907 23946) (-37 "ALGEBRA.spad" 23445 23456 23672 23677) (-36 "ALAGG.spad" 22943 22964 23401 23440) (-35 "AHYP.spad" 22324 22331 22933 22938) (-34 "AGG.spad" 20623 20630 22304 22319) (-33 "AGG.spad" 18896 18905 20579 20584) (-32 "AF.spad" 17321 17336 18831 18836) (-31 "ADDAST.spad" 16999 17006 17311 17316) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2264428 2264433 2264438 2264443) (-2 NIL 2264408 2264413 2264418 2264423) (-1 NIL 2264388 2264393 2264398 2264403) (0 NIL 2264368 2264373 2264378 2264383) (-1253 "ZMOD.spad" 2264177 2264190 2264306 2264363) (-1252 "ZLINDEP.spad" 2263221 2263232 2264167 2264172) (-1251 "ZDSOLVE.spad" 2253070 2253092 2263211 2263216) (-1250 "YSTREAM.spad" 2252563 2252574 2253060 2253065) (-1249 "XRPOLY.spad" 2251783 2251803 2252419 2252488) (-1248 "XPR.spad" 2249512 2249525 2251501 2251600) (-1247 "XPOLYC.spad" 2248829 2248845 2249438 2249507) (-1246 "XPOLY.spad" 2248384 2248395 2248685 2248754) (-1245 "XPBWPOLY.spad" 2246821 2246841 2248164 2248233) (-1244 "XFALG.spad" 2243845 2243861 2246747 2246816) (-1243 "XF.spad" 2242306 2242321 2243747 2243840) (-1242 "XF.spad" 2240747 2240764 2242190 2242195) (-1241 "XEXPPKG.spad" 2239998 2240024 2240737 2240742) (-1240 "XDPOLY.spad" 2239612 2239628 2239854 2239923) (-1239 "XALG.spad" 2239210 2239221 2239568 2239607) (-1238 "WUTSET.spad" 2235049 2235066 2238856 2238883) (-1237 "WP.spad" 2234063 2234107 2234907 2234974) (-1236 "WHILEAST.spad" 2233861 2233870 2234053 2234058) (-1235 "WHEREAST.spad" 2233532 2233541 2233851 2233856) (-1234 "WFFINTBS.spad" 2231095 2231117 2233522 2233527) (-1233 "WEIER.spad" 2229309 2229320 2231085 2231090) (-1232 "VSPACE.spad" 2228982 2228993 2229277 2229304) (-1231 "VSPACE.spad" 2228675 2228688 2228972 2228977) (-1230 "VOID.spad" 2228265 2228274 2228665 2228670) (-1229 "VIEWDEF.spad" 2223462 2223471 2228255 2228260) (-1228 "VIEW3D.spad" 2207297 2207306 2223452 2223457) (-1227 "VIEW2D.spad" 2195034 2195043 2207287 2207292) (-1226 "VIEW.spad" 2192656 2192665 2195024 2195029) (-1225 "VECTOR2.spad" 2191283 2191296 2192646 2192651) (-1224 "VECTOR.spad" 2189958 2189969 2190209 2190236) (-1223 "VECTCAT.spad" 2187846 2187857 2189914 2189953) (-1222 "VECTCAT.spad" 2185554 2185567 2187624 2187629) (-1221 "VARIABLE.spad" 2185334 2185349 2185544 2185549) (-1220 "UTYPE.spad" 2184968 2184977 2185314 2185329) (-1219 "UTSODETL.spad" 2184261 2184285 2184924 2184929) (-1218 "UTSODE.spad" 2182449 2182469 2184251 2184256) (-1217 "UTSCAT.spad" 2179900 2179916 2182347 2182444) (-1216 "UTSCAT.spad" 2176995 2177013 2179444 2179449) (-1215 "UTS2.spad" 2176588 2176623 2176985 2176990) (-1214 "UTS.spad" 2171377 2171405 2175055 2175152) (-1213 "URAGG.spad" 2165999 2166010 2171357 2171372) (-1212 "URAGG.spad" 2160595 2160608 2165955 2165960) (-1211 "UPXSSING.spad" 2158238 2158264 2159676 2159809) (-1210 "UPXSCONS.spad" 2155995 2156015 2156370 2156519) (-1209 "UPXSCCA.spad" 2154453 2154473 2155841 2155990) (-1208 "UPXSCCA.spad" 2153053 2153075 2154443 2154448) (-1207 "UPXSCAT.spad" 2151634 2151650 2152899 2153048) (-1206 "UPXS2.spad" 2151175 2151228 2151624 2151629) (-1205 "UPXS.spad" 2148202 2148230 2149307 2149456) (-1204 "UPSQFREE.spad" 2146615 2146629 2148192 2148197) (-1203 "UPSCAT.spad" 2144208 2144232 2146513 2146610) (-1202 "UPSCAT.spad" 2141507 2141533 2143814 2143819) (-1201 "UPOLYC2.spad" 2140976 2140995 2141497 2141502) (-1200 "UPOLYC.spad" 2135954 2135965 2140818 2140971) (-1199 "UPOLYC.spad" 2130824 2130837 2135690 2135695) (-1198 "UPMP.spad" 2129714 2129727 2130814 2130819) (-1197 "UPDIVP.spad" 2129277 2129291 2129704 2129709) (-1196 "UPDECOMP.spad" 2127514 2127528 2129267 2129272) (-1195 "UPCDEN.spad" 2126721 2126737 2127504 2127509) (-1194 "UP2.spad" 2126083 2126104 2126711 2126716) (-1193 "UP.spad" 2123125 2123140 2123633 2123786) (-1192 "UNISEG2.spad" 2122618 2122631 2123081 2123086) (-1191 "UNISEG.spad" 2121971 2121982 2122537 2122542) (-1190 "UNIFACT.spad" 2121072 2121084 2121961 2121966) (-1189 "ULSCONS.spad" 2115111 2115131 2115483 2115632) (-1188 "ULSCCAT.spad" 2112708 2112728 2114931 2115106) (-1187 "ULSCCAT.spad" 2110439 2110461 2112664 2112669) (-1186 "ULSCAT.spad" 2108655 2108671 2110285 2110434) (-1185 "ULS2.spad" 2108167 2108220 2108645 2108650) (-1184 "ULS.spad" 2098721 2098749 2099814 2100243) (-1183 "UFD.spad" 2097786 2097795 2098647 2098716) (-1182 "UFD.spad" 2096913 2096924 2097776 2097781) (-1181 "UDVO.spad" 2095760 2095769 2096903 2096908) (-1180 "UDPO.spad" 2093187 2093198 2095716 2095721) (-1179 "TYPEAST.spad" 2093106 2093115 2093177 2093182) (-1178 "TYPE.spad" 2093028 2093037 2093086 2093101) (-1177 "TWOFACT.spad" 2091678 2091693 2093018 2093023) (-1176 "TUPLE.spad" 2091064 2091075 2091577 2091582) (-1175 "TUBETOOL.spad" 2087901 2087910 2091054 2091059) (-1174 "TUBE.spad" 2086542 2086559 2087891 2087896) (-1173 "TSETCAT.spad" 2073657 2073674 2086498 2086537) (-1172 "TSETCAT.spad" 2060770 2060789 2073613 2073618) (-1171 "TS.spad" 2059359 2059375 2060335 2060432) (-1170 "TRMANIP.spad" 2053725 2053742 2059065 2059070) (-1169 "TRIMAT.spad" 2052684 2052709 2053715 2053720) (-1168 "TRIGMNIP.spad" 2051201 2051218 2052674 2052679) (-1167 "TRIGCAT.spad" 2050713 2050722 2051191 2051196) (-1166 "TRIGCAT.spad" 2050223 2050234 2050703 2050708) (-1165 "TREE.spad" 2048794 2048805 2049830 2049857) (-1164 "TRANFUN.spad" 2048625 2048634 2048784 2048789) (-1163 "TRANFUN.spad" 2048454 2048465 2048615 2048620) (-1162 "TOPSP.spad" 2048128 2048137 2048444 2048449) (-1161 "TOOLSIGN.spad" 2047791 2047802 2048118 2048123) (-1160 "TEXTFILE.spad" 2046348 2046357 2047781 2047786) (-1159 "TEX1.spad" 2045904 2045915 2046338 2046343) (-1158 "TEX.spad" 2042921 2042930 2045894 2045899) (-1157 "TEMUTL.spad" 2042476 2042485 2042911 2042916) (-1156 "TBCMPPK.spad" 2040569 2040592 2042466 2042471) (-1155 "TBAGG.spad" 2039593 2039616 2040537 2040564) (-1154 "TBAGG.spad" 2038637 2038662 2039583 2039588) (-1153 "TANEXP.spad" 2038013 2038024 2038627 2038632) (-1152 "TABLEAU.spad" 2037494 2037505 2038003 2038008) (-1151 "TABLE.spad" 2035905 2035928 2036175 2036202) (-1150 "TABLBUMP.spad" 2032688 2032699 2035895 2035900) (-1149 "SYSTEM.spad" 2031962 2031971 2032678 2032683) (-1148 "SYSSOLP.spad" 2029435 2029446 2031952 2031957) (-1147 "SYNTAX.spad" 2025627 2025636 2029425 2029430) (-1146 "SYMTAB.spad" 2023683 2023692 2025617 2025622) (-1145 "SYMS.spad" 2019674 2019683 2023673 2023678) (-1144 "SYMPOLY.spad" 2018681 2018692 2018763 2018890) (-1143 "SYMFUNC.spad" 2018156 2018167 2018671 2018676) (-1142 "SYMBOL.spad" 2015492 2015501 2018146 2018151) (-1141 "SWITCH.spad" 2012249 2012258 2015482 2015487) (-1140 "SUTS.spad" 2009148 2009176 2010716 2010813) (-1139 "SUPXS.spad" 2006162 2006190 2007280 2007429) (-1138 "SUPFRACF.spad" 2005267 2005285 2006152 2006157) (-1137 "SUP2.spad" 2004657 2004670 2005257 2005262) (-1136 "SUP.spad" 2001426 2001437 2002207 2002360) (-1135 "SUMRF.spad" 2000392 2000403 2001416 2001421) (-1134 "SUMFS.spad" 2000025 2000042 2000382 2000387) (-1133 "SULS.spad" 1990566 1990594 1991672 1992101) (-1132 "SUCHTAST.spad" 1990335 1990344 1990556 1990561) (-1131 "SUCH.spad" 1990015 1990030 1990325 1990330) (-1130 "SUBSPACE.spad" 1982022 1982037 1990005 1990010) (-1129 "SUBRESP.spad" 1981182 1981196 1981978 1981983) (-1128 "STTFNC.spad" 1977650 1977666 1981172 1981177) (-1127 "STTF.spad" 1973749 1973765 1977640 1977645) (-1126 "STTAYLOR.spad" 1966147 1966158 1973630 1973635) (-1125 "STRTBL.spad" 1964652 1964669 1964801 1964828) (-1124 "STRING.spad" 1964061 1964070 1964075 1964102) (-1123 "STRICAT.spad" 1963837 1963846 1964017 1964056) (-1122 "STREAM3.spad" 1963382 1963397 1963827 1963832) (-1121 "STREAM2.spad" 1962450 1962463 1963372 1963377) (-1120 "STREAM1.spad" 1962154 1962165 1962440 1962445) (-1119 "STREAM.spad" 1958922 1958933 1961679 1961694) (-1118 "STINPROD.spad" 1957828 1957844 1958912 1958917) (-1117 "STEP.spad" 1957029 1957038 1957818 1957823) (-1116 "STBL.spad" 1955555 1955583 1955722 1955737) (-1115 "STAGG.spad" 1954620 1954631 1955535 1955550) (-1114 "STAGG.spad" 1953693 1953706 1954610 1954615) (-1113 "STACK.spad" 1953044 1953055 1953300 1953327) (-1112 "SREGSET.spad" 1950748 1950765 1952690 1952717) (-1111 "SRDCMPK.spad" 1949293 1949313 1950738 1950743) (-1110 "SRAGG.spad" 1944378 1944387 1949249 1949288) (-1109 "SRAGG.spad" 1939495 1939506 1944368 1944373) (-1108 "SQMATRIX.spad" 1937111 1937129 1938027 1938114) (-1107 "SPLTREE.spad" 1931663 1931676 1936547 1936574) (-1106 "SPLNODE.spad" 1928251 1928264 1931653 1931658) (-1105 "SPFCAT.spad" 1927028 1927037 1928241 1928246) (-1104 "SPECOUT.spad" 1925578 1925587 1927018 1927023) (-1103 "SPADXPT.spad" 1917707 1917716 1925558 1925573) (-1102 "spad-parser.spad" 1917172 1917181 1917697 1917702) (-1101 "SPADAST.spad" 1916873 1916882 1917162 1917167) (-1100 "SPACEC.spad" 1900886 1900897 1916863 1916868) (-1099 "SPACE3.spad" 1900662 1900673 1900876 1900881) (-1098 "SORTPAK.spad" 1900207 1900220 1900618 1900623) (-1097 "SOLVETRA.spad" 1897964 1897975 1900197 1900202) (-1096 "SOLVESER.spad" 1896484 1896495 1897954 1897959) (-1095 "SOLVERAD.spad" 1892494 1892505 1896474 1896479) (-1094 "SOLVEFOR.spad" 1890914 1890932 1892484 1892489) (-1093 "SNTSCAT.spad" 1890502 1890519 1890870 1890909) (-1092 "SMTS.spad" 1888762 1888788 1890067 1890164) (-1091 "SMP.spad" 1886201 1886221 1886591 1886718) (-1090 "SMITH.spad" 1885044 1885069 1886191 1886196) (-1089 "SMATCAT.spad" 1883142 1883172 1884976 1885039) (-1088 "SMATCAT.spad" 1881184 1881216 1883020 1883025) (-1087 "SKAGG.spad" 1880133 1880144 1881140 1881179) (-1086 "SINT.spad" 1878441 1878450 1879999 1880128) (-1085 "SIMPAN.spad" 1878169 1878178 1878431 1878436) (-1084 "SIGNRF.spad" 1877284 1877295 1878159 1878164) (-1083 "SIGNEF.spad" 1876560 1876577 1877274 1877279) (-1082 "SIGAST.spad" 1875941 1875950 1876550 1876555) (-1081 "SIG.spad" 1875269 1875278 1875931 1875936) (-1080 "SHP.spad" 1873187 1873202 1875225 1875230) (-1079 "SHDP.spad" 1864172 1864199 1864681 1864812) (-1078 "SGROUP.spad" 1863780 1863789 1864162 1864167) (-1077 "SGROUP.spad" 1863386 1863397 1863770 1863775) (-1076 "SGCF.spad" 1856267 1856276 1863376 1863381) (-1075 "SFRTCAT.spad" 1855183 1855200 1856223 1856262) (-1074 "SFRGCD.spad" 1854246 1854266 1855173 1855178) (-1073 "SFQCMPK.spad" 1848883 1848903 1854236 1854241) (-1072 "SFORT.spad" 1848318 1848332 1848873 1848878) (-1071 "SEXOF.spad" 1848161 1848201 1848308 1848313) (-1070 "SEXCAT.spad" 1845265 1845305 1848151 1848156) (-1069 "SEX.spad" 1845157 1845166 1845255 1845260) (-1068 "SETMN.spad" 1843593 1843610 1845147 1845152) (-1067 "SETCAT.spad" 1843078 1843087 1843583 1843588) (-1066 "SETCAT.spad" 1842561 1842572 1843068 1843073) (-1065 "SETAGG.spad" 1839070 1839081 1842529 1842556) (-1064 "SETAGG.spad" 1835599 1835612 1839060 1839065) (-1063 "SET.spad" 1833899 1833910 1835020 1835059) (-1062 "SEQAST.spad" 1833602 1833611 1833889 1833894) (-1061 "SEGXCAT.spad" 1832714 1832727 1833582 1833597) (-1060 "SEGCAT.spad" 1831533 1831544 1832694 1832709) (-1059 "SEGBIND2.spad" 1831229 1831242 1831523 1831528) (-1058 "SEGBIND.spad" 1830301 1830312 1831184 1831189) (-1057 "SEGAST.spad" 1830015 1830024 1830291 1830296) (-1056 "SEG2.spad" 1829440 1829453 1829971 1829976) (-1055 "SEG.spad" 1829253 1829264 1829359 1829364) (-1054 "SDVAR.spad" 1828529 1828540 1829243 1829248) (-1053 "SDPOL.spad" 1825919 1825930 1826210 1826337) (-1052 "SCPKG.spad" 1823998 1824009 1825909 1825914) (-1051 "SCOPE.spad" 1823143 1823152 1823988 1823993) (-1050 "SCACHE.spad" 1821825 1821836 1823133 1823138) (-1049 "SASTCAT.spad" 1821734 1821743 1821815 1821820) (-1048 "SAOS.spad" 1821606 1821615 1821724 1821729) (-1047 "SAERFFC.spad" 1821319 1821339 1821596 1821601) (-1046 "SAEFACT.spad" 1821020 1821040 1821309 1821314) (-1045 "SAE.spad" 1819195 1819211 1819806 1819941) (-1044 "RURPK.spad" 1816836 1816852 1819185 1819190) (-1043 "RULESET.spad" 1816277 1816301 1816826 1816831) (-1042 "RULECOLD.spad" 1816129 1816142 1816267 1816272) (-1041 "RULE.spad" 1814333 1814357 1816119 1816124) (-1040 "RSTRCAST.spad" 1814050 1814059 1814323 1814328) (-1039 "RSETGCD.spad" 1810428 1810448 1814040 1814045) (-1038 "RSETCAT.spad" 1800200 1800217 1810384 1810423) (-1037 "RSETCAT.spad" 1790004 1790023 1800190 1800195) (-1036 "RSDCMPK.spad" 1788456 1788476 1789994 1789999) (-1035 "RRCC.spad" 1786840 1786870 1788446 1788451) (-1034 "RRCC.spad" 1785222 1785254 1786830 1786835) (-1033 "RPTAST.spad" 1784924 1784933 1785212 1785217) (-1032 "RPOLCAT.spad" 1764284 1764299 1784792 1784919) (-1031 "RPOLCAT.spad" 1743358 1743375 1763868 1763873) (-1030 "ROUTINE.spad" 1739221 1739230 1742005 1742032) (-1029 "ROMAN.spad" 1738453 1738462 1739087 1739216) (-1028 "ROIRC.spad" 1737533 1737565 1738443 1738448) (-1027 "RNS.spad" 1736436 1736445 1737435 1737528) (-1026 "RNS.spad" 1735425 1735436 1736426 1736431) (-1025 "RNG.spad" 1735160 1735169 1735415 1735420) (-1024 "RMODULE.spad" 1734798 1734809 1735150 1735155) (-1023 "RMCAT2.spad" 1734206 1734263 1734788 1734793) (-1022 "RMATRIX.spad" 1732885 1732904 1733373 1733412) (-1021 "RMATCAT.spad" 1728406 1728437 1732829 1732880) (-1020 "RMATCAT.spad" 1723829 1723862 1728254 1728259) (-1019 "RINTERP.spad" 1723717 1723737 1723819 1723824) (-1018 "RING.spad" 1723074 1723083 1723697 1723712) (-1017 "RING.spad" 1722439 1722450 1723064 1723069) (-1016 "RIDIST.spad" 1721823 1721832 1722429 1722434) (-1015 "RGCHAIN.spad" 1720402 1720418 1721308 1721335) (-1014 "RFFACTOR.spad" 1719864 1719875 1720392 1720397) (-1013 "RFFACT.spad" 1719599 1719611 1719854 1719859) (-1012 "RFDIST.spad" 1718587 1718596 1719589 1719594) (-1011 "RF.spad" 1716201 1716212 1718577 1718582) (-1010 "RETSOL.spad" 1715618 1715631 1716191 1716196) (-1009 "RETRACT.spad" 1714967 1714978 1715608 1715613) (-1008 "RETRACT.spad" 1714314 1714327 1714957 1714962) (-1007 "RETAST.spad" 1714126 1714135 1714304 1714309) (-1006 "RESULT.spad" 1712186 1712195 1712773 1712800) (-1005 "RESRING.spad" 1711533 1711580 1712124 1712181) (-1004 "RESLATC.spad" 1710857 1710868 1711523 1711528) (-1003 "REPSQ.spad" 1710586 1710597 1710847 1710852) (-1002 "REPDB.spad" 1710291 1710302 1710576 1710581) (-1001 "REP2.spad" 1699863 1699874 1710133 1710138) (-1000 "REP1.spad" 1693853 1693864 1699813 1699818) (-999 "REP.spad" 1691406 1691414 1693843 1693848) (-998 "REGSET.spad" 1689204 1689220 1691052 1691079) (-997 "REF.spad" 1688534 1688544 1689159 1689164) (-996 "REDORDER.spad" 1687711 1687727 1688524 1688529) (-995 "RECLOS.spad" 1686495 1686514 1687198 1687291) (-994 "REALSOLV.spad" 1685628 1685636 1686485 1686490) (-993 "REAL0Q.spad" 1682911 1682925 1685618 1685623) (-992 "REAL0.spad" 1679740 1679754 1682901 1682906) (-991 "REAL.spad" 1679613 1679621 1679730 1679735) (-990 "RDUCEAST.spad" 1679335 1679343 1679603 1679608) (-989 "RDIV.spad" 1678987 1679011 1679325 1679330) (-988 "RDIST.spad" 1678551 1678561 1678977 1678982) (-987 "RDETRS.spad" 1677348 1677365 1678541 1678546) (-986 "RDETR.spad" 1675456 1675473 1677338 1677343) (-985 "RDEEFS.spad" 1674530 1674546 1675446 1675451) (-984 "RDEEF.spad" 1673527 1673543 1674520 1674525) (-983 "RCFIELD.spad" 1670714 1670722 1673429 1673522) (-982 "RCFIELD.spad" 1667987 1667997 1670704 1670709) (-981 "RCAGG.spad" 1665890 1665900 1667967 1667982) (-980 "RCAGG.spad" 1663730 1663742 1665809 1665814) (-979 "RATRET.spad" 1663091 1663101 1663720 1663725) (-978 "RATFACT.spad" 1662784 1662795 1663081 1663086) (-977 "RANDSRC.spad" 1662104 1662112 1662774 1662779) (-976 "RADUTIL.spad" 1661859 1661867 1662094 1662099) (-975 "RADIX.spad" 1658650 1658663 1660327 1660420) (-974 "RADFF.spad" 1657064 1657100 1657182 1657338) (-973 "RADCAT.spad" 1656658 1656666 1657054 1657059) (-972 "RADCAT.spad" 1656250 1656260 1656648 1656653) (-971 "QUEUE.spad" 1655593 1655603 1655857 1655884) (-970 "QUATCT2.spad" 1655212 1655230 1655583 1655588) (-969 "QUATCAT.spad" 1653377 1653387 1655142 1655207) (-968 "QUATCAT.spad" 1651293 1651305 1653060 1653065) (-967 "QUAT.spad" 1649875 1649885 1650217 1650282) (-966 "QUAGG.spad" 1648689 1648699 1649831 1649870) (-965 "QQUTAST.spad" 1648458 1648466 1648679 1648684) (-964 "QFORM.spad" 1647921 1647935 1648448 1648453) (-963 "QFCAT2.spad" 1647612 1647628 1647911 1647916) (-962 "QFCAT.spad" 1646303 1646313 1647502 1647607) (-961 "QFCAT.spad" 1644598 1644610 1645799 1645804) (-960 "QEQUAT.spad" 1644155 1644163 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. -541) 123660) ((-1138 . -47) 123637) ((-348 . -1018) T) ((-345 . -1018) T) ((-474 . -23) 123507) ((-337 . -1018) T) ((-257 . -1018) T) ((-241 . -1018) T) ((-1091 . -47) 123479) ((-117 . -1025) T) ((-1005 . -624) 123453) ((-929 . -34) T) ((-348 . -227) 123432) ((-348 . -237) T) ((-345 . -227) 123411) ((-345 . -237) T) ((-241 . -319) 123368) ((-337 . -227) 123347) ((-337 . -237) T) ((-257 . -319) 123319) ((-257 . -227) 123298) ((-1122 . -149) 123282) ((-244 . -871) 123214) ((-243 . -871) 123146) ((-1048 . -823) T) ((-1192 . -1179) T) ((-407 . -1078) T) ((-1022 . -23) T) ((-881 . -1018) T) ((-315 . -624) 123128) ((-995 . -821) T) ((-1173 . -973) 123094) ((-1139 . -891) 123073) ((-1133 . -891) 123052) ((-881 . -237) T) ((-793 . -356) 123031) ((-378 . -23) T) ((-127 . -1066) 123009) ((-121 . -1066) 122987) ((-881 . -227) T) ((-1133 . -796) NIL) ((-372 . -624) 122952) ((-841 . -694) 122939) ((-1015 . -149) 122904) ((-40 . -170) T) ((-670 . -404) 122886) ((-689 . -302) 122873) ((-810 . 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-624) 116183) ((-347 . -694) 116128) ((-167 . -871) 116087) ((-675 . -283) T) ((-670 . -170) T) ((-688 . -111) 116043) ((-1253 . -1025) T) ((-1198 . -370) 116027) ((-411 . -1183) 116005) ((-1084 . -593) 115987) ((-306 . -821) NIL) ((-411 . -541) T) ((-219 . -300) T) ((-1188 . -767) 115940) ((-1188 . -770) 115893) ((-1209 . -703) T) ((-1188 . -703) T) ((-48 . -694) 115858) ((-219 . -993) T) ((-344 . -1232) 115835) ((-1211 . -404) 115801) ((-695 . -703) T) ((-1198 . -871) 115744) ((-112 . -593) 115726) ((-112 . -594) 115708) ((-695 . -465) T) ((-474 . -21) 115618) ((-127 . -481) 115602) ((-121 . -481) 115586) ((-474 . -25) 115437) ((-601 . -283) T) ((-567 . -1024) 115412) ((-430 . -1066) T) ((-1029 . -300) T) ((-117 . -283) T) ((-1070 . -101) T) ((-974 . -101) T) ((-567 . -111) 115380) ((-1108 . -302) 115318) ((-1173 . -1018) T) ((-1029 . -993) T) ((-65 . -1179) T) ((-1022 . -25) T) ((-1022 . -21) T) ((-688 . -1018) T) ((-378 . -21) T) ((-378 . -25) T) ((-670 . -505) NIL) ((-995 . -170) T) ((-688 . -237) T) ((-1029 . -534) T) ((-497 . -101) T) ((-493 . -101) T) ((-347 . -170) T) ((-336 . -593) 115300) ((-387 . -593) 115282) ((-466 . -703) T) ((-1086 . -821) T) ((-863 . -1009) 115250) ((-107 . -823) T) ((-634 . -1024) 115234) ((-479 . -130) T) ((-1211 . -1025) T) ((-211 . -130) T) ((-1122 . -101) 115212) ((-98 . -1066) T) ((-239 . -642) 115196) ((-239 . -627) 115180) ((-634 . -111) 115159) ((-309 . -404) 115143) ((-239 . -366) 115127) ((-1125 . -229) 115074) ((-970 . -225) 115058) ((-73 . -1179) T) ((-48 . -170) T) ((-677 . -380) T) ((-677 . -141) T) ((-1248 . -101) T) ((-1053 . -1024) 114901) ((-257 . -880) 114880) ((-241 . -880) 114859) ((-758 . -1024) 114682) ((-756 . -1024) 114525) ((-588 . -1179) T) ((-1130 . -593) 114507) ((-1053 . -111) 114336) ((-1015 . -101) T) ((-467 . -1179) T) ((-453 . -1024) 114307) ((-446 . -1024) 114150) ((-640 . -624) 114134) ((-842 . -300) T) ((-758 . -111) 113943) ((-756 . -111) 113772) ((-348 . -624) 113724) ((-345 . -624) 113676) 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-283) T) ((-263 . -812) T) ((-262 . -812) T) ((-261 . -812) T) ((-187 . -763) T) ((-592 . -823) T) ((-630 . -404) 111327) ((-110 . -823) T) ((-629 . -21) T) ((-629 . -25) T) ((-1248 . -38) 111297) ((-117 . -279) 111248) ((-1225 . -19) 111232) ((-1225 . -584) 111209) ((-1238 . -1066) T) ((-1043 . -1066) T) ((-958 . -1066) T) ((-934 . -130) T) ((-714 . -1066) T) ((-712 . -130) T) ((-692 . -130) T) ((-502 . -769) T) ((-400 . -1117) 111187) ((-445 . -130) T) ((-502 . -770) T) ((-217 . -1018) T) ((-287 . -101) 110969) ((-139 . -1066) T) ((-675 . -973) T) ((-90 . -1179) T) ((-127 . -593) 110901) ((-121 . -593) 110833) ((-1253 . -170) T) ((-1139 . -356) 110812) ((-1133 . -356) 110791) ((-309 . -1066) T) ((-411 . -130) T) ((-306 . -1066) T) ((-400 . -38) 110743) ((-1099 . -101) T) ((-1211 . -694) 110635) ((-630 . -1025) T) ((-1101 . -1220) T) ((-312 . -143) 110614) ((-312 . -145) 110593) ((-135 . -1066) T) ((-114 . -1066) T) ((-831 . -101) T) ((-562 . -593) 110575) ((-549 . -594) 110474) 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108805) ((-1046 . -145) 108784) ((-1046 . -143) 108735) ((-975 . -356) T) ((-312 . -1167) 108701) ((-372 . -300) T) ((-312 . -1164) 108667) ((-309 . -170) 108646) ((-306 . -170) T) ((-974 . -225) 108623) ((-885 . -356) T) ((-563 . -1244) 108610) ((-509 . -1244) 108587) ((-352 . -145) 108566) ((-352 . -143) 108517) ((-346 . -145) 108496) ((-346 . -143) 108447) ((-588 . -1155) 108423) ((-338 . -145) 108402) ((-338 . -143) 108353) ((-312 . -35) 108319) ((-467 . -1155) 108298) ((0 . |EnumerationCategory|) T) ((-312 . -94) 108264) ((-372 . -993) T) ((-107 . -145) T) ((-107 . -143) NIL) ((-45 . -229) 108214) ((-630 . -1066) T) ((-588 . -106) 108161) ((-477 . -130) T) ((-467 . -106) 108111) ((-234 . -1078) 108021) ((-843 . -370) 108005) ((-843 . -331) 107989) ((-234 . -23) 107859) ((-1029 . -891) T) ((-1029 . -796) T) ((-563 . -361) T) ((-509 . -361) T) ((-344 . -1117) T) ((-320 . -34) T) ((-44 . -410) 107843) ((-844 . -1179) T) ((-383 . -721) 107827) ((-1238 . -505) 107760) ((-708 . -130) T) 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. -771) T) ((-675 . -768) T) ((-974 . -404) 100747) ((-347 . -111) 100676) ((-372 . -891) T) ((-400 . -821) 100655) ((-689 . -283) 100566) ((-217 . -703) T) ((-1217 . -484) 100532) ((-1210 . -484) 100498) ((-1189 . -484) 100464) ((-309 . -973) 100443) ((-216 . -1066) 100421) ((-312 . -944) 100383) ((-104 . -101) T) ((-48 . -1024) 100348) ((-1249 . -101) T) ((-374 . -101) T) ((-48 . -111) 100304) ((-975 . -617) 100286) ((-1211 . -593) 100268) ((-521 . -101) T) ((-491 . -101) T) ((-1099 . -1100) 100252) ((-150 . -1232) 100236) ((-239 . -1179) T) ((-1178 . -101) T) ((-1138 . -1183) 100215) ((-1091 . -1183) 100194) ((-234 . -21) 100104) ((-234 . -25) 99955) ((-127 . -119) 99939) ((-121 . -119) 99923) ((-44 . -721) 99907) ((-1138 . -541) 99818) ((-1091 . -541) 99749) ((-1006 . -279) 99724) ((-1132 . -1049) T) ((-965 . -1049) T) ((-792 . -130) T) ((-117 . -771) NIL) ((-117 . -768) NIL) ((-348 . -300) T) ((-345 . -300) T) ((-337 . -300) T) ((-1060 . -1179) T) ((-244 . -1078) 99634) ((-243 . 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. -823) T) ((-712 . -145) 95322) ((-712 . -143) 95301) ((-942 . -823) T) ((-466 . -891) 95280) ((-309 . -1024) 95190) ((-306 . -1024) 95119) ((-970 . -279) 95077) ((-400 . -694) 95029) ((-128 . -823) T) ((-677 . -821) T) ((-1211 . -1018) T) ((-309 . -111) 94925) ((-306 . -111) 94838) ((-935 . -101) T) ((-791 . -101) 94628) ((-689 . -594) NIL) ((-689 . -593) 94610) ((-634 . -1009) 94506) ((-1211 . -319) 94450) ((-1006 . -281) 94425) ((-562 . -703) T) ((-549 . -770) T) ((-167 . -356) 94376) ((-549 . -767) T) ((-549 . -703) T) ((-486 . -703) T) ((-1112 . -481) 94360) ((-1053 . -857) NIL) ((-842 . -1078) T) ((-117 . -880) NIL) ((-1247 . -1246) 94336) ((-1245 . -1246) 94315) ((-758 . -857) NIL) ((-756 . -857) 94174) ((-1240 . -25) T) ((-1240 . -21) T) ((-1176 . -101) 94152) ((-1072 . -388) T) ((-601 . -624) 94139) ((-446 . -857) NIL) ((-651 . -101) 94117) ((-1053 . -1009) 93944) ((-842 . -23) T) ((-758 . -1009) 93803) ((-756 . -1009) 93660) ((-117 . -624) 93605) ((-446 . -1009) 93481) 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. -1117) 88823) ((-1139 . -1164) 88789) ((-1139 . -1167) 88755) ((-1005 . -23) T) ((-1139 . -94) 88721) ((-556 . -484) T) ((-1139 . -35) 88687) ((-1133 . -1164) 88653) ((-1133 . -1167) 88619) ((-1133 . -94) 88585) ((-354 . -1078) T) ((-352 . -1117) 88564) ((-346 . -1117) 88543) ((-338 . -1117) 88522) ((-1133 . -35) 88488) ((-1092 . -35) 88454) ((-1092 . -94) 88420) ((-107 . -1117) T) ((-1092 . -1167) 88386) ((-809 . -1025) 88365) ((-623 . -302) 88303) ((-610 . -302) 88154) ((-1092 . -1164) 88120) ((-689 . -1018) T) ((-1029 . -617) 88102) ((-1046 . -38) 87970) ((-923 . -617) 87918) ((-975 . -145) T) ((-975 . -143) NIL) ((-372 . -1078) T) ((-317 . -25) T) ((-315 . -23) T) ((-914 . -823) 87897) ((-689 . -319) 87874) ((-473 . -617) 87822) ((-40 . -1009) 87710) ((-677 . -694) 87697) ((-689 . -227) T) ((-332 . -1066) T) ((-172 . -1066) T) ((-324 . -823) T) ((-411 . -444) 87647) ((-372 . -23) T) ((-352 . -38) 87612) ((-346 . -38) 87577) ((-338 . -38) 87542) ((-79 . -433) T) ((-79 . -388) T) 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. -593) 38630) ((-411 . -594) 38538) ((-621 . -1115) 38522) ((-110 . -627) 38504) ((-172 . -300) T) ((-126 . -302) 38442) ((-110 . -366) 38424) ((-391 . -1179) T) ((-309 . -130) 38295) ((-306 . -130) T) ((-68 . -388) T) ((-110 . -123) T) ((-511 . -481) 38279) ((-630 . -1078) T) ((-574 . -19) 38261) ((-60 . -433) T) ((-60 . -388) T) ((-800 . -1066) T) ((-574 . -584) 38236) ((-469 . -1009) 38196) ((-629 . -1018) T) ((-630 . -23) T) ((-1240 . -1066) T) ((-31 . -101) T) ((-792 . -694) 38045) ((-117 . -823) NIL) ((-1138 . -404) 38029) ((-1091 . -404) 38013) ((-827 . -404) 37997) ((-844 . -101) 37948) ((-1209 . -101) T) ((-1189 . -505) 37717) ((-516 . -92) T) ((-1165 . -302) 37655) ((-305 . -593) 37637) ((-1188 . -101) T) ((-1068 . -1066) T) ((-1140 . -279) 37622) ((-1139 . -279) 37607) ((-282 . -703) T) ((-107 . -880) NIL) ((-665 . -593) 37539) ((-665 . -594) 37500) ((-1046 . -624) 37410) ((-581 . -593) 37392) ((-535 . -594) NIL) ((-535 . -593) 37374) ((-1133 . -279) 37222) ((-479 . -1024) 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-617) 30743) ((-827 . -694) 30713) ((-646 . -1179) T) ((-1 . -101) T) ((-234 . -593) 30444) ((-1081 . -1066) T) ((-1198 . -404) 30428) ((-1152 . -302) 30232) ((-934 . -1018) T) ((-712 . -1018) T) ((-692 . -1018) T) ((-621 . -1066) 30182) ((-1022 . -624) 30166) ((-828 . -404) 30150) ((-502 . -101) T) ((-498 . -101) T) ((-241 . -302) 30137) ((-257 . -302) 30124) ((-934 . -319) 30103) ((-378 . -624) 30087) ((-471 . -302) 29891) ((-244 . -505) 29824) ((-646 . -1009) 29720) ((-243 . -505) 29653) ((-1107 . -302) 29579) ((-795 . -1066) T) ((-775 . -1024) 29563) ((-1217 . -279) 29548) ((-1210 . -279) 29533) ((-1189 . -279) 29381) ((-379 . -1066) T) ((-317 . -1066) T) ((-411 . -1018) T) ((-167 . -1025) T) ((-58 . -302) 29319) ((-775 . -111) 29298) ((-576 . -279) 29283) ((-510 . -302) 29221) ((-507 . -302) 29159) ((-488 . -302) 29097) ((-487 . -302) 29035) ((-411 . -227) 29014) ((-474 . -34) T) ((-975 . -594) 28944) ((-219 . -1066) T) ((-975 . -593) 28926) ((-942 . -593) 28908) ((-942 . -594) 28883) ((-885 . -593) 28865) ((-675 . -145) T) ((-677 . -891) T) ((-677 . -796) T) ((-420 . -593) 28847) ((-1086 . -21) T) ((-128 . -594) NIL) ((-128 . -593) 28829) ((-1086 . -25) T) ((-646 . -370) 28813) ((-116 . -891) T) ((-843 . -225) 28797) ((-77 . -1179) T) ((-126 . -125) 28781) ((-1022 . -34) T) ((-1247 . -1009) 28755) ((-1245 . -1009) 28712) ((-1198 . -1025) T) ((-828 . -1025) T) ((-474 . -767) 28691) ((-348 . -1117) 28670) ((-345 . -1117) 28649) ((-337 . -1117) 28628) ((-474 . -770) 28579) ((-474 . -769) 28558) ((-221 . -34) T) ((-474 . -703) 28468) ((-59 . -481) 28452) ((-556 . -1025) T) ((-1138 . -170) 28343) ((-1091 . -170) 28254) ((-1029 . -1066) T) ((-1053 . -920) 28199) ((-923 . -1066) T) ((-793 . -624) 28150) ((-758 . -920) 28119) ((-690 . -1066) T) ((-756 . -920) 28086) ((-507 . -275) 28070) ((-646 . -871) 28029) ((-473 . -1066) T) ((-446 . -920) 27996) ((-78 . -1179) T) ((-348 . -38) 27961) ((-345 . -38) 27926) ((-337 . -38) 27891) ((-257 . -38) 27740) ((-241 . -38) 27589) ((-881 . -1117) T) ((-601 . -145) 27568) ((-601 . -143) 27547) ((-515 . -593) 27513) ((-117 . -145) T) ((-117 . -143) NIL) ((-407 . -703) T) ((-775 . -1018) T) ((-336 . -444) T) ((-1217 . -973) 27479) ((-1210 . -973) 27445) ((-1189 . -973) 27411) ((-881 . -38) 27376) ((-219 . -694) 27341) ((-312 . -47) 27311) ((-40 . -402) 27283) ((-138 . -593) 27265) ((-970 . -130) T) ((-791 . -1179) T) ((-172 . -891) T) ((-336 . -395) T) ((-511 . -281) 27242) ((-791 . -1009) 27069) ((-45 . -34) T) ((-657 . -101) T) ((-652 . -101) T) ((-638 . -101) T) ((-630 . -21) T) ((-630 . -25) T) ((-1188 . -225) 27039) ((-1068 . -481) 27023) ((-470 . -101) T) ((-651 . -1179) T) ((-239 . -101) 26973) ((-137 . -101) T) ((-136 . -101) T) ((-132 . -101) T) ((-842 . -1066) T) ((-1144 . -624) 26898) ((-1029 . -694) 26885) ((-708 . -1024) 26728) ((-1138 . -505) 26675) ((-923 . -694) 26524) ((-1091 . -505) 26476) ((-1236 . -1066) T) ((-1235 . -1066) T) ((-473 . -694) 26325) ((-66 . -593) 26307) ((-708 . -111) 26136) ((-914 . -481) 26120) ((-1237 . -624) 26080) ((-793 . -703) T) ((-1140 . -1024) 25963) ((-1139 . -1024) 25798) ((-1133 . -1024) 25588) ((-1092 . -1024) 25471) ((-974 . -1183) T) ((-1060 . -101) 25449) ((-791 . -370) 25418) ((-974 . -541) T) ((-1140 . -111) 25287) ((-1139 . -111) 25108) ((-1133 . -111) 24877) ((-1092 . -111) 24746) ((-1071 . -1069) 24710) ((-372 . -821) T) ((-1217 . -593) 24692) ((-1210 . -593) 24674) ((-1189 . -593) 24656) ((-1189 . -594) NIL) ((-234 . -281) 24633) ((-40 . -444) T) ((-219 . -170) T) ((-167 . -1066) T) ((-670 . -145) T) ((-670 . -143) NIL) ((-577 . -593) 24615) ((-576 . -593) 24597) ((-869 . -1066) T) ((-814 . -1066) T) ((-784 . -1066) T) ((-745 . -1066) T) ((-634 . -825) 24581) ((-653 . -1066) T) ((-791 . -871) 24513) ((-40 . -395) NIL) ((-1086 . -637) T) ((-842 . -694) 24458) ((-244 . -481) 24442) ((-243 . -481) 24426) ((-689 . -617) 24374) ((-629 . -624) 24348) ((-288 . -34) T) ((-708 . -1018) T) ((-563 . -1232) 24335) ((-509 . -1232) 24312) 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. -1066) T) ((-1053 . -246) 6207) ((-348 . -1066) T) ((-345 . -1066) T) ((-337 . -1066) T) ((-257 . -1066) T) ((-241 . -1066) T) ((-83 . -1179) T) ((-127 . -101) 6185) ((-121 . -101) 6163) ((-128 . -34) T) ((-1152 . -590) 6142) ((-471 . -1066) T) ((-1107 . -1066) T) ((-471 . -590) 6121) ((-244 . -771) 6072) ((-244 . -768) 6023) ((-243 . -771) 5974) ((-40 . -1117) NIL) ((-243 . -768) 5925) ((-1046 . -891) 5876) ((-975 . -770) T) ((-975 . -767) T) ((-975 . -703) T) ((-942 . -770) T) ((-885 . -703) T) ((-90 . -481) 5860) ((-479 . -871) NIL) ((-881 . -1066) T) ((-219 . -1024) 5825) ((-843 . -283) T) ((-211 . -871) NIL) ((-809 . -1078) 5804) ((-58 . -1066) 5754) ((-510 . -1066) 5732) ((-507 . -1066) 5682) ((-488 . -1066) 5660) ((-487 . -1066) 5610) ((-562 . -101) T) ((-549 . -101) T) ((-486 . -101) T) ((-466 . -170) 5541) ((-352 . -891) T) ((-346 . -891) T) ((-338 . -891) T) ((-219 . -111) 5497) ((-809 . -23) 5449) ((-420 . -703) T) ((-107 . -891) T) ((-40 . -38) 5394) ((-107 . -796) T) 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888) ((-549 . -38) 875) ((-486 . -38) 840) ((-211 . -993) T) ((-842 . -1018) T) ((-810 . -593) 822) ((-803 . -593) 804) ((-801 . -593) 786) ((-792 . -880) 765) ((-1249 . -1078) T) ((-1198 . -1024) 588) ((-828 . -1024) 572) ((-842 . -237) T) ((-842 . -227) NIL) ((-665 . -1179) T) ((-1249 . -23) T) ((-792 . -624) 497) ((-535 . -1179) T) ((-411 . -331) 481) ((-556 . -1024) 468) ((-1198 . -111) 277) ((-677 . -617) 259) ((-828 . -111) 238) ((-374 . -23) T) ((-1152 . -505) 30) ((-638 . -1066) T) ((-657 . -1066) T) ((-652 . -1066) T))
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T)) +(((-1253 . -170) T) ((-1253 . -703) T) ((-1253 . -1078) T) ((-1253 . -1025) T) ((-1253 . -1018) T) ((-1253 . -624) 144993) ((-1253 . -130) T) ((-1253 . -25) T) ((-1253 . -101) T) ((-1253 . -593) 144975) ((-1253 . -1067) T) ((-1253 . -23) T) ((-1253 . -21) T) ((-1253 . -1024) 144962) ((-1253 . -111) 144947) ((-1253 . -361) T) ((-1253 . -594) 144929) ((-1253 . -1117) T) ((-1249 . -1247) 144908) ((-1249 . -1009) 144885) ((-1249 . -1018) T) ((-1249 . -1025) T) ((-1249 . -1078) T) ((-1249 . -703) T) ((-1249 . -21) T) ((-1249 . -23) T) ((-1249 . -1067) T) ((-1249 . -593) 144867) ((-1249 . -101) T) ((-1249 . -25) T) ((-1249 . -130) T) ((-1249 . -624) 144841) ((-1249 . -1239) 144825) ((-1249 . -694) 144795) ((-1249 . -1024) 144779) ((-1249 . -111) 144758) ((-1249 . -38) 144728) ((-1249 . -1244) 144707) ((-1248 . -1018) T) ((-1248 . -1025) T) ((-1248 . -1078) T) ((-1248 . -703) T) ((-1248 . -21) T) ((-1248 . -23) T) ((-1248 . -1067) T) ((-1248 . -593) 144689) ((-1248 . -101) T) ((-1248 . 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143444) ((-1237 . -101) T) ((-1237 . -25) T) ((-1237 . -130) T) ((-1237 . -624) 143404) ((-1237 . -38) 143374) ((-1237 . -111) 143339) ((-1237 . -1024) 143309) ((-1237 . -694) 143279) ((-1236 . -1049) T) ((-1236 . -593) 143245) ((-1236 . -1067) T) ((-1236 . -101) T) ((-1236 . -92) T) ((-1235 . -1049) T) ((-1235 . -593) 143211) ((-1235 . -1067) T) ((-1235 . -101) T) ((-1235 . -92) T) ((-1228 . -1067) T) ((-1228 . -593) 143193) ((-1228 . -101) T) ((-1227 . -1067) T) ((-1227 . -593) 143175) ((-1227 . -101) T) ((-1224 . -1223) 143159) ((-1224 . -365) 143143) ((-1224 . -823) 143122) ((-1224 . -149) 143106) ((-1224 . -34) T) ((-1224 . -1178) T) ((-1224 . -593) 143018) ((-1224 . -302) 142956) ((-1224 . -505) 142889) ((-1224 . -1067) 142839) ((-1224 . -101) 142789) ((-1224 . -481) 142773) ((-1224 . -594) 142734) ((-1224 . -584) 142711) ((-1224 . -279) 142688) ((-1224 . -281) 142665) ((-1224 . -627) 142649) ((-1224 . -19) 142633) ((-1221 . -1067) T) ((-1221 . -593) 142599) ((-1221 . -101) T) 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135551) ((-1193 . -300) 135530) ((-1193 . -279) 135457) ((-1193 . -227) T) ((-1193 . -130) T) ((-1193 . -25) T) ((-1193 . -101) T) ((-1193 . -593) 135439) ((-1193 . -1067) T) ((-1193 . -23) T) ((-1193 . -21) T) ((-1193 . -703) T) ((-1193 . -1078) T) ((-1193 . -1025) T) ((-1193 . -1018) T) ((-1193 . -225) 135423) ((-1191 . -1060) 135407) ((-1191 . -1178) T) ((-1191 . -1067) 135385) ((-1191 . -593) 135352) ((-1191 . -101) 135330) ((-1191 . -1061) 135287) ((-1189 . -1188) 135266) ((-1189 . -973) 135232) ((-1189 . -1164) 135198) ((-1189 . -1167) 135164) ((-1189 . -484) 135130) ((-1189 . -277) 135096) ((-1189 . -94) 135062) ((-1189 . -35) 135028) ((-1189 . -1203) 135005) ((-1189 . -47) 134982) ((-1189 . -694) 134796) ((-1189 . -624) 134666) ((-1189 . -1024) 134474) ((-1189 . -111) 134263) ((-1189 . -38) 134077) ((-1189 . -944) 134046) ((-1189 . -279) 133966) ((-1189 . -1186) 133950) ((-1189 . -703) T) ((-1189 . -1078) T) ((-1189 . -1025) T) ((-1189 . -1018) T) ((-1189 . -21) T) ((-1189 . 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129166) ((-1184 . -505) 128935) ((-1184 . -302) 128820) ((-1184 . -370) 128772) ((-1184 . -617) 128724) ((-1184 . -393) 128676) ((-1184 . -1178) 128655) ((-1184 . -857) NIL) ((-1184 . -796) NIL) ((-1184 . -767) NIL) ((-1184 . -768) NIL) ((-1184 . -823) NIL) ((-1184 . -770) NIL) ((-1184 . -773) NIL) ((-1184 . -821) NIL) ((-1184 . -855) 128607) ((-1184 . -881) NIL) ((-1184 . -991) NIL) ((-1184 . -1009) 128573) ((-1184 . -1117) NIL) ((-1184 . -962) 128525) ((-1179 . -1049) T) ((-1179 . -593) 128491) ((-1179 . -1067) T) ((-1179 . -101) T) ((-1179 . -92) T) ((-1176 . -593) 128403) ((-1176 . -1067) 128381) ((-1176 . -101) 128359) ((-1171 . -717) 128335) ((-1171 . -35) 128301) ((-1171 . -94) 128267) ((-1171 . -277) 128233) ((-1171 . -484) 128199) ((-1171 . -1167) 128165) ((-1171 . -1164) 128131) ((-1171 . -973) 128097) ((-1171 . -47) 128066) ((-1171 . -38) 127963) ((-1171 . -694) 127860) ((-1171 . -283) 127839) ((-1171 . -542) 127818) ((-1171 . -111) 127687) ((-1171 . -1024) 127570) ((-1171 . -170) 127521) ((-1171 . -145) 127500) ((-1171 . -143) 127479) ((-1171 . -624) 127404) ((-1171 . -944) 127366) ((-1171 . -1018) T) ((-1171 . -1025) T) ((-1171 . -1078) T) ((-1171 . -703) T) ((-1171 . -21) T) ((-1171 . -23) T) ((-1171 . -1067) T) ((-1171 . -593) 127348) ((-1171 . -101) T) ((-1171 . -25) T) ((-1171 . -130) T) ((-1171 . -871) 127329) ((-1171 . -505) 127296) ((-1171 . -302) 127283) ((-1165 . -981) 127267) ((-1165 . -34) T) ((-1165 . -1178) T) ((-1165 . -593) 127199) ((-1165 . -302) 127137) ((-1165 . -505) 127070) ((-1165 . -1067) 127048) ((-1165 . -101) 127026) ((-1165 . -481) 127010) ((-1160 . -358) 126984) ((-1160 . -101) T) ((-1160 . -593) 126966) ((-1160 . -1067) T) ((-1158 . -1067) T) ((-1158 . -593) 126948) ((-1158 . -101) T) ((-1151 . -1155) 126927) ((-1151 . -223) 126877) ((-1151 . -106) 126827) ((-1151 . -302) 126631) ((-1151 . -505) 126423) ((-1151 . -481) 126360) ((-1151 . -149) 126310) ((-1151 . -594) NIL) ((-1151 . -229) 126260) ((-1151 . -590) 126239) ((-1151 . -281) 126218) ((-1151 . -279) 126197) ((-1151 . -101) T) ((-1151 . -1067) T) ((-1151 . -593) 126179) ((-1151 . -1178) T) ((-1151 . -34) T) ((-1151 . -584) 126158) ((-1147 . -1220) T) ((-1147 . -1067) T) ((-1147 . -593) 126140) ((-1147 . -101) T) ((-1146 . -593) 126122) ((-1145 . -593) 126104) ((-1144 . -319) 126081) ((-1144 . -1009) 125977) ((-1144 . -405) 125961) ((-1144 . -38) 125858) ((-1144 . -624) 125783) ((-1144 . -703) T) ((-1144 . -1078) T) ((-1144 . -1025) T) ((-1144 . -1018) T) ((-1144 . -111) 125652) ((-1144 . -1024) 125535) ((-1144 . -21) T) ((-1144 . -23) T) ((-1144 . -1067) T) ((-1144 . -593) 125517) ((-1144 . -101) T) ((-1144 . -25) T) ((-1144 . -130) T) ((-1144 . -694) 125414) ((-1144 . -143) 125393) ((-1144 . -145) 125372) ((-1144 . -170) 125323) ((-1144 . -542) 125302) ((-1144 . -283) 125281) ((-1144 . -47) 125258) ((-1142 . -823) T) ((-1142 . -101) T) ((-1142 . -593) 125240) ((-1142 . -1067) T) ((-1142 . -594) 125162) ((-1142 . -797) T) ((-1142 . -857) 125129) ((-1141 . -593) 125111) ((-1140 . -1217) 125095) ((-1140 . -227) 125054) ((-1140 . -624) 124979) ((-1140 . -130) T) ((-1140 . -25) T) ((-1140 . -101) T) ((-1140 . -593) 124961) ((-1140 . -1067) T) ((-1140 . -23) T) ((-1140 . -21) T) ((-1140 . -703) T) ((-1140 . -1078) T) ((-1140 . -1025) T) ((-1140 . -1018) T) ((-1140 . -279) 124946) ((-1140 . -871) 124859) ((-1140 . -944) 124828) ((-1140 . -38) 124725) ((-1140 . -111) 124594) ((-1140 . -1024) 124477) ((-1140 . -694) 124374) ((-1140 . -143) 124353) ((-1140 . -145) 124332) ((-1140 . -170) 124283) ((-1140 . -542) 124262) ((-1140 . -283) 124241) ((-1140 . -47) 124218) ((-1140 . -1203) 124195) ((-1140 . -35) 124161) ((-1140 . -94) 124127) ((-1140 . -277) 124093) ((-1140 . -484) 124059) ((-1140 . -1167) 124025) ((-1140 . -1164) 123991) ((-1140 . -973) 123957) ((-1139 . -1209) 123918) ((-1139 . -356) 123897) ((-1139 . -1183) 123876) ((-1139 . -892) 123855) ((-1139 . -542) 123806) ((-1139 . -170) 123737) ((-1139 . -694) 123578) ((-1139 . -38) 123419) ((-1139 . -444) 123398) ((-1139 . -300) 123377) ((-1139 . -624) 123274) ((-1139 . -703) T) ((-1139 . -1078) T) ((-1139 . -1025) T) ((-1139 . -1018) T) ((-1139 . -111) 123095) ((-1139 . -1024) 122930) ((-1139 . -21) T) ((-1139 . -23) T) ((-1139 . -1067) T) ((-1139 . -593) 122912) ((-1139 . -101) T) ((-1139 . -25) T) ((-1139 . -130) T) ((-1139 . -283) 122863) ((-1139 . -237) 122842) ((-1139 . -973) 122808) ((-1139 . -1164) 122774) ((-1139 . -1167) 122740) ((-1139 . -484) 122706) ((-1139 . -277) 122672) ((-1139 . -94) 122638) ((-1139 . -35) 122604) ((-1139 . -1203) 122574) ((-1139 . -47) 122544) ((-1139 . -145) 122523) ((-1139 . -143) 122502) ((-1139 . -944) 122464) ((-1139 . -871) 122370) ((-1139 . -279) 122355) ((-1139 . -227) 122307) ((-1139 . -1207) 122291) ((-1139 . -1009) 122226) ((-1136 . -1200) 122210) ((-1136 . -1117) 122188) ((-1136 . -594) NIL) ((-1136 . -302) 122175) ((-1136 . -505) 122122) ((-1136 . -319) 122099) ((-1136 . -1009) 121979) ((-1136 . -405) 121963) ((-1136 . -38) 121792) ((-1136 . -111) 121601) ((-1136 . -1024) 121424) ((-1136 . -624) 121349) ((-1136 . -694) 121178) ((-1136 . -143) 121157) ((-1136 . -145) 121136) ((-1136 . -47) 121113) ((-1136 . -370) 121097) ((-1136 . -617) 121045) ((-1136 . -823) 121024) ((-1136 . -871) 120967) ((-1136 . -857) NIL) ((-1136 . -881) 120946) ((-1136 . -1183) 120925) ((-1136 . -921) 120894) ((-1136 . -892) 120873) ((-1136 . -542) 120784) ((-1136 . -283) 120695) ((-1136 . -170) 120586) ((-1136 . -444) 120517) ((-1136 . -300) 120496) ((-1136 . -279) 120423) ((-1136 . -227) T) ((-1136 . -130) T) ((-1136 . -25) T) ((-1136 . -101) T) ((-1136 . -593) 120405) ((-1136 . -1067) T) ((-1136 . -23) T) ((-1136 . -21) T) ((-1136 . -703) T) ((-1136 . -1078) T) ((-1136 . -1025) T) ((-1136 . -1018) T) ((-1136 . -225) 120389) ((-1133 . -1188) 120350) ((-1133 . -973) 120316) ((-1133 . -1164) 120282) ((-1133 . -1167) 120248) ((-1133 . -484) 120214) ((-1133 . -277) 120180) ((-1133 . -94) 120146) ((-1133 . -35) 120112) ((-1133 . -1203) 120089) ((-1133 . -47) 120066) ((-1133 . -694) 119862) ((-1133 . -624) 119714) ((-1133 . -1024) 119504) ((-1133 . -111) 119273) ((-1133 . -38) 119069) ((-1133 . -944) 119038) ((-1133 . -279) 118886) ((-1133 . -1186) 118870) ((-1133 . -703) T) ((-1133 . -1078) T) ((-1133 . -1025) T) ((-1133 . -1018) T) ((-1133 . -21) T) ((-1133 . -23) T) ((-1133 . -1067) T) ((-1133 . -593) 118852) ((-1133 . -101) T) ((-1133 . -25) T) ((-1133 . -130) T) ((-1133 . -143) 118759) ((-1133 . -145) 118666) ((-1133 . -594) NIL) ((-1133 . -225) 118618) ((-1133 . -871) 118451) ((-1133 . -227) 118338) ((-1133 . -356) 118317) ((-1133 . -1183) 118296) ((-1133 . -892) 118275) ((-1133 . -542) 118226) ((-1133 . -170) 118157) ((-1133 . -444) 118136) ((-1133 . -300) 118115) ((-1133 . -283) 118066) ((-1133 . -237) 118045) ((-1133 . -331) 117997) ((-1133 . -505) 117766) ((-1133 . -302) 117651) ((-1133 . -370) 117603) ((-1133 . -617) 117555) ((-1133 . -393) 117507) ((-1133 . -1178) 117486) ((-1133 . -857) NIL) ((-1133 . -796) NIL) ((-1133 . -767) NIL) ((-1133 . -768) NIL) ((-1133 . -823) NIL) ((-1133 . -770) NIL) ((-1133 . -773) NIL) ((-1133 . -821) NIL) ((-1133 . -855) 117438) ((-1133 . -881) NIL) ((-1133 . -991) NIL) ((-1133 . -1009) 117404) ((-1133 . -1117) NIL) ((-1133 . -962) 117356) ((-1132 . -1049) T) ((-1132 . -593) 117322) ((-1132 . -1067) T) ((-1132 . -101) T) ((-1132 . -92) T) ((-1131 . -1067) T) ((-1131 . -593) 117304) ((-1131 . -101) T) ((-1130 . -1067) T) ((-1130 . -593) 117286) ((-1130 . -101) T) ((-1125 . -1155) 117262) ((-1125 . -223) 117209) ((-1125 . -106) 117156) ((-1125 . -302) 116951) ((-1125 . -505) 116734) ((-1125 . -481) 116668) ((-1125 . -149) 116615) ((-1125 . -594) NIL) ((-1125 . -229) 116562) ((-1125 . -590) 116538) ((-1125 . -281) 116514) ((-1125 . -279) 116490) ((-1125 . -101) T) ((-1125 . -1067) T) ((-1125 . -593) 116472) ((-1125 . -1178) T) ((-1125 . -34) T) ((-1125 . -584) 116448) ((-1124 . -1123) T) ((-1124 . -19) 116430) ((-1124 . -627) 116412) ((-1124 . -281) 116387) ((-1124 . -279) 116362) ((-1124 . -584) 116337) ((-1124 . -594) NIL) ((-1124 . -481) 116319) ((-1124 . -505) NIL) ((-1124 . -302) NIL) ((-1124 . -1178) T) ((-1124 . -34) T) ((-1124 . -149) 116301) ((-1124 . -823) T) ((-1124 . -365) 116283) ((-1124 . -1110) T) ((-1124 . -101) T) ((-1124 . -593) 116265) ((-1124 . -1067) T) ((-1124 . -797) T) ((-1119 . -650) 116249) ((-1119 . -627) 116233) ((-1119 . -281) 116210) ((-1119 . -279) 116187) ((-1119 . -584) 116164) ((-1119 . -594) 116125) ((-1119 . -481) 116109) ((-1119 . -101) 116087) ((-1119 . -1067) 116065) ((-1119 . -505) 115998) ((-1119 . -302) 115936) ((-1119 . -593) 115868) ((-1119 . -1178) T) ((-1119 . -34) T) ((-1119 . -149) 115852) ((-1119 . -1213) 115836) ((-1119 . -981) 115820) ((-1119 . -1115) 115804) ((-1116 . -1155) 115783) ((-1116 . -223) 115733) ((-1116 . -106) 115683) ((-1116 . -302) 115487) ((-1116 . -505) 115279) ((-1116 . -481) 115216) ((-1116 . -149) 115166) ((-1116 . -594) NIL) ((-1116 . -229) 115116) ((-1116 . -590) 115095) ((-1116 . -281) 115074) ((-1116 . -279) 115053) ((-1116 . -101) T) ((-1116 . -1067) T) ((-1116 . -593) 115035) ((-1116 . -1178) T) ((-1116 . -34) T) ((-1116 . -584) 115014) ((-1113 . -1087) 114998) ((-1113 . -481) 114982) ((-1113 . -101) 114960) ((-1113 . -1067) 114938) ((-1113 . -505) 114871) ((-1113 . -302) 114809) ((-1113 . -593) 114741) ((-1113 . -1178) T) ((-1113 . -34) T) ((-1113 . -106) 114725) ((-1112 . -1075) 114694) ((-1112 . -1173) 114663) ((-1112 . -593) 114625) ((-1112 . -149) 114609) ((-1112 . -34) T) ((-1112 . -1178) T) ((-1112 . -302) 114547) ((-1112 . -505) 114480) ((-1112 . -1067) T) ((-1112 . -101) T) ((-1112 . -481) 114464) ((-1112 . -594) 114425) ((-1112 . -947) 114394) ((-1112 . -1038) 114363) ((-1108 . -1089) 114308) ((-1108 . -481) 114292) ((-1108 . -505) 114225) ((-1108 . -302) 114163) ((-1108 . -1178) T) ((-1108 . -34) T) ((-1108 . -1021) 114103) ((-1108 . -1009) 113999) ((-1108 . -405) 113983) ((-1108 . -617) 113931) ((-1108 . -370) 113915) ((-1108 . -227) 113894) ((-1108 . -871) 113853) ((-1108 . -225) 113837) ((-1108 . -694) 113769) ((-1108 . -624) 113743) ((-1108 . -130) T) ((-1108 . -25) T) ((-1108 . -101) T) ((-1108 . -593) 113705) ((-1108 . -1067) T) ((-1108 . -23) T) ((-1108 . -21) T) ((-1108 . -1024) 113689) ((-1108 . -111) 113668) ((-1108 . -1018) T) ((-1108 . -1025) T) ((-1108 . -1078) T) ((-1108 . -703) T) ((-1108 . -38) 113628) ((-1108 . -594) 113589) ((-1107 . -981) 113560) ((-1107 . -34) T) ((-1107 . -1178) T) ((-1107 . -593) 113542) ((-1107 . -302) 113468) ((-1107 . -505) 113387) ((-1107 . -1067) T) ((-1107 . -101) T) ((-1107 . -481) 113358) ((-1106 . -1067) T) ((-1106 . -593) 113340) ((-1106 . -101) T) ((-1101 . -1103) T) ((-1101 . -1220) T) ((-1101 . -92) T) ((-1101 . -101) T) ((-1101 . -593) 113306) ((-1101 . -1067) T) ((-1101 . -1049) T) ((-1099 . -1100) 113290) ((-1099 . -101) T) ((-1099 . -593) 113272) ((-1099 . -1067) T) ((-1092 . -717) 113251) ((-1092 . -35) 113217) ((-1092 . -94) 113183) ((-1092 . -277) 113149) ((-1092 . -484) 113115) ((-1092 . -1167) 113081) ((-1092 . -1164) 113047) ((-1092 . -973) 113013) ((-1092 . -47) 112985) ((-1092 . -38) 112882) ((-1092 . -694) 112779) ((-1092 . -283) 112758) ((-1092 . -542) 112737) ((-1092 . -111) 112606) ((-1092 . -1024) 112489) ((-1092 . -170) 112440) ((-1092 . -145) 112419) ((-1092 . -143) 112398) ((-1092 . -624) 112323) ((-1092 . -944) 112290) ((-1092 . -1018) T) ((-1092 . -1025) T) ((-1092 . -1078) T) ((-1092 . -703) T) ((-1092 . -21) T) ((-1092 . -23) T) ((-1092 . -1067) T) ((-1092 . -593) 112272) ((-1092 . -101) T) ((-1092 . -25) T) ((-1092 . -130) T) ((-1092 . -871) 112256) ((-1092 . -505) 112226) ((-1092 . -302) 112213) ((-1091 . -921) 112180) ((-1091 . -1009) 112063) ((-1091 . -1183) 112042) ((-1091 . -881) 112021) ((-1091 . -857) 111880) ((-1091 . -871) 111864) ((-1091 . -823) 111843) ((-1091 . -505) 111795) ((-1091 . -444) 111746) ((-1091 . -617) 111694) ((-1091 . -370) 111678) ((-1091 . -47) 111650) ((-1091 . -38) 111499) ((-1091 . -694) 111348) ((-1091 . -283) 111279) ((-1091 . -542) 111210) ((-1091 . -111) 111039) ((-1091 . -1024) 110882) ((-1091 . -170) 110793) ((-1091 . -145) 110772) ((-1091 . -143) 110751) ((-1091 . -624) 110676) ((-1091 . -130) T) ((-1091 . -25) T) ((-1091 . -101) T) ((-1091 . -593) 110658) ((-1091 . -1067) T) ((-1091 . -23) T) ((-1091 . -21) T) ((-1091 . -1018) T) ((-1091 . -1025) T) ((-1091 . -1078) T) ((-1091 . -703) T) ((-1091 . -405) 110642) ((-1091 . -319) 110614) ((-1091 . -302) 110601) ((-1091 . -594) 110349) ((-1086 . -534) T) ((-1086 . -1183) T) ((-1086 . -1117) T) ((-1086 . -1009) 110331) ((-1086 . -594) 110246) ((-1086 . -991) T) ((-1086 . -857) 110228) ((-1086 . -821) T) ((-1086 . -773) T) ((-1086 . -770) T) ((-1086 . -823) T) ((-1086 . -768) T) ((-1086 . -767) T) ((-1086 . -796) T) ((-1086 . -617) 110210) ((-1086 . -892) T) ((-1086 . -542) T) ((-1086 . -283) T) ((-1086 . -170) T) ((-1086 . -694) 110197) ((-1086 . -1024) 110184) ((-1086 . -111) 110169) ((-1086 . -38) 110156) ((-1086 . -444) T) ((-1086 . -300) T) ((-1086 . -227) T) ((-1086 . -141) T) ((-1086 . -1018) T) ((-1086 . -1025) T) ((-1086 . -1078) T) ((-1086 . -703) T) ((-1086 . -21) T) ((-1086 . -23) T) ((-1086 . -1067) T) ((-1086 . -593) 110138) ((-1086 . -101) T) ((-1086 . -25) T) ((-1086 . -130) T) ((-1086 . -624) 110125) ((-1086 . -145) T) ((-1086 . -638) T) ((-1086 . -797) T) ((-1082 . -1049) T) ((-1082 . -593) 110091) ((-1082 . -1067) T) ((-1082 . -101) T) ((-1082 . -92) T) ((-1081 . -1067) T) ((-1081 . -593) 110073) ((-1081 . -101) T) ((-1079 . -232) 110052) ((-1079 . -1232) 110022) ((-1079 . -767) 110001) ((-1079 . -821) 109980) ((-1079 . -773) 109931) ((-1079 . -770) 109882) ((-1079 . -823) 109833) ((-1079 . -768) 109784) ((-1079 . -769) 109763) ((-1079 . -281) 109740) ((-1079 . -279) 109717) ((-1079 . -481) 109701) ((-1079 . -505) 109634) ((-1079 . -302) 109572) ((-1079 . -1178) T) ((-1079 . -34) T) ((-1079 . -584) 109549) ((-1079 . -1009) 109376) ((-1079 . -405) 109345) ((-1079 . -617) 109251) ((-1079 . -370) 109220) ((-1079 . -361) 109199) ((-1079 . -227) 109151) ((-1079 . -871) 109083) ((-1079 . -225) 109052) ((-1079 . -111) 108942) ((-1079 . -1024) 108839) ((-1079 . -170) 108818) ((-1079 . -593) 108549) ((-1079 . -694) 108491) ((-1079 . -624) 108339) ((-1079 . -130) 108209) ((-1079 . -23) 108079) ((-1079 . -21) 107989) ((-1079 . -1018) 107919) ((-1079 . -1025) 107849) ((-1079 . -1078) 107759) ((-1079 . -703) 107669) ((-1079 . -38) 107639) ((-1079 . -1067) 107429) ((-1079 . -101) 107219) ((-1079 . -25) 107070) ((-1072 . -389) T) ((-1072 . -1178) T) ((-1072 . -593) 107052) ((-1071 . -1070) 107016) ((-1071 . -101) T) ((-1071 . -593) 106998) ((-1071 . -1067) T) ((-1069 . -1070) 106950) ((-1069 . -101) T) ((-1069 . -593) 106932) ((-1069 . -1067) T) ((-1068 . -361) T) ((-1068 . -101) T) ((-1068 . -593) 106914) ((-1068 . -1067) T) ((-1063 . -419) 106898) ((-1063 . -1065) 106882) ((-1063 . -361) 106861) ((-1063 . -229) 106845) ((-1063 . -594) 106806) ((-1063 . -149) 106790) ((-1063 . -481) 106774) ((-1063 . -101) T) ((-1063 . -1067) T) ((-1063 . -505) 106707) ((-1063 . -302) 106645) ((-1063 . -593) 106627) ((-1063 . -1178) T) ((-1063 . -34) T) ((-1063 . -106) 106611) ((-1063 . -223) 106595) ((-1062 . -1049) T) ((-1062 . -593) 106561) ((-1062 . -1067) T) ((-1062 . -101) T) ((-1062 . -92) T) ((-1058 . -1178) T) ((-1058 . -1067) 106539) ((-1058 . -593) 106506) ((-1058 . -101) 106484) ((-1057 . -1049) T) ((-1057 . -593) 106450) ((-1057 . -1067) T) ((-1057 . -101) T) ((-1057 . -92) T) ((-1055 . -1060) 106434) ((-1055 . -1178) T) ((-1055 . -1067) 106412) ((-1055 . -593) 106379) ((-1055 . -101) 106357) ((-1055 . -1061) 106315) ((-1054 . -259) 106299) ((-1054 . -1009) 106283) ((-1054 . -1067) T) ((-1054 . -593) 106265) ((-1054 . -101) T) ((-1054 . -823) T) ((-1053 . -246) 106202) ((-1053 . -1009) 106029) ((-1053 . -594) NIL) ((-1053 . -319) 105990) ((-1053 . -405) 105974) ((-1053 . -38) 105823) ((-1053 . -111) 105652) ((-1053 . -1024) 105495) ((-1053 . -624) 105420) ((-1053 . -694) 105269) ((-1053 . -143) 105248) ((-1053 . -145) 105227) ((-1053 . -170) 105138) ((-1053 . -542) 105069) ((-1053 . -283) 105000) ((-1053 . -47) 104961) ((-1053 . -370) 104945) ((-1053 . -617) 104893) ((-1053 . -444) 104844) ((-1053 . -505) 104711) ((-1053 . -823) 104690) ((-1053 . -871) 104625) ((-1053 . -857) NIL) ((-1053 . -881) 104604) ((-1053 . -1183) 104583) ((-1053 . -921) 104528) ((-1053 . -302) 104515) ((-1053 . -227) 104494) ((-1053 . -130) T) ((-1053 . -25) T) ((-1053 . -101) T) ((-1053 . -593) 104476) ((-1053 . -1067) T) ((-1053 . -23) T) ((-1053 . -21) T) ((-1053 . -703) T) ((-1053 . -1078) T) ((-1053 . -1025) T) ((-1053 . -1018) T) ((-1053 . -225) 104460) ((-1051 . -593) 104442) ((-1048 . -823) T) ((-1048 . -101) T) ((-1048 . -593) 104424) ((-1048 . -1067) T) ((-1045 . -701) 104403) ((-1045 . -1009) 104299) ((-1045 . -405) 104283) ((-1045 . -617) 104231) ((-1045 . -370) 104215) ((-1045 . -363) 104194) ((-1045 . -145) 104173) ((-1045 . -694) 104041) ((-1045 . -624) 103951) ((-1045 . -1024) 103861) ((-1045 . -111) 103757) ((-1045 . -38) 103625) ((-1045 . -403) 103604) ((-1045 . -395) 103583) ((-1045 . -143) 103534) ((-1045 . -1117) 103513) ((-1045 . -343) 103492) ((-1045 . -361) 103443) ((-1045 . -237) 103394) ((-1045 . -283) 103345) ((-1045 . -300) 103296) ((-1045 . -444) 103247) ((-1045 . -542) 103198) ((-1045 . -892) 103149) ((-1045 . -1183) 103100) ((-1045 . -356) 103051) ((-1045 . -227) 102976) ((-1045 . -871) 102909) ((-1045 . -225) 102879) ((-1045 . -594) 102863) ((-1045 . -21) T) ((-1045 . -23) T) ((-1045 . -1067) T) ((-1045 . -593) 102845) ((-1045 . -101) T) ((-1045 . -25) T) ((-1045 . -130) T) ((-1045 . -1018) T) ((-1045 . -1025) T) ((-1045 . -1078) T) ((-1045 . -703) T) ((-1045 . -170) T) ((-1043 . -1067) T) ((-1043 . -593) 102827) ((-1043 . -101) T) ((-1043 . -279) 102806) ((-1042 . -1067) T) ((-1042 . -593) 102788) ((-1042 . -101) T) ((-1041 . -1067) T) ((-1041 . -593) 102770) ((-1041 . -101) T) ((-1041 . -279) 102749) ((-1041 . -1009) 102726) ((-1040 . -1049) T) ((-1040 . -593) 102692) ((-1040 . -1067) T) ((-1040 . -101) T) ((-1040 . -92) T) ((-1033 . -1049) T) ((-1033 . -593) 102658) ((-1033 . -1067) T) ((-1033 . -101) T) ((-1033 . -92) T) ((-1030 . -1155) 102633) ((-1030 . -223) 102579) ((-1030 . -106) 102525) ((-1030 . -302) 102376) ((-1030 . -505) 102220) ((-1030 . -481) 102151) ((-1030 . -149) 102097) ((-1030 . -594) NIL) ((-1030 . -229) 102043) ((-1030 . -590) 102018) ((-1030 . -281) 101993) ((-1030 . -279) 101968) ((-1030 . -101) T) ((-1030 . -1067) T) ((-1030 . -593) 101950) ((-1030 . -1178) T) ((-1030 . -34) T) ((-1030 . -584) 101925) ((-1029 . -534) T) ((-1029 . -1183) T) ((-1029 . -1117) T) ((-1029 . -1009) 101907) ((-1029 . -594) 101822) ((-1029 . -991) T) ((-1029 . -857) 101804) ((-1029 . -821) T) ((-1029 . -773) T) ((-1029 . -770) T) ((-1029 . -823) T) ((-1029 . -768) T) ((-1029 . -767) T) ((-1029 . -796) T) ((-1029 . -617) 101786) ((-1029 . -892) T) 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. -1038) 101168) ((-1015 . -947) 101097) ((-1015 . -594) 101039) ((-1015 . -481) 101004) ((-1015 . -101) T) ((-1015 . -1067) T) ((-1015 . -505) 100905) ((-1015 . -302) 100813) ((-1015 . -593) 100756) ((-1015 . -1178) T) ((-1015 . -34) T) ((-1015 . -149) 100721) ((-1015 . -1173) 100650) ((-1007 . -1049) T) ((-1007 . -593) 100616) ((-1007 . -1067) T) ((-1007 . -101) T) ((-1007 . -92) T) ((-1006 . -1155) 100591) ((-1006 . -223) 100537) ((-1006 . -106) 100483) ((-1006 . -302) 100334) ((-1006 . -505) 100178) ((-1006 . -481) 100109) ((-1006 . -149) 100055) ((-1006 . -594) NIL) ((-1006 . -229) 100001) ((-1006 . -590) 99976) ((-1006 . -281) 99951) ((-1006 . -279) 99926) ((-1006 . -101) T) ((-1006 . -1067) T) ((-1006 . -593) 99908) ((-1006 . -1178) T) ((-1006 . -34) T) ((-1006 . -584) 99883) ((-1005 . -170) T) ((-1005 . -703) T) ((-1005 . -1078) T) ((-1005 . -1025) T) ((-1005 . -1018) T) ((-1005 . -624) 99857) ((-1005 . -130) T) ((-1005 . -25) T) ((-1005 . -101) T) ((-1005 . -593) 99839) 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. -130) T) ((-708 . -25) T) ((-708 . -101) T) ((-708 . -593) 72884) ((-708 . -1067) T) ((-708 . -23) T) ((-708 . -21) T) ((-708 . -1018) T) ((-708 . -1025) T) ((-708 . -1078) T) ((-708 . -703) T) ((-708 . -405) 72868) ((-708 . -319) 72833) ((-708 . -302) 72820) ((-708 . -594) 72681) ((-695 . -465) T) ((-695 . -1078) T) ((-695 . -101) T) ((-695 . -593) 72663) ((-695 . -1067) T) ((-695 . -703) T) ((-692 . -1018) T) ((-692 . -1025) T) ((-692 . -1078) T) ((-692 . -703) T) ((-692 . -21) T) ((-692 . -23) T) ((-692 . -1067) T) ((-692 . -593) 72645) ((-692 . -101) T) ((-692 . -25) T) ((-692 . -130) T) ((-692 . -624) 72632) ((-691 . -1018) T) ((-691 . -1025) T) ((-691 . -1078) T) ((-691 . -703) T) ((-691 . -21) T) ((-691 . -23) T) ((-691 . -1067) T) ((-691 . -593) 72614) ((-691 . -101) T) ((-691 . -25) T) ((-691 . -130) T) ((-691 . -624) 72574) ((-691 . -1009) 72543) ((-691 . -279) 72522) ((-691 . -145) 72501) ((-691 . -143) 72480) ((-691 . -38) 72450) ((-691 . -111) 72415) ((-691 . -1024) 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. -130) T) ((-677 . -624) 70138) ((-677 . -694) 70125) ((-677 . -170) T) ((-677 . -283) T) ((-677 . -542) T) ((-677 . -534) T) ((-677 . -1183) T) ((-677 . -1117) T) ((-677 . -594) 70040) ((-677 . -991) T) ((-677 . -857) 70022) ((-677 . -821) T) ((-677 . -773) T) ((-677 . -770) T) ((-677 . -768) T) ((-677 . -767) T) ((-677 . -796) T) ((-677 . -617) 70004) ((-677 . -892) T) ((-677 . -444) T) ((-677 . -300) T) ((-677 . -227) T) ((-677 . -141) T) ((-677 . -145) T) ((-675 . -397) T) ((-675 . -145) T) ((-675 . -624) 69969) ((-675 . -130) T) ((-675 . -25) T) ((-675 . -101) T) ((-675 . -593) 69951) ((-675 . -1067) T) ((-675 . -23) T) ((-675 . -21) T) ((-675 . -703) T) ((-675 . -1078) T) ((-675 . -1025) T) ((-675 . -1018) T) ((-675 . -594) 69896) ((-675 . -356) T) ((-675 . -1183) T) ((-675 . -892) T) ((-675 . -542) T) ((-675 . -170) T) ((-675 . -694) 69861) ((-675 . -38) 69826) ((-675 . -444) T) ((-675 . -300) T) ((-675 . -111) 69782) ((-675 . -1024) 69747) ((-675 . -283) T) ((-675 . -237) T) 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. -300) T) ((-337 . -111) 35146) ((-337 . -1024) 35091) ((-337 . -283) T) ((-337 . -237) T) ((-337 . -395) T) ((-337 . -143) T) ((-337 . -1009) 35068) ((-337 . -1232) 35045) ((-337 . -1243) 35022) ((-333 . -322) 34999) ((-333 . -227) T) ((-333 . -361) T) ((-333 . -1117) T) ((-333 . -343) T) ((-333 . -145) 34981) ((-333 . -624) 34926) ((-333 . -130) T) ((-333 . -25) T) ((-333 . -101) T) ((-333 . -593) 34908) ((-333 . -1067) T) ((-333 . -23) T) ((-333 . -21) T) ((-333 . -703) T) ((-333 . -1078) T) ((-333 . -1025) T) ((-333 . -1018) T) ((-333 . -356) T) ((-333 . -1183) T) ((-333 . -892) T) ((-333 . -542) T) ((-333 . -170) T) ((-333 . -694) 34853) ((-333 . -38) 34818) ((-333 . -444) T) ((-333 . -300) T) ((-333 . -111) 34747) ((-333 . -1024) 34692) ((-333 . -283) T) ((-333 . -237) T) ((-333 . -395) T) ((-333 . -143) T) ((-333 . -1009) 34669) ((-333 . -1232) 34646) ((-333 . -1243) 34623) ((-332 . -291) T) ((-332 . -1009) 34590) ((-332 . -1067) T) ((-332 . -593) 34572) ((-332 . -101) T) 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. -101) T) ((-128 . -593) 7554) ((-128 . -1067) T) ((-127 . -125) 7538) ((-127 . -981) 7522) ((-127 . -34) T) ((-127 . -1178) T) ((-127 . -593) 7454) ((-127 . -302) 7392) ((-127 . -505) 7325) ((-127 . -1067) 7303) ((-127 . -101) 7281) ((-127 . -481) 7265) ((-127 . -119) 7249) ((-126 . -125) 7233) ((-126 . -981) 7217) ((-126 . -34) T) ((-126 . -1178) T) ((-126 . -593) 7149) ((-126 . -302) 7087) ((-126 . -505) 7020) ((-126 . -1067) 6998) ((-126 . -101) 6976) ((-126 . -481) 6960) ((-126 . -119) 6944) ((-121 . -125) 6928) ((-121 . -981) 6912) ((-121 . -34) T) ((-121 . -1178) T) ((-121 . -593) 6844) ((-121 . -302) 6782) ((-121 . -505) 6715) ((-121 . -1067) 6693) ((-121 . -101) 6671) ((-121 . -481) 6655) ((-121 . -119) 6639) ((-117 . -962) 6616) ((-117 . -1117) NIL) ((-117 . -1009) 6593) ((-117 . -594) NIL) ((-117 . -991) NIL) ((-117 . -881) NIL) ((-117 . -855) 6570) ((-117 . -821) NIL) ((-117 . -773) NIL) ((-117 . -770) NIL) ((-117 . -823) NIL) ((-117 . -768) NIL) ((-117 . -767) NIL) ((-117 . -796) NIL) ((-117 . -857) NIL) ((-117 . -1178) T) ((-117 . -393) 6547) ((-117 . -617) 6524) ((-117 . -370) 6501) ((-117 . -279) 6452) ((-117 . -302) 6409) ((-117 . -505) 6317) ((-117 . -331) 6294) ((-117 . -237) T) ((-117 . -111) 6223) ((-117 . -1024) 6168) ((-117 . -283) T) ((-117 . -694) 6113) ((-117 . -624) 6058) ((-117 . -38) 6003) ((-117 . -300) T) ((-117 . -444) T) ((-117 . -170) T) ((-117 . -542) T) ((-117 . -892) T) ((-117 . -1183) T) ((-117 . -356) T) ((-117 . -227) NIL) ((-117 . -871) NIL) ((-117 . -225) 5980) ((-117 . -145) T) ((-117 . -143) NIL) ((-117 . -130) T) ((-117 . -25) T) ((-117 . -101) T) ((-117 . -593) 5962) ((-117 . -1067) T) ((-117 . -23) T) ((-117 . -21) T) ((-117 . -1018) T) ((-117 . -1025) T) ((-117 . -1078) T) ((-117 . -703) T) ((-116 . -841) 5946) ((-116 . -892) T) ((-116 . -542) T) ((-116 . -283) T) ((-116 . -170) T) ((-116 . -694) 5933) ((-116 . -1024) 5920) ((-116 . -111) 5905) ((-116 . -38) 5892) ((-116 . -444) T) ((-116 . -300) T) ((-116 . -1018) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index da168a38..86f2c6fd 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,1120 +1,993 @@ -(30 . 3431185326) +(30 . 3431436951) (4339 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| - |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| - |AbelianMonoid&| |AbelianMonoid| |AbelianSemiGroup&| - |AbelianSemiGroup| |AlgebraicallyClosedField&| - |AlgebraicallyClosedField| |AlgebraicallyClosedFunctionSpace&| - |AlgebraicallyClosedFunctionSpace| |PlaneAlgebraicCurvePlot| |AddAst| - |AlgebraicFunction| |Aggregate&| |Aggregate| - |ArcHyperbolicFunctionCategory| |AssociationListAggregate| |Algebra&| - |Algebra| |AlgFactor| |AlgebraicFunctionField| + |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| + |AbelianMonoid| |AbelianSemiGroup&| |AbelianSemiGroup| + |AlgebraicallyClosedField&| |AlgebraicallyClosedField| + |AlgebraicallyClosedFunctionSpace&| |AlgebraicallyClosedFunctionSpace| + |PlaneAlgebraicCurvePlot| |AddAst| |AlgebraicFunction| |Aggregate&| + |Aggregate| |ArcHyperbolicFunctionCategory| |AssociationListAggregate| + |Algebra&| |Algebra| |AlgFactor| |AlgebraicFunctionField| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraPackage| - 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|CRApackage| |CoerceAst| |ComplexRootFindingPackage| - |CyclicStreamTools| |ConstructorCall| - |ComplexTrigonometricManipulations| |CoerceVectorMatrixPackage| - |CycleIndicators| |CyclotomicPolynomialPackage| |d01AgentsPackage| - |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| - |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| - |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType| - |d01WeightsPackage| |d02AgentsPackage| |d02bbfAnnaType| - |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| - |d03eefAnnaType| |d03fafAnnaType| |DataBuffer| |Database| - |DoubleResultantPackage| |DistinctDegreeFactorize| |DecimalExpansion| - |DefinitionAst| |ElementaryFunctionDefiniteIntegration| - |RationalFunctionDefiniteIntegration| |DegreeReductionPackage| - |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| |DoubleFloat| - |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| |Dictionary&| - |Dictionary| |DifferentialExtension&| |DifferentialExtension| + |CRApackage| |CoerceAst| |ComplexRootFindingPackage| |CyclicStreamTools| + |ConstructorCall| |ComplexTrigonometricManipulations| + |CoerceVectorMatrixPackage| |CycleIndicators| |CyclotomicPolynomialPackage| + |d01AgentsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| + |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| + |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType| + |d01WeightsPackage| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| + |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| + |d03fafAnnaType| |DataBuffer| |Database| |DoubleResultantPackage| + |DistinctDegreeFactorize| |DecimalExpansion| |DefinitionAst| + |ElementaryFunctionDefiniteIntegration| |RationalFunctionDefiniteIntegration| + |DegreeReductionPackage| |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| + |DoubleFloat| |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| + |Dictionary&| |Dictionary| |DifferentialExtension&| |DifferentialExtension| |DifferentialRing&| |DifferentialRing| |DictionaryOperations&| - |DictionaryOperations| |DiophantineSolutionPackage| - |DirectProductCategory&| |DirectProductCategory| - |DirectProductFunctions2| |DirectProduct| |DisplayPackage| - |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| |DataList| - |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| + |DictionaryOperations| |DiophantineSolutionPackage| |DirectProductCategory&| + |DirectProductCategory| |DirectProduct| |DirectProductFunctions2| + |DisplayPackage| |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| + |DataList| |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| |Domain| |DirectProductMatrixModule| |DirectProductModule| |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory| - |DequeueAggregate| |TopLevelDrawFunctionsForCompiledFunctions| - |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| - |DrawNumericHack| |TopLevelDrawFunctions| - |TopLevelDrawFunctionsForPoints| |DrawOptionFunctions0| - |DrawOptionFunctions1| |DrawOption| - |DifferentialSparseMultivariatePolynomial| + |DequeueAggregate| |TopLevelDrawFunctions| + |TopLevelDrawFunctionsForCompiledFunctions| + |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| |DrawNumericHack| + |TopLevelDrawFunctionsForPoints| |DrawOption| |DrawOptionFunctions0| + |DrawOptionFunctions1| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DifferentialVariableCategory| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType| - |ExtAlgBasis| |ElementaryFunction| - |ElementaryFunctionStructurePackage| + |ExtAlgBasis| |ElementaryFunction| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElaboratedExpression| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate| |ElementaryFunctionCategory&| |ElementaryFunctionCategory| - |EllipticFunctionsUnivariateTaylorSeries| |Eltable| - |EltableAggregate&| |EltableAggregate| |EuclideanModularRing| - |EntireRing| |Environment| |EigenPackage| |EquationFunctions2| - |Equation| |EqTable| |ErrorFunctions| |ExpressionSpaceFunctions1| - |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage1| - |ExpertSystemContinuityPackage| |ExpressionSpace&| |ExpressionSpace| - |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| - |ExpertSystemToolsPackage| |EuclideanDomain&| |EuclideanDomain| - |Evalable&| |Evalable| |EvaluateCycleIndicators| |ExitAst| |Exit| - |ExponentialExpansion| |ExpressionFunctions2| - |ExpressionToUnivariatePowerSeries| |Expression| - |ExpressionSpaceODESolver| |ExpressionTubePlot| - |ExponentialOfUnivariatePuiseuxSeries| |FactoredFunctions| - |FactoringUtilities| |FreeAbelianGroup| |FreeAbelianMonoidCategory| - |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| - |FiniteAbelianMonoidRing| |FlexibleArray| - |FiniteAlgebraicExtensionField&| |FiniteAlgebraicExtensionField| - |FortranCode| |FourierComponent| |FortranCodePackage1| - |FiniteDivisorFunctions2| |FiniteDivisorCategory&| - |FiniteDivisorCategory| |FiniteDivisor| |FullyEvalableOver&| - |FullyEvalableOver| |FortranExpression| - |FunctionFieldCategoryFunctions2| |FunctionFieldCategory&| - |FunctionFieldCategory| |FiniteFieldCyclicGroup| - |FiniteFieldCyclicGroupExtensionByPolynomial| + |EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&| + |EltableAggregate| |EuclideanModularRing| |EntireRing| |Environment| + |EigenPackage| |Equation| |EquationFunctions2| |EqTable| |ErrorFunctions| + |ExpressionSpace&| |ExpressionSpace| |ExpressionSpaceFunctions1| + |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage| + |ExpertSystemContinuityPackage1| |ExpertSystemToolsPackage| + |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |EuclideanDomain&| + |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit| + |ExitAst| |ExponentialExpansion| |Expression| |ExpressionFunctions2| + |ExpressionToUnivariatePowerSeries| |ExpressionSpaceODESolver| + |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries| + |FactoredFunctions| |FactoringUtilities| |FreeAbelianGroup| + |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| + |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&| + |FiniteAlgebraicExtensionField| |FortranCode| |FourierComponent| + |FortranCodePackage1| |FiniteDivisor| |FiniteDivisorFunctions2| + |FiniteDivisorCategory&| |FiniteDivisorCategory| |FullyEvalableOver&| + |FullyEvalableOver| |FortranExpression| |FiniteField| |FunctionFieldCategory&| + |FunctionFieldCategory| |FunctionFieldCategoryFunctions2| + |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldCyclicGroupExtension| |FiniteFieldFunctions| - |FiniteFieldHomomorphisms| |FiniteFieldCategory&| - |FiniteFieldCategory| |FunctionFieldIntegralBasis| - |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtensionByPolynomial| - |FiniteFieldNormalBasisExtension| |FiniteField| - |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage2| - |FiniteFieldPolynomialPackage| + |FiniteFieldHomomorphisms| |FiniteFieldCategory&| |FiniteFieldCategory| + |FunctionFieldIntegralBasis| |FiniteFieldNormalBasis| + |FiniteFieldNormalBasisExtensionByPolynomial| + |FiniteFieldNormalBasisExtension| |FiniteFieldExtensionByPolynomial| + |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldExtension| - |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |FileCategory| |File| - |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| - |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra| - |FiniteLinearAggregateFunctions2| |FiniteLinearAggregate&| - |FiniteLinearAggregate| |FreeLieAlgebra| |FiniteLinearAggregateSort| - |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| - |FloatingComplexPackage| |Float| |FloatingRealPackage| |FreeModule1| - |FreeModuleCat| |FortranMatrixCategory| - |FortranMatrixFunctionCategory| |FreeModule| |FreeMonoid| - |FortranMachineTypeCategory| |FileName| |FileNameCategory| - |FreeNilpotentLie| |FortranOutputStackPackage| |FindOrderFinite| - |ScriptFormulaFormat1| |ScriptFormulaFormat| |FortranProgramCategory| - |FortranFunctionCategory| |FortranPackage| |FortranProgram| - |FullPartialFractionExpansion| |FullyPatternMatchable| - |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic| - |FloatingPointSystem&| |FloatingPointSystem| |FactoredFunctions2| - |FractionFunctions2| |Fraction| |FramedAlgebra&| |FramedAlgebra| - |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdealFunctions2| - |FractionalIdeal| |FramedModule| + |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |File| |FileCategory| + |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite| + |FiniteRankAlgebra&| |FiniteRankAlgebra| |FiniteLinearAggregate&| + |FiniteLinearAggregate| |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| + |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&| + |FullyLinearlyExplicitRingOver| |Float| |FloatingComplexPackage| + |FloatingRealPackage| |FreeModule| |FreeModule1| |FortranMatrixCategory| + |FreeModuleCat| |FortranMatrixFunctionCategory| |FreeMonoid| + |FortranMachineTypeCategory| |FileName| |FileNameCategory| |FreeNilpotentLie| + |FortranOutputStackPackage| |FindOrderFinite| |ScriptFormulaFormat| + |ScriptFormulaFormat1| |FortranPackage| |FortranProgramCategory| + |FortranFunctionCategory| |FortranProgram| |FullPartialFractionExpansion| + |FullyPatternMatchable| |FieldOfPrimeCharacteristic&| + |FieldOfPrimeCharacteristic| |FloatingPointSystem&| |FloatingPointSystem| + |Factored| |FactoredFunctions2| |Fraction| |FractionFunctions2| + |FramedAlgebra&| |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo| + |FractionalIdeal| |FractionalIdealFunctions2| |FramedModule| |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&| - 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|GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| - |GaloisGroupUtilities| |GaussianFactorizationPackage| + |FunctionSpaceUnivariatePolynomialFactor| |FortranType| |FortranTemplate| + |FunctionCalled| |FortranVectorCategory| |FortranVectorFunctionCategory| + |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| + |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| + |GaussianFactorizationPackage| |GroebnerPackage| |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| - |GroebnerInternalPackage| |GroebnerPackage| |GcdDomain&| |GcdDomain| - |GenericNonAssociativeAlgebra| - |GeneralDistributedMultivariatePolynomial| |GenExEuclid| - |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| + |GroebnerInternalPackage| |GcdDomain&| |GcdDomain| + |GenericNonAssociativeAlgebra| |GeneralDistributedMultivariatePolynomial| + |GenExEuclid| |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| |GenUFactorize| |GenerateUnivariatePowerSeries| |GeneralHenselPackage| - |GeneralModulePolynomial| |GosperSummationMethod| - |GeneralPolynomialSet| |GradedAlgebra&| |GradedAlgebra| |GrayCode| - |GraphicsDefaults| |GraphImage| |GradedModule&| |GradedModule| - |GroebnerSolve| |Group&| |Group| |GeneralUnivariatePowerSeries| - |GeneralSparseTable| |GeneralTriangularSet| |Pi| |HasAst| |HashTable| - |HallBasis| |HomogeneousDistributedMultivariatePolynomial| - |HomogeneousDirectProduct| |HeadAst| |Heap| - |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| + |GeneralModulePolynomial| |GosperSummationMethod| |GeneralPolynomialSet| + |GradedAlgebra&| |GradedAlgebra| |GrayCode| |GraphicsDefaults| |GraphImage| + |GradedModule&| |GradedModule| |GroebnerSolve| |Group&| |Group| + |GeneralUnivariatePowerSeries| |GeneralSparseTable| |GeneralTriangularSet| + |Pi| |HasAst| |HashTable| |HallBasis| + |HomogeneousDistributedMultivariatePolynomial| |HomogeneousDirectProduct| + |HeadAst| |Heap| |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousAggregate| |Hostname| - |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| - |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| + |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| + |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |IndexedTwoDimensionalArray| |ChineseRemainderToolsForIntegralBases| - |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| - |IndexCard| |InnerCommonDenominator| |PolynomialIdeals| - |IdealDecompositionPackage| |Identifier| - |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| - |IndexedDirectProductCategory| - |IndexedDirectProductOrderedAbelianMonoid| - |IndexedDirectProductOrderedAbelianMonoidSup| - |IndexedDirectProductObject| |InnerEvalable&| |InnerEvalable| - |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| - |InnerFiniteField| |InnerIndexedTwoDimensionalArray| |IndexedList| - |InnerMatrixLinearAlgebraFunctions| - |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |ImportAst| - |InAst| |InputByteConduit&| |InputByteConduit| + |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| |IndexCard| + |InnerCommonDenominator| |PolynomialIdeals| |IdealDecompositionPackage| + |Identifier| |IndexedDirectProductAbelianGroup| + |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| + |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| + |IndexedDirectProductOrderedAbelianMonoidSup| |InnerEvalable&| |InnerEvalable| + |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| |InnerFiniteField| + |InnerIndexedTwoDimensionalArray| |IndexedList| + |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| + |IndexedMatrix| |ImportAst| |InAst| |InputByteConduit&| |InputByteConduit| |InnerNormalBasisFieldFunctions| |IncrementingMaps| |IndexedExponents| - |InnerNumericEigenPackage| |Infinity| |InputFormFunctions1| - |InputForm| |InfiniteProductCharacteristicZero| - |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| - |InfiniteProductFiniteField| |InfiniteProductPrimeField| - |InnerPolySign| |IntegerNumberSystem&| |IntegerNumberSystem| - |InnerTable| |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| - |IntervalCategory| |IntegralDomain&| |IntegralDomain| - |ElementaryIntegration| |IntegerFactorizationPackage| + |InnerNumericEigenPackage| |Infinity| |InputForm| |InputFormFunctions1| + |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| + |InnerModularGcd| |InnerMultFact| |InfiniteProductFiniteField| + |InfiniteProductPrimeField| |InnerPolySign| |IntegerNumberSystem&| + |IntegerNumberSystem| |Integer| |InnerTable| |AlgebraicIntegration| + |AlgebraicIntegrate| |IntegerBits| |IntervalCategory| |IntegralDomain&| + |IntegralDomain| |ElementaryIntegration| |IntegerFactorizationPackage| |IntegrationFunctionsTable| |GenusZeroIntegration| |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration| - |TranscendentalHermiteIntegration| |Integer| - |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| - |PatternMatchIntegration| |RationalIntegration| |IntegerRetractions| - |RationalFunctionIntegration| |Interval| + |TranscendentalHermiteIntegration| |AnnaNumericalIntegrationPackage| + |PureAlgebraicIntegration| |PatternMatchIntegration| |RationalIntegration| + |IntegerRetractions| |RationalFunctionIntegration| |Interval| |IntegerSolveLinearPolynomialEquation| |IntegrationTools| - |TranscendentalIntegration| |InverseLaplaceTransform| - |InputOutputByteConduit| |InnerPAdicInteger| |InnerPrimeField| - |InternalPrintPackage| |IntegrationResultToFunction| - |IntegrationResultFunctions2| |IntegrationResult| |IntegerRoots| - |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| - |IrrRepSymNatPackage| - |InternalRationalUnivariateRepresentationPackage| |IsAst| - |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| - |InnerTaylorSeries| |InfiniteTupleFunctions2| - |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| - |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| - |JavaBytecode| |JoinAst| |AssociatedJordanAlgebra| |KeyedAccessFile| - |KeyedDictionary&| |KeyedDictionary| |KernelFunctions2| |Kernel| - |CoercibleTo| |ConvertibleTo| |Kovacic| |KleeneTrivalentLogic| - |LeftAlgebra&| |LeftAlgebra| |LocalAlgebra| |LaplaceTransform| - |LaurentPolynomial| |LazardSetSolvingPackage| - |LeadingCoefDetermination| |LetAst| |LieExponentials| - |LexTriangularPackage| |LiouvillianFunctionCategory| - |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&| - |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage| - |RationalFunctionLimitPackage| |LinearDependence| - |LinearlyExplicitRingOver| |ListToMap| |ListFunctions2| - |ListFunctions3| |List| |Literal| |ListMultiDictionary| |LeftModule| - |ListMonoidOps| |LinearAggregate&| |LinearAggregate| - |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator1| + |TranscendentalIntegration| |InverseLaplaceTransform| |InputOutputByteConduit| + |InnerPAdicInteger| |InnerPrimeField| |InternalPrintPackage| + |IntegrationResult| |IntegrationResultFunctions2| + |IntegrationResultToFunction| |IntegerRoots| |IrredPolyOverFiniteField| + |IntegrationResultRFToFunction| |IrrRepSymNatPackage| + |InternalRationalUnivariateRepresentationPackage| |IsAst| |IndexedString| + |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| + |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| + |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| + |IndexedAggregate&| |IndexedAggregate| |JavaBytecode| |JoinAst| + |AssociatedJordanAlgebra| |KeyedAccessFile| |KeyedDictionary&| + |KeyedDictionary| |Kernel| |KernelFunctions2| |CoercibleTo| |ConvertibleTo| + |Kovacic| |KleeneTrivalentLogic| |LocalAlgebra| |LeftAlgebra&| |LeftAlgebra| + |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| + |LeadingCoefDetermination| |LetAst| |LieExponentials| |LexTriangularPackage| + |LiouvillianFunction| |LiouvillianFunctionCategory| |LinGroebnerPackage| + |Library| |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| + |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearDependence| + |LinearlyExplicitRingOver| |List| |ListFunctions2| |ListToMap| + |ListFunctions3| |Literal| |ListMultiDictionary| |LeftModule| |ListMonoidOps| + |LinearAggregate&| |LinearAggregate| |Localize| |ElementaryFunctionLODESolver| + |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorFactorizer| - |LinearOrdinaryDifferentialOperator| - |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |Localize| + |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| - |ListAggregate| |LinearSystemMatrixPackage1| - |LinearSystemMatrixPackage| |LinearSystemPolynomialPackage| - |LieSquareMatrix| |ConstructAst| |LyndonWord| |LazyStreamAggregate&| - |LazyStreamAggregate| |ThreeDimensionalMatrix| |MacroAst| |Magma| - |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| - |MappingPackageInternalHacks3| |MappingAst| |MappingPackage1| - |MappingPackage2| |MappingPackage3| |MatrixCategoryFunctions2| - |MatrixCategory&| |MatrixCategory| |MatrixLinearAlgebraFunctions| + |ListAggregate| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| + |LinearSystemPolynomialPackage| |LieSquareMatrix| |ConstructAst| |LyndonWord| + |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| + |MacroAst| |Magma| |MappingPackageInternalHacks1| + |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingAst| + |MappingPackage1| |MappingPackage2| |MappingPackage3| |MatrixCategory&| + |MatrixCategory| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |Matrix| |StorageEfficientMatrixOperations| |Maybe| - |MultiVariableCalculusFunctions| |MatrixCommonDenominator| - |MachineComplex| |MultiDictionary| |ModularDistinctDegreeFactorizer| - |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| - |MachineFloat| |ModularHermitianRowReduction| |MachineInteger| - |MakeBinaryCompiledFunction| |MakeCachableSet| - |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| - |MakeUnaryCompiledFunction| |MultivariateLifting| - |MonogenicLinearOperator| |MultipleMap| |MathMLFormat| |ModularField| - |ModMonic| |ModuleMonomial| |ModuleOperator| |ModularRing| |Module&| - |Module| |MoebiusTransform| |Monad&| |Monad| |MonadWithUnit&| - |MonadWithUnit| |MonogenicAlgebra&| |MonogenicAlgebra| |Monoid&| - |Monoid| |MonomialExtensionTools| |MPolyCatFunctions2| - |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MultivariatePolynomial| - |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| - |MonoidRingFunctions2| |MonoidRing| |MultisetAggregate| |Multiset| - |MoreSystemCommands| |MergeThing| |MultivariateTaylorSeriesCategory| - |MultivariateFactorize| |MultivariateSquareFree| - |NonAssociativeAlgebra&| |NonAssociativeAlgebra| + |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| + |MultiDictionary| |ModularDistinctDegreeFactorizer| + |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| + |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| + |MakeCachableSet| |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| + |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| + |MultipleMap| |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| + |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| |Monad&| + |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| + |MonogenicAlgebra| |Monoid&| |Monoid| |MonomialExtensionTools| + |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| + |MultivariatePolynomial| |MPolyCatRationalFunctionFactorizer| + |MRationalFactorize| |MonoidRingFunctions2| |MonoidRing| |Multiset| + |MultisetAggregate| |MoreSystemCommands| |MergeThing| + |MultivariateTaylorSeriesCategory| |MultivariateFactorize| + |MultivariateSquareFree| |NonAssociativeAlgebra&| |NonAssociativeAlgebra| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagIntegrationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagInterpolationPackage| - |NagFittingPackage| |NagOptimisationPackage| - |NagMatrixOperationsPackage| |NagEigenPackage| - |NagLinearEquationSolvingPackage| |NagLapack| - |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| - |NonAssociativeRng&| |NonAssociativeRng| |NonAssociativeRing&| - |NonAssociativeRing| |NumericComplexEigenPackage| - |NumericContinuedFraction| |NonCommutativeOperatorDivision| - |NumberFieldIntegralBasis| |NumericalIntegrationProblem| - |NonLinearSolvePackage| |NonNegativeInteger| - |NonLinearFirstOrderODESolver| |NoneFunctions1| |None| - |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| - |NPCoef| |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| - |NewSparseUnivariatePolynomialFunctions2| - |NewSparseUnivariatePolynomial| |NumberTheoreticPolynomialFunctions| - |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| - |NumericalIntegrationCategory| + |NagFittingPackage| |NagOptimisationPackage| |NagMatrixOperationsPackage| + |NagEigenPackage| |NagLinearEquationSolvingPackage| |NagLapack| + |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| |NonAssociativeRng&| + |NonAssociativeRng| |NonAssociativeRing&| |NonAssociativeRing| + |NumericComplexEigenPackage| |NumericContinuedFraction| + |NonCommutativeOperatorDivision| |NumberFieldIntegralBasis| + |NumericalIntegrationProblem| |NonLinearSolvePackage| |NonNegativeInteger| + |NonLinearFirstOrderODESolver| |None| |NoneFunctions1| + |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NPCoef| + |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| + |NewSparseUnivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| + |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| + |Numeric| |NumberFormats| |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup| |OrderedAbelianMonoid| - |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| - |OrderedCancellationAbelianMonoid| |OctonionCategory&| - |OctonionCategory| |OctonionCategoryFunctions2| |Octonion| - |OrdinaryDifferentialEquationsSolverCategory| |ConstantLODE| - |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| - |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| - |PureAlgebraicLODE| |PrimitiveRatDE| |NumericalODEProblem| - |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| |RationalRicDE| - |SystemODESolver| |ODETools| |OrderedDirectProduct| - |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| - |OrderlyDifferentialVariable| |OrderedFreeMonoid| - |OrderedIntegralDomain| |OpenMathConnection| |OpenMathDevice| - |OpenMathEncoding| |OpenMathErrorKind| |OpenMathError| - |ExpressionToOpenMath| |OppositeMonogenicLinearOperator| |OpenMath| - |OpenMathPackage| |OrderedMultisetAggregate| |OpenMathServerPackage| - |OnePointCompletionFunctions2| |OnePointCompletion| |Operator| - |OperationsQuery| |NumericalOptimizationCategory| + |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |OctonionCategory&| + |OctonionCategory| |OrderedCancellationAbelianMonoid| |Octonion| + |OctonionCategoryFunctions2| |OrdinaryDifferentialEquationsSolverCategory| + |ConstantLODE| |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| + |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| |PureAlgebraicLODE| + |PrimitiveRatDE| |NumericalODEProblem| |PrimitiveRatRicDE| |RationalLODE| + |ReduceLODE| |RationalRicDE| |SystemODESolver| |ODETools| + |OrderedDirectProduct| |OrderlyDifferentialPolynomial| + |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid| + |OrderedIntegralDomain| |OpenMath| |OpenMathConnection| |OpenMathDevice| + |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |ExpressionToOpenMath| + |OppositeMonogenicLinearOperator| |OpenMathPackage| |OrderedMultisetAggregate| + |OpenMathServerPackage| |OnePointCompletion| |OnePointCompletionFunctions2| + |Operator| |OperationsQuery| |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| - |OrderedCompletionFunctions2| |OrderedCompletion| |OrderedFinite| - |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| - |OrderedSet&| |OrderedSet| |UnivariateSkewPolynomialCategory&| - |UnivariateSkewPolynomialCategory| - |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| - |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| - |OrderedSemiGroup| |OrdSetInts| |OutputByteConduit&| - |OutputByteConduit| |OutputForm| |OutputPackage| |OrderedVariableList| - |OrdinaryWeightedPolynomials| |PadeApproximants| - |PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger| - |PAdicRational| |PAdicRationalConstructor| |Pair| |Palette| - |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| - |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| - |ParametricSpaceCurve| |Parser| |ParametricSurfaceFunctions2| - |ParametricSurface| |PartitionsAndPermutations| |Patternable| - |PatternMatchListResult| |PatternMatchable| |PatternMatch| - |PatternMatchResultFunctions2| |PatternMatchResult| - |PatternFunctions1| |PatternFunctions2| |Pattern| - |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| - |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| - |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| - |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| - |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| - |PolynomialFactorizationByRecursion| + |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedFinite| + |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| |OrderedSet&| + |OrderedSet| |UnivariateSkewPolynomialCategory&| + |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| + |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| + |OrthogonalPolynomialFunctions| |OrderedSemiGroup| |OrdSetInts| + |OutputPackage| |OutputByteConduit&| |OutputByteConduit| |OutputForm| + |OrderedVariableList| |OrdinaryWeightedPolynomials| |PadeApproximants| + |PadeApproximantPackage| |PAdicInteger| |PAdicIntegerCategory| |PAdicRational| + |PAdicRationalConstructor| |Pair| |Palette| |PolynomialAN2Expression| + |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| + |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |Parser| + |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| + |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| + |PatternMatchResult| |PatternMatchResultFunctions2| |Pattern| + |PatternFunctions1| |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| + |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| + |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| + |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| + |PendantTree| |Permutation| |Permanent| |PermutationCategory| + |PermutationGroup| |PrimeField| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| - |PrimeField| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| - |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| - |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| - |PiCoercions| |PrincipalIdealDomain| |PositiveInteger| - |PolynomialInterpolationAlgorithms| |PolynomialInterpolation| - |ParametricLinearEquations| |PlotFunctions1| |Plot3D| |Plot| - |PlotTools| |FunctionSpaceAssertions| |PatternMatchAssertions| - |PatternMatchPushDown| |PatternMatchFunctionSpace| + |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| + |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| + |PermutationGroupExamples| |PolyGroebner| |PositiveInteger| |PiCoercions| + |PrincipalIdealDomain| |PolynomialInterpolation| + |PolynomialInterpolationAlgorithms| |ParametricLinearEquations| |Plot| + |PlotFunctions1| |Plot3D| |PlotTools| |PatternMatchAssertions| + |FunctionSpaceAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| - |FunctionSpaceAttachPredicates| |AttachPredicates| - |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| - |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| - |PolToPol| |RealPolynomialUtilitiesPackage| |PolynomialFunctions2| - |PolynomialToUnivariatePolynomial| |PolynomialCategory&| - |PolynomialCategory| |PolynomialCategoryQuotientFunctions| - |PolynomialCategoryLifting| |Polynomial| |PolynomialRoots| - |PortNumber| |PlottablePlaneCurveCategory| - |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| - |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| - |IntegerPrimesPackage| |PrintPackage| |PolynomialRing| |Product| - |Property| |PropositionalFormula| |PropositionalLogic| - |PriorityQueueAggregate| |PseudoRemainderSequence| |PretendAst| - |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| - |PlottableSpaceCurveCategory| |PolynomialSetCategory&| - |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| - |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory| - |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions| - |PushVariables| |PAdicWildFunctionFieldIntegralBasis| - |QuasiAlgebraicSet2| |QuasiAlgebraicSet| |QuasiComponentPackage| - |QueryEquation| |QuotientFieldCategoryFunctions2| - |QuotientFieldCategory&| |QuotientFieldCategory| |QuadraticForm| - |QuasiquoteAst| |QueueAggregate| |QuaternionCategory&| - |QuaternionCategory| |QuaternionCategoryFunctions2| |Quaternion| - |Queue| |RadicalCategory&| |RadicalCategory| |RadicalFunctionField| - |RadixExpansion| |RadixUtilities| |RandomNumberSource| - |RationalFactorize| |RationalRetractions| |RecursiveAggregate&| - |RecursiveAggregate| |RealClosedField&| |RealClosedField| - |ElementaryRischDE| |ElementaryRischDESystem| |TranscendentalRischDE| - |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| - |ReduceAst| |RealZeroPackage| |RealZeroPackageQ| |RealConstant| - |RealSolvePackage| |RealClosure| |ReductionOfOrder| |Reference| - |RegularTriangularSet| |RepresentationPackage1| - |RepresentationPackage2| |RepeatedDoubling| |RadicalEigenPackage| + |AttachPredicates| |FunctionSpaceAttachPredicates| + |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| + |PolynomialNumberTheoryFunctions| |Point| |PolToPol| + |RealPolynomialUtilitiesPackage| |Polynomial| |PolynomialFunctions2| + |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| + |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| + |PolynomialRoots| |PortNumber| |PlottablePlaneCurveCategory| |PolynomialRing| + |PrecomputedAssociatedEquations| |PrimitiveArray| |PrimitiveArrayFunctions2| + |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| + |PrintPackage| |Product| |Property| |PropositionalFormula| + |PropositionalLogic| |PriorityQueueAggregate| |PseudoRemainderSequence| + |PretendAst| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| + |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| + |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm| + |PolynomialSquareFree| |PointCategory| |PointFunctions2| |PointPackage| + |PartialTranscendentalFunctions| |PushVariables| + |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| + |QuasiComponentPackage| |QueryEquation| |QuotientFieldCategory&| + |QuotientFieldCategory| |QuotientFieldCategoryFunctions2| |QuadraticForm| + |QuasiquoteAst| |QueueAggregate| |Quaternion| |QuaternionCategory&| + |QuaternionCategory| |QuaternionCategoryFunctions2| |Queue| |RadicalCategory&| + |RadicalCategory| |RadicalFunctionField| |RadixExpansion| |RadixUtilities| + |RandomNumberSource| |RationalFactorize| |RationalRetractions| + |RecursiveAggregate&| |RecursiveAggregate| |RealClosedField&| + |RealClosedField| |ElementaryRischDE| |ElementaryRischDESystem| + |TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| + |ReducedDivisor| |ReduceAst| |RealConstant| |RealZeroPackage| + |RealZeroPackageQ| |RealSolvePackage| |RealClosure| |ReductionOfOrder| + |Reference| |RegularTriangularSet| |RadicalEigenPackage| + |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| |ReturnAst| |RetractableTo&| |RetractableTo| |RetractSolvePackage| - |RandomFloatDistributions| |RationalFunctionFactor| - |RationalFunctionFactorizer| |RationalFunction| |RegularChain| - |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| - |RectangularMatrixCategory&| |RectangularMatrixCategory| - |RectangularMatrix| |RectangularMatrixCategoryFunctions2| - |RightModule| |Rng| |RealNumberSystem&| |RealNumberSystem| - |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| - |RecursivePolynomialCategory&| |RecursivePolynomialCategory| + |RationalFunction| |RandomFloatDistributions| |RationalFunctionFactor| + |RationalFunctionFactorizer| |RegularChain| |RandomIntegerDistributions| + |Ring&| |Ring| |RationalInterpolation| |RectangularMatrixCategory&| + |RectangularMatrixCategory| |RectangularMatrix| + |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RealNumberSystem&| + |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| + |RoutinesTable| |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RepeatAst| |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| |RegularTriangularSetCategory| - |RegularTriangularSetGcdPackage| |RestrictAst| |RuleCalled| - |RewriteRule| |Ruleset| |RationalUnivariateRepresentationPackage| - |SimpleAlgebraicExtensionAlgFactor| |SimpleAlgebraicExtension| - |SAERationalFunctionAlgFactor| |SingletonAsOrderedSet| - |SpadSyntaxCategory| |SortedCache| |Scope| + |RegularTriangularSetGcdPackage| |RestrictAst| |RewriteRule| |RuleCalled| + |Ruleset| |RationalUnivariateRepresentationPackage| |SimpleAlgebraicExtension| + |SimpleAlgebraicExtensionAlgFactor| |SAERationalFunctionAlgFactor| + |SingletonAsOrderedSet| |SpadSyntaxCategory| |SortedCache| |Scope| |StructuralConstantsPackage| |SequentialDifferentialPolynomial| - |SequentialDifferentialVariable| |SegmentFunctions2| |SegmentAst| - |SegmentBindingFunctions2| |SegmentBinding| |SegmentCategory| - |Segment| |SegmentExpansionCategory| |SequenceAst| |SetAggregate&| - |SetAggregate| |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| - |Set| |SExpressionCategory| |SExpression| |SExpressionOf| - |SimpleFortranProgram| |SquareFreeQuasiComponentPackage| - |SquareFreeRegularTriangularSetGcdPackage| - |SquareFreeRegularTriangularSetCategory| - |SymmetricGroupCombinatoricFunctions| |SemiGroup&| |SemiGroup| - |SplitHomogeneousDirectProduct| |SturmHabichtPackage| |SignatureAst| - |ElementaryFunctionSign| |RationalFunctionSign| |Signature| - |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| - |StackAggregate| |SquareMatrixCategory&| |SquareMatrixCategory| - |SmithNormalForm| |SparseMultivariatePolynomial| - |SparseMultivariateTaylorSeries| - |SquareFreeNormalizedTriangularSetCategory| - |PolynomialSolveByFormulas| |RadicalSolvePackage| - |TransSolvePackageService| |TransSolvePackage| |SortPackage| - |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| + |SequentialDifferentialVariable| |Segment| |SegmentFunctions2| |SegmentAst| + |SegmentBinding| |SegmentBindingFunctions2| |SegmentCategory| + |SegmentExpansionCategory| |SequenceAst| |Set| |SetAggregate&| |SetAggregate| + |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| |SExpression| + |SExpressionCategory| |SExpressionOf| |SimpleFortranProgram| + |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage| + |SquareFreeRegularTriangularSetCategory| |SymmetricGroupCombinatoricFunctions| + |SemiGroup&| |SemiGroup| |SplitHomogeneousDirectProduct| |SturmHabichtPackage| + |Signature| |SignatureAst| |ElementaryFunctionSign| |RationalFunctionSign| + |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| |StackAggregate| + |SquareMatrixCategory&| |SquareMatrixCategory| |SmithNormalForm| + |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| + |SquareFreeNormalizedTriangularSetCategory| |PolynomialSolveByFormulas| + |RadicalSolvePackage| |TransSolvePackageService| |TransSolvePackage| + |SortPackage| |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| |SpadAstExports| |SpecialOutputPackage| |SpecialFunctionCategory| |SplittingNode| |SplittingTree| |SquareMatrix| |StringAggregate&| |StringAggregate| |SquareFreeRegularSetDecompositionPackage| - |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| - |StreamAggregate| |SparseTable| |StepThrough| |StreamInfiniteProduct| - |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |Stream| - |StringCategory| |String| |StringTable| |StreamTaylorSeriesOperations| - |StreamTranscendentalFunctionsNonCommutative| - |StreamTranscendentalFunctions| |SubResultantPackage| |SubSpace| - |SuchThat| |SuchThatAst| |SparseUnivariateLaurentSeries| - |FunctionSpaceSum| |RationalFunctionSum| - |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| - |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| + |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| |StreamAggregate| + |SparseTable| |StepThrough| |StreamInfiniteProduct| |Stream| + |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StringCategory| + |String| |StringTable| |StreamTaylorSeriesOperations| + |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| + |SubResultantPackage| |SubSpace| |SuchThat| |SuchThatAst| + |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| + |SparseUnivariatePolynomial| |SparseUnivariatePolynomialFunctions2| + |SupFractionFactorizer| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| - |SystemSolvePackage| |System| |TableauxBumpers| |Tableau| |Table| + |SystemSolvePackage| |System| |TableauxBumpers| |Table| |Tableau| |TangentExpansions| |TableAggregate&| |TableAggregate| - |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| - |TexFormat| |TextFile| |ToolsForSign| |TopLevelThreeSpace| - |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| - |Tree| |TrigonometricFunctionCategory&| - |TrigonometricFunctionCategory| |TrigonometricManipulations| - |TriangularMatrixOperations| |TranscendentalManipulations| - |TriangularSetCategory&| |TriangularSetCategory| |TaylorSeries| - |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |TypeAst| |Type| - |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| + |TabulatedComputationPackage| |TemplateUtilities| |TexFormat| |TexFormat1| + |TextFile| |ToolsForSign| |TopLevelThreeSpace| + |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| |Tree| + |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| + |TrigonometricManipulations| |TriangularMatrixOperations| + |TranscendentalManipulations| |TaylorSeries| |TriangularSetCategory&| + |TriangularSetCategory| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| + |Type| |TypeAst| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| |UniqueFactorizationDomain| - |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| + |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| + |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| - |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeries| - |UnivariateFactorize| |UniversalSegmentFunctions2| |UniversalSegment| - |UnivariatePolynomialFunctions2| - |UnivariatePolynomialCommonDenominator| + |UnivariateLaurentSeriesConstructor| |UnivariateFactorize| |UniversalSegment| + |UniversalSegmentFunctions2| |UnivariatePolynomial| + |UnivariatePolynomialFunctions2| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| - |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomial| - |UnivariatePolynomialCategoryFunctions2| - |UnivariatePolynomialCategory&| |UnivariatePolynomialCategory| + |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialCategory&| + |UnivariatePolynomialCategory| |UnivariatePolynomialCategoryFunctions2| |UnivariatePowerSeriesCategory&| |UnivariatePowerSeriesCategory| - |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesFunctions2| - |UnivariatePuiseuxSeriesCategory| + |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| + |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesConstructorCategory| - |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeries| - |UnivariatePuiseuxSeriesWithExponentialSingularity| - |UnaryRecursiveAggregate&| |UnaryRecursiveAggregate| + |UnivariatePuiseuxSeriesConstructor| + |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnaryRecursiveAggregate&| + |UnaryRecursiveAggregate| |UnivariateTaylorSeries| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesCategory&| - |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeries| - |UnivariateTaylorSeriesODESolver| |UTSodetools| |UnionType| |Variable| - |VectorCategory&| |VectorCategory| |VectorFunctions2| |Vector| - |TwoDimensionalViewport| |ThreeDimensionalViewport| - |ViewDefaultsPackage| |ViewportPackage| |Void| |VectorSpace&| - |VectorSpace| |WeierstrassPreparation| - |WildFunctionFieldIntegralBasis| |WhereAst| |WhileAst| - |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| - |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| - |ExtensionField&| |ExtensionField| |XPBWPolynomial| |XPolynomialsCat| - |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| + |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeriesODESolver| + |UTSodetools| |UnionType| |Variable| |VectorCategory&| |VectorCategory| + |Vector| |VectorFunctions2| |ViewportPackage| |TwoDimensionalViewport| + |ThreeDimensionalViewport| |ViewDefaultsPackage| |Void| |VectorSpace&| + |VectorSpace| |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| + |WhereAst| |WhileAst| |WeightedPolynomials| |WuWenTsunTriangularSet| + |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |ExtensionField&| + |ExtensionField| |XFreeAlgebra| |XPBWPolynomial| |XPolynomial| + |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| - |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |writeBytes!| |supDimElseRittWu?| |fractionPart| - |comment| |getZechTable| |invmod| |lo| |viewDeltaYDefault| - |acschIfCan| |reducedContinuedFraction| |iisec| |showTypeInOutput| - |obj| |s17aff| |nonSingularModel| |OMencodingBinary| |cAcot| |incr| - |failed?| |prepareSubResAlgo| |positiveRemainder| |cCosh| - |subResultantChain| |uncouplingMatrices| |f01rdf| |cache| |f02akf| - |symbolIfCan| |index?| |duplicates?| |hi| |patternMatch| |notOperand| - |usingTable?| |checkRur| |OMUnknownCD?| |incrementKthElement| - |argumentList!| |lifting| |overlabel| |monomials| |startTableGcd!| - |coord| |cothIfCan| |showIntensityFunctions| |rischNormalize| - |BasicMethod| |stronglyReduce| |char| |d01alf| |expIfCan| |shift| - |gcdcofactprim| |cosSinInfo| |region| |mapUp!| |d03faf| - |leftRegularRepresentation| |realSolve| |elseBranch| |fortran| |depth| - |graphs| |readBytes!| |cyclicCopy| |size?| - |functionIsContinuousAtEndPoints| |ref| - |solveLinearPolynomialEquationByFractions| |primitiveElement| - |patternVariable| |lighting| |palgLODE| |expextendedint| |d01amf| - |edf2ef| |numberOfIrreduciblePoly| |completeSmith| |nthr| - |topPredicate| |UpTriBddDenomInv| ~ |c06frf| |scripted?| |tail| - |extension| |nullary?| |integralDerivationMatrix| |divide| |clikeUniv| - |xn| |midpoints| |invertible?| |bracket| |printingInfo?| |part?| - |float| |fortranInteger| |safeFloor| |shade| |open| |leftTrace| - |showFortranOutputStack| |nil?| |setrest!| |realEigenvectors| - |orOperands| |createZechTable| |asecIfCan| |genericLeftTrace| - |divisors| |derivationCoordinates| |padicallyExpand| |zeroVector| - |OMcloseConn| |powerAssociative?| |updatF| |c06gbf| |asimpson| - |hexDigit?| |solve1| |mainExpression| |musserTrials| |eulerE| - |lazyPseudoQuotient| |indicialEquations| |subTriSet?| |leftZero| - |explimitedint| |d01akf| |youngGroup| |reducedForm| |head| |linear| - |iiasin| |numer| |factor1| |coerceP| |nextNormalPrimitivePoly| - |limitedIntegrate| |hasSolution?| |rightTrace| |rowEchelonLocal| - |polar| |nonQsign| |tubePlot| |denom| |mapUnivariate| |rootNormalize| - |recur| |curryLeft| |leftExactQuotient| |coth2trigh| |generate| - |startTableInvSet!| |polynomial| |bernoulli| |selectfirst| - |rootProduct| |minPoly| |rightTraceMatrix| |permutationGroup| |cross| - F |iisqrt2| |cAcos| |logIfCan| |pi| |genericLeftMinimalPolynomial| - |regime| |generalPosition| |contract| |create| |algint| |erf| - |incrementBy| |numFunEvals3D| |OMgetAtp| |rewriteIdealWithRemainder| - |infinity| |indiceSubResultant| |stFunc2| |union| |SturmHabicht| - |linearDependence| |gcdPolynomial| |subCase?| |split| |script| - |purelyAlgebraicLeadingMonomial?| |expand| |internalAugment| |write!| - |complexNormalize| |sncndn| |lyndonIfCan| |sequence| |laplace| - |lyndon| |internal?| |solveRetract| |filterWhile| |mantissa| |empty| - |isPlus| |status| |fintegrate| |lepol| |graphCurves| |eigenvector| - |infieldint| |e02def| |dilog| |quoByVar| |OMgetAttr| |filterUntil| - |leftRank| |primaryDecomp| |viewZoomDefault| |kernel| |roman| - |alternatingGroup| |terms| |stirling2| |qPot| |extendedResultant| - |tex| |sin| |options| |implies?| |select| |draw| |block| |OMputEndApp| - |OMserve| |level| |Nul| |rubiksGroup| |multiEuclidean| |leftUnit| - |result| |evaluateInverse| |cos| |setright!| |iicos| |meatAxe| - |whileLoop| |resize| |partialDenominators| |rightExactQuotient| - |newReduc| |coHeight| |numberOfComposites| |tan| - |solveLinearPolynomialEquation| |lagrange| |finiteBasis| - |primlimintfrac| |indicialEquation| |optimize| |expintfldpoly| |Ci| - |iterationVar| |extendedIntegrate| NOT |ScanFloatIgnoreSpacesIfCan| - |string| |cot| |factorSFBRlcUnit| |quasiRegular?| |dom| |nilFactor| - |pquo| |integrate| |rightMult| |chiSquare1| |factorList| |e01bgf| OR - |shuffle| |sec| |fTable| |pointPlot| |makeObject| |minordet| - |att2Result| |binomThmExpt| |exponents| |plotPolar| |has?| |maxIndex| - AND |minimumExponent| |csc| |selectAndPolynomials| |algebraicOf| - |pointColorDefault| |mkPrim| |getOrder| |dn| |cscIfCan| - |rationalPoints| |makeRecord| |d02cjf| |asin| |cot2trig| |moebius| - |setValue!| |iiacoth| |semiResultantEuclidean2| - |inverseIntegralMatrixAtInfinity| |coef| - |standardBasisOfCyclicSubmodule| |refine| |isPower| |closedCurve| - |preprocess| |acos| |Si| |imagi| |simplifyExp| |leftOne| - |createLowComplexityTable| |is?| |headReduced?| |thetaCoord| |randomR| - |atan| |merge| |digits| |generalTwoFactor| |nand| |separateDegrees| - |safeCeiling| |listConjugateBases| |mainCharacterization| - |radicalEigenvector| |title| |d02bbf| |areEquivalent?| |fixedDivisor| - |acot| |associatorDependence| |diagonalMatrix| |sumOfSquares| |iilog| - |zeroMatrix| |pushup| |c05adf| |writeByteIfCan!| |rangeIsFinite| - |OMgetBind| |OMputBind| |selectIntegrationRoutines| |asec| - |removeRedundantFactorsInPols| |evenInfiniteProduct| |alternative?| - |numeric| |viewport3D| |rightNorm| |eulerPhi| |green| |hue| |dfRange| - |d03eef| |integralLastSubResultant| |acsc| |product| |orbits| - |dmp2rfi| |iroot| |radical| |makeSeries| |c06ekf| |f02axf| |e| - |functionIsFracPolynomial?| |moebiusMu| |mapmult| |selectPDERoutines| - |sinh| |numberOfFractionalTerms| |patternMatchTimes| |setAdaptive| - |tanIfCan| |acothIfCan| |companionBlocks| |triangularSystems| - |factorsOfCyclicGroupSize| |matrixConcat3D| |cosh| |sin2csc| - |collectUpper| |enterPointData| |splitSquarefree| |antiAssociative?| - |relationsIdeal| |lexico| |mightHaveRoots| |Ei| |f04atf| |tree| * - |OMputAttr| |tanh| |simplifyPower| |copyInto!| |removeCoshSq| - |setsubMatrix!| |rationalPower| |OMputInteger| |mainVariables| - |graeffe| |OMUnknownSymbol?| |errorInfo| |coth| |factorsOfDegree| - |OMgetEndAttr| |OMbindTCP| |matrixGcd| |cycleSplit!| - |removeRedundantFactorsInContents| |rootOf| |schwerpunkt| |rotatez| - |elements| |sech| |pack!| |lex| |debug| |totalDegree| |derivative| - |augment| |factorial| |linearMatrix| |fortranComplex| - |semiLastSubResultantEuclidean| |optional?| |csch| |reducedSystem| - |qqq| D |nullSpace| |getMultiplicationTable| |transcendenceDegree| - |wronskianMatrix| |sample| |interval| |s17adf| |asinh| |insert!| - |setRealSteps| |lazyPseudoRemainder| |li| |calcRanges| |innerSolve| - |removeSuperfluousCases| |reverseLex| |roughUnitIdeal?| |setPosition| - |edf2df| |unrankImproperPartitions0| |acosh| |compactFraction| - |characteristic| |listLoops| |multinomial| |gderiv| - |differentialVariables| |f01qef| |primitive?| |numberOfComponents| - |setelt!| |atanh| |applyRules| |port| |nthExponent| |divisorCascade| - |Is| |entries| |createRandomElement| |factorAndSplit| |ldf2lst| - |node?| |permutationRepresentation| |acoth| - |createLowComplexityNormalBasis| |nullity| |unknown| |OMputObject| - |cyclicSubmodule| |supRittWu?| |tryFunctionalDecomposition?| |tValues| - |mapCoef| |pushdterm| |addPoint2| |Gamma| |asech| |pile| |orbit| - |viewPosDefault| |coercePreimagesImages| |extendIfCan| - |hypergeometric0F1| |genericLeftDiscriminant| |bag| |roughSubIdeal?| - |defineProperty| |jordanAlgebra?| |setref| |s21bdf| |triangular?| - |outlineRender| |c02agf| |setAdaptive3D| |scaleRoots| |normDeriv2| - |multiple| |characteristicSerie| |leftTraceMatrix| - |stoseInvertible?sqfreg| |mdeg| |subResultantsChain| - |invertibleElseSplit?| |build| |child| |alphanumeric?| |hyperelliptic| - |applyQuote| |degreeSubResultantEuclidean| |mainVariable| - |clearTheSymbolTable| |entry| |deleteRoutine!| |d02ejf| |intersect| - |OMsetEncoding| |hasPredicate?| |critMTonD1| |redPol| |dequeue!| - |redPo| |toseLastSubResultant| |zeroDim?| |print| |LazardQuotient| - |partition| |empty?| |qelt| |true| |maxPoints3D| |cycleTail| |cyclic| - |tanh2trigh| |complete| |expt| |taylorQuoByVar| |bsolve| |symmetric?| - |largest| |and| |collectQuasiMonic| |exteriorDifferential| |cAsech| - |readByteIfCan!| |ruleset| |makeEq| |cyclicEntries| |perfectNthRoot| - |stoseSquareFreePart| |orthonormalBasis| |xRange| |idealSimplify| - |tanAn| |exponential1| |f01qcf| |legendreP| |OMputError| |loopPoints| - |integerBound| |c05nbf| |hasTopPredicate?| |yRange| - |lazyIrreducibleFactors| |geometric| |palgintegrate| |swapRows!| - |dmpToHdmp| |SturmHabichtMultiple| |objects| |Beta| - |leastAffineMultiple| |finite?| |setClosed| |getOperands| |zRange| - SEGMENT |rotate| |basisOfLeftNucloid| |mat| |linearlyDependent?| - |FormatArabic| |suchThat| |base| |rightExtendedGcd| |map!| |c06gcf| - |multiset| |wholeRadix| |createMultiplicationMatrix| |setTopPredicate| - |iidsum| |lazyEvaluate| |factorSquareFreePolynomial| |symbol?| - |removeCosSq| |delete!| |UP2ifCan| |qsetelt!| |qualifier| - |integralCoordinates| |anticoord| |df2st| - |removeIrreducibleRedundantFactors| |sinhcosh| |setleft!| |gcdcofact| - |prefix| |polygon?| |binary| |modularGcd| |s17akf| |antiCommutator| - |recolor| |quatern| |c06ebf| |po| |dec| |color| |OMencodingXML| - |setchildren!| |expint| |legendre| |janko2| |baseRDEsys| |taylorIfCan| - |selectSumOfSquaresRoutines| |mapdiv| |tanQ| |getConstant| |subMatrix| - |commutator| |squareFreePart| |push!| |generators| |setRow!| - |unmakeSUP| |find| |approximants| |imaginary| |neglist| - |repeatUntilLoop| |subHeight| |paraboloidal| |pointSizeDefault| |lllp| - |condition| |cubic| |dimensions| |super| |move| |content| |llprop| - |acsch| |conical| |children| |top!| |yellow| |rk4a| |conjugates| - |besselI| |hclf| |d01anf| |PDESolve| |branchPoint?| |torsion?| - |numericIfCan| |gcdprim| |normInvertible?| |degreeSubResultant| - |tanh2coth| |concat| |middle| |distance| |bumprow| |someBasis| - |radicalRoots| |deref| |members| |indicialEquationAtInfinity| |dmpToP| - |factorSquareFree| |changeThreshhold| |alphabetic| |int| |e01sff| - |upperCase| |sturmSequence| |contains?| |makeYoungTableau| |cap| - |c02aff| |algebraicCoefficients?| |monicModulo| - |subResultantGcdEuclidean| |cos2sec| |symmetricProduct| |newTypeLists| - |prologue| |previous| |tower| |genericRightTrace| |maximumExponent| - |subSet| |stirling1| |hconcat| |chebyshevT| |irreducible?| |hdmpToDmp| - |e04gcf| |atanhIfCan| |inv| |tubePointsDefault| |sorted?| |aCubic| - |separateFactors| |weight| |property| |reduction| |sinhIfCan| |limit| - |buildSyntax| |ground?| |dimensionOfIrreducibleRepresentation| - |f04arf| |scalarMatrix| |eisensteinIrreducible?| - |generalInfiniteProduct| |solveid| |spherical| |subPolSet?| - |printInfo!| |ground| |moduloP| |leftRankPolynomial| |operator| - |radicalOfLeftTraceForm| |seriesToOutputForm| - |solveLinearPolynomialEquationByRecursion| |makeViewport2D| - |continuedFraction| |setStatus!| |primitivePart!| |setButtonValue| - |smith| |unary?| |qroot| |leadingMonomial| |infLex?| - |halfExtendedResultant1| |strongGenerators| |printStats!| |front| - |inconsistent?| |hostPlatform| |units| |flexible?| |s17agf| |exquo| - |LowTriBddDenomInv| |doubleDisc| |cycleLength| |leadingCoefficient| - |null?| |complexNumeric| |setleaves!| |pleskenSplit| |besselY| |sin?| - |csch2sinh| |comparison| |corrPoly| |localReal?| |numerator| - |getProperties| |div| |leadingCoefficientRicDE| |primitiveMonomials| - |setColumn!| |reflect| |moduleSum| |retractable?| |range| |kernels| - |denomLODE| |nextsousResultant2| |quo| |primPartElseUnitCanonical!| - |startStats!| |reductum| |infinite?| |equivOperands| - |sizePascalTriangle| |element?| |isAbsolutelyIrreducible?| |output| - |parabolic| |constantKernel| |order| |numberOfNormalPoly| |leftGcd| - |useSingleFactorBound| |univariate| |showTheRoutinesTable| |contours| - |logGamma| |formula| |putGraph| |mulmod| |trim| |compile| |cAsinh| - |symmetricGroup| |graphState| |rem| |variable?| |minPoints| - |lazyPseudoDivide| |yCoordinates| |target| |df2ef| |code| |f02agf| - |minColIndex| |tan2trig| |normalise| |summation| |karatsubaOnce| - |ratPoly| |ReduceOrder| |seriesSolve| |sPol| |quotient| - |listYoungTableaus| |tensorProduct| |radicalEigenvalues| |outputFixed| - |groebgen| |times!| |univariatePolynomialsGcds| |factor| |htrigs| BY - |measure2Result| |s01eaf| |raisePolynomial| |pr2dmp| |represents| - |writeLine!| |genericRightNorm| |ksec| |drawToScale| |viewPhiDefault| - |s19aaf| |sqrt| |goodPoint| |complexRoots| |multiEuclideanTree| - |commutative?| |unitNormal| |cCoth| |nrows| |nextNormalPoly| - |irreducibleFactors| |pushuconst| |s17aef| |real| |acotIfCan| - |critBonD| |linearPolynomials| |any?| |lifting1| |palgextint0| - |positiveSolve| |ncols| |pointColor| |nextPrimitivePoly| - |splitConstant| |ode| |complexIntegrate| |imag| |setProperty| |escape| - |singularAtInfinity?| |absolutelyIrreducible?| |typeLists| |delete| - |unaryFunction| |directProduct| |adaptive| |coerceS| |toseInvertible?| - |critpOrder| |univcase| |rootSplit| |signAround| |extendedint| - |minPol| |irreducibleRepresentation| |polCase| |validExponential| - |basisOfRightAnnihilator| |modularGcdPrimitive| |cot2tan| - |unitsColorDefault| |push| |rightAlternative?| |s13acf| |diag| |lhs| - |definingEquations| |tan2cot| |insertBottom!| |leftRecip| |dAndcExp| - |frst| |destruct| |autoReduced?| |constantOperator| |df2fi| - |padicFraction| |realZeros| |rhs| |genus| |curve?| |headRemainder| - |decrease| |over| |totalfract| |OMreceive| |clipWithRanges| - |moreAlgebraic?| |matrixDimensions| |selectMultiDimensionalRoutines| - |unitNormalize| |listOfMonoms| |particularSolution| |perfectNthPower?| - |traverse| |polyRicDE| |extractProperty| |antiCommutative?| |tablePow| - |pToDmp| |binomial| |fortranLiteral| |rowEchelon| - |nextLatticePermutation| |elColumn2!| |setStatus| |bitTruth| - |henselFact| |addmod| |minrank| |interpretString| |quasiComponent| - |rewriteIdealWithQuasiMonicGenerators| |simplify| |localUnquote| - |HenselLift| |increase| |node| |convergents| |cylindrical| |monomial| - |expressIdealMember| |bindings| |fortranLogical| |lexTriangular| - |polyred| |list?| |numberOfChildren| |resultant| |setelt| - |oblateSpheroidal| |realElementary| |combineFeatureCompatibility| - |initial| |multivariate| |listRepresentation| |supersub| |axes| - |domainOf| |divergence| |c06gqf| |completeEchelonBasis| - |mainCoefficients| |s17def| |scanOneDimSubspaces| |basisOfCenter| - |pmComplexintegrate| |variables| |selectOrPolynomials| |member?| - |bubbleSort!| |nary?| |reindex| |cycleEntry| |createPrimitivePoly| - |figureUnits| |iiabs| |copy| |OMconnectTCP| |rdHack1| |intensity| - |euclideanNormalForm| |atoms| |idealiserMatrix| |LyndonBasis| - |FormatRoman| |e02daf| |currentScope| |substring?| |outputAsScript| - |oneDimensionalArray| |genericRightTraceForm| |fortranTypeOf| - |OMputAtp| |string?| |log10| |leftQuotient| - |indiceSubResultantEuclidean| |hspace| |maxRowIndex| |getGraph| - |truncate| |drawComplexVectorField| |unparse| |normalElement| |imagE| - |seed| |match?| |bitand| |hexDigit| |sortConstraints| |tanhIfCan| - |top| |wordInStrongGenerators| |acscIfCan| |suffix?| |autoCoerce| - |and?| |solid| |rst| |fixedPoints| |iitan| |crest| |bitior| |blue| - |clipBoolean| |changeNameToObjf| |continue| |harmonic| |cCsc| - |mergeDifference| |prindINFO| |optpair| |halfExtendedSubResultantGcd1| - |laurentIfCan| |taylor| |semiResultantEuclideannaif| |width| - |leftAlternative?| |cardinality| |stronglyReduced?| |fglmIfCan| - |LyndonWordsList1| |e01saf| |prefix?| |inspect| |mainMonomials| - |rightDiscriminant| |OMconnOutDevice| |rightPower| |laurent| - |basisOfRightNucloid| |dihedral| |fullPartialFraction| |makeCrit| - |upperCase!| |inGroundField?| |doublyTransitive?| |maxColIndex| - |clipPointsDefault| |wholePart| |critM| |puiseux| |curveColorPalette| - |getIdentifier| |linSolve| |s17dlf| |getRef| |withPredicates| |iiperm| - |jacobi| |readLineIfCan!| |sdf2lst| |plenaryPower| |iicsch| |zerosOf| - |singular?| |stoseLastSubResultant| |s19acf| |chebyshevU| - |subtractIfCan| |leastPower| |movedPoints| |f07adf| = |equation| - |rationalFunction| |associatedEquations| |initTable!| |ipow| - |irreducibleFactor| |minPoints3D| |OMParseError?| |lazyPquo| - |fortranCompilerName| |pop!| |zCoord| |poisson| |logical?| |repSq| - |genericRightDiscriminant| |e01sbf| |genericLeftTraceForm| |e01bff| - |unitCanonical| |hdmpToP| |blankSeparate| < |padecf| |row| |optional| - |operators| |badNum| |minGbasis| |increment| |infix?| |resetBadValues| - |say| |symbolTableOf| |OMputEndBind| > |pair?| |plot| |monomial?| - |mask| |transpose| |hermiteH| |monicCompleteDecompose| |collect| - |asinIfCan| |iipow| |elliptic?| <= |minRowIndex| |setImagSteps| - |leftFactorIfCan| |callForm?| |implies| |thenBranch| |dark| - |distdfact| |wordsForStrongGenerators| |s13aaf| |getMatch| >= - |stFunc1| |d01apf| |B1solve| |shellSort| |isList| - |resultantEuclideannaif| |hcrf| |leaf?| |cycles| |noLinearFactor?| - |palginfieldint| |ratpart| |squareFreePolynomial| |nullary| |xor| - |interReduce| |countRealRoots| |sayLength| |connect| - |totalDifferential| |pointLists| |every?| |prime?| - |viewWriteAvailable| |currentSubProgram| |match| |byte| - |shanksDiscLogAlgorithm| |unit?| |resultantReduitEuclidean| - |rationalPoint?| |name| |skewSFunction| |trapezoidal| |rroot| - |eigenMatrix| + |setMinPoints3D| |nextsubResultant2| |fracPart| - |quadraticNorm| |bivariatePolynomials| |diagonals| |cAtanh| |body| - |exptMod| |lowerCase| |reset| |wholeRagits| |roughBase?| - - |allRootsOf| |viewSizeDefault| |ocf2ocdf| |parabolicCylindrical| - |hitherPlane| |totalLex| |sh| |basisOfLeftNucleus| |binaryTree| |cExp| - |firstDenom| |divideIfCan| / |rombergo| |removeZero| |constructorName| - |generateIrredPoly| |equality| |sumOfDivisors| |sumSquares| |f02awf| - |wreath| |rationalApproximation| |showArrayValues| |write| - |outputArgs| |nextPartition| |mainValue| |setEpilogue!| - |createNormalPrimitivePoly| |rightZero| |meshPar1Var| |qinterval| - |components| |ratDenom| |red| |save| |perfectSquare?| |conjugate| - |definingPolynomial| |e02bbf| |showClipRegion| |elRow2!| - |algebraicDecompose| |e02gaf| |screenResolution3D| |lift| - |mainMonomial| |insertTop!| |expintegrate| |selectPolynomials| - |constantOpIfCan| |s18def| |objectOf| |removeSinSq| |mapGen| - |ScanArabic| |complexEigenvalues| |reduce| |squareFreeLexTriangular| - |cCos| |purelyAlgebraic?| |heap| |complexLimit| |flagFactor| - |subscriptedVariables| |quadratic?| |constantToUnaryFunction| - |leftMinimalPolynomial| |subNodeOf?| |completeEval| - |toseInvertibleSet| |tableForDiscreteLogarithm| |imagk| |s18aef| - |socf2socdf| |makeSin| |multMonom| |OMsupportsCD?| |stopTableInvSet!| - |f02bbf| |integralBasis| |prolateSpheroidal| |completeHensel| - |OMputString| |sinIfCan| |monicRightFactorIfCan| |lastSubResultant| - |constant| |heapSort| |numberOfCycles| |discreteLog| LODO2FUN - |chineseRemainder| |countRealRootsMultiple| |minimize| - |identityMatrix| |center| |cTanh| |prepareDecompose| - |balancedFactorisation| |halfExtendedResultant2| |squareFreePrim| - |semiResultantEuclidean1| |leviCivitaSymbol| |makeSUP| |primes| - |s21bbf| |OMputEndError| |adjoint| - |removeRoughlyRedundantFactorsInPol| |mapDown!| |squareFreeFactors| - |invertibleSet| |insert| |ddFact| |rename| |iisech| |primintegrate| - |infix| |outputGeneral| |antisymmetricTensors| |functionIsOscillatory| - |nil| |mainPrimitivePart| |OMconnInDevice| |showRegion| |setfirst!| - |lazyGintegrate| |extract!| |t| |clearCache| |commonDenominator| - |genericPosition| |rectangularMatrix| |btwFact| |f01bsf| - |monicDecomposeIfCan| |mainContent| |inR?| |linkToFortran| |exprToXXP| - |transcendent?| |rotate!| |radicalSolve| |copy!| |divideExponents| - |sizeLess?| |reduceBasisAtInfinity| |shiftRoots| |eq| - |showScalarValues| |setTex!| |biRank| |flexibleArray| |OMgetSymbol| - |delta| |cotIfCan| |retract| |pointData| |approximate| - |subQuasiComponent?| Y |c06fqf| |iter| |An| |OMlistCDs| |OMgetEndBind| - |maxrow| |modularFactor| |e01bef| |roughEqualIdeals?| |mathieu22| - |modifyPointData| |diagonal| |localIntegralBasis| |drawStyle| |latex| - |weierstrass| |SturmHabichtCoefficients| |close| |clipParametric| - |exprHasWeightCosWXorSinWX| |setprevious!| |GospersMethod| |eval| - |setFieldInfo| |powern| |setVariableOrder| |nextSublist| |f04asf| - |algebraicVariables| |cLog| |crushedSet| |cAcoth| |rootPoly| - |nonLinearPart| |display| |ode1| |unit| |factorByRecursion| |e02aef| - |returns| |leftFactor| |leadingIndex| |mapSolve| |deriv| |kind| - |simpleBounds?| |nativeModuleExtension| |omError| |component| - |cosIfCan| |retractIfCan| |minset| |clearDenominator| |limitPlus| - |decreasePrecision| |exp| |op| |maxdeg| |enterInCache| |iiasech| - |lookup| |lambda| |cAcsch| |leftExtendedGcd| |dim| |lazyPrem| - |ListOfTerms| |besselK| |Frobenius| |eq?| |oddInfiniteProduct| - |addiag| |bipolar| |d01asf| |Aleph| |mappingAst| |resetVariableOrder| - |input| |initiallyReduce| |leftDiscriminant| |tab1| - |ellipticCylindrical| |external?| |showSummary| |isobaric?| - |OMgetEndBVar| |exists?| |factorFraction| |fortranCharacter| |library| - |sparsityIF| |quadraticForm| |iiexp| |OMgetString| |fixedPoint| - |normalize| |createGenericMatrix| |f01maf| |Vectorise| |f02wef| - |showAttributes| |pastel| |swap| |e02zaf| |zeroOf| |mix| - |multiplyExponents| |singRicDE| |resultantEuclidean| |properties| - |OMgetEndError| |host| |stoseIntegralLastSubResultant| |headAst| - |transform| |ptree| |LagrangeInterpolation| |alphanumeric| - |OMlistSymbols| |translate| |solid?| |term| |getVariableOrder| - |linear?| |set| |equiv| |removeSuperfluousQuasiComponents| |lp| - |eigenvalues| |boundOfCauchy| |accuracyIF| |rk4qc| |generalSqFr| |map| - |point| |diagonal?| |gethi| |nsqfree| |selectOptimizationRoutines| - |atom?| |debug3D| |binaryTournament| |copies| |separate| |bit?| - |solve| |getStream| |OMencodingSGML| |rightRegularRepresentation| - |setFormula!| |e02agf| |approxNthRoot| |normal?| |complexNumericIfCan| - |topFortranOutputStack| |structuralConstants| |iicosh| |sum| |bitCoef| - |numberOfDivisors| |predicate| |update| |series| |weakBiRank| - |numberOfHues| |second| |drawCurves| |prinb| |charpol| |rdregime| - |xCoord| |randnum| |outputSpacing| |aspFilename| |s18adf| |third| - |vark| |splitDenominator| |f2df| |prinpolINFO| |firstUncouplingMatrix| - |convert| |goto| |e04jaf| |negative?| |iExquo| |ricDsolve| - |setMinPoints| |e01daf| |f02adf| |leadingExponent| |OMgetFloat| - |selectNonFiniteRoutines| |minimumDegree| - |removeRoughlyRedundantFactorsInPols| |localAbs| |interpret| |s18aff| - |semicolonSeparate| |min| |iiacot| |stiffnessAndStabilityOfODEIF| - |integralMatrix| |bipolarCylindrical| |iiatanh| |evenlambert| |d01fcf| - |revert| |arguments| |phiCoord| |bringDown| |d02raf| |triangSolve| - |packageCall| |constantIfCan| |laguerreL| |getCode| |infiniteProduct| - |leftPower| |position| |leadingIdeal| |cAcsc| |show| |factors| |queue| - |frobenius| |printHeader| |equiv?| |forLoop| |d01ajf| - |groebnerFactorize| |showAll?| |OMputEndAtp| |bumptab1| |backOldPos| - |monomialIntegrate| |inrootof| |in?| |antisymmetric?| |void| - |parameters| |infinityNorm| |trace| |alternating| UTS2UP - |intcompBasis| |mathieu23| |adaptive3D?| |mainVariable?| |shiftLeft| - |mainSquareFreePart| |totolex| |f04faf| |setErrorBound| |tube| - |ratDsolve| |nthFlag| |asechIfCan| |baseRDE| |realRoots| |algebraic?| - |expenseOfEvaluation| |physicalLength!| |ceiling| |mathieu11| - |splitNodeOf!| |semiSubResultantGcdEuclidean2| |compBound| |leftMult| - |swap!| |s17ajf| |leftCharacteristicPolynomial| |setScreenResolution| - |clearTable!| |child?| |f07fef| |OMgetEndObject| |mkIntegral| |psolve| - |superHeight| |internalIntegrate0| |coefficient| |minus!| |f02xef| - |binarySearchTree| |expandTrigProducts| |atanIfCan| |monomRDE| GF2FG - |mapBivariate| |curve| |s19adf| |octon| |nextIrreduciblePoly| - |consnewpol| |surface| |interpolate| |replaceKthElement| - |startPolynomial| |closedCurve?| |makeVariable| |physicalLength| - |d02gaf| |ramifiedAtInfinity?| |internalSubQuasiComponent?| |modulus| - |degreePartition| |notelem| |linGenPos| |elem?| |simpsono| |romberg| - |extend| |expr| |imagI| |iCompose| |rur| |abelianGroup| |slash| - |postfix| |rightUnits| |univariatePolynomial| |s17dhf| |OMgetError| - |nodeOf?| |regularRepresentation| |showTheIFTable| |parts| - |returnType!| |removeDuplicates!| |normalDenom| |npcoef| - |complementaryBasis| |resultantnaif| |univariatePolynomials| - |eigenvectors| |trailingCoefficient| |integralMatrixAtInfinity| - |rewriteIdealWithHeadRemainder| |subspace| |mapMatrixIfCan| |compdegd| - |branchIfCan| |ord| |solveLinear| |resetAttributeButtons| |light| - |variable| |vspace| |getDatabase| |quartic| |subst| - |complexEigenvectors| |ODESolve| |secIfCan| |kovacic| |merge!| - |loadNativeModule| |iterators| |homogeneous?| - |setLegalFortranSourceExtensions| |acoshIfCan| |iibinom| |elementary| - |modifyPoint| |printCode| |upDateBranches| |rootSimp| - |sylvesterMatrix| |commaSeparate| |palglimint| |identification| - |viewDefaults| |screenResolution| |oddintegers| |dequeue| |chvar| - |deepCopy| |error| |next| |e04fdf| |OMputBVar| |plusInfinity| |low| - |uniform| |ode2| |bottom!| |logpart| |adaptive?| |assert| - |knownInfBasis| |magnitude| |lieAdmissible?| |OMreadFile| F2FG - |minusInfinity| |rightQuotient| |init| |odd?| - |removeRoughlyRedundantFactorsInContents| |reverse| |s17dcf| |c06fuf| - |OMsend| |binding| |degree| |select!| |monicLeftDivide| |insertMatch| - |iiatan| |imagK| |rewriteSetWithReduction| |findBinding| |scan| - |mathieu12| |basisOfLeftAnnihilator| |positive?| |datalist| - |badValues| |iiacsch| |e02bef| |powmod| FG2F |discriminant| - |listBranches| |endSubProgram| |ScanFloatIgnoreSpaces| |module| - |concat!| |getSyntaxFormsFromFile| |iteratedInitials| |lSpaceBasis| - |complexSolve| |rischDEsys| |determinant| |pointColorPalette| - |PollardSmallFactor| |sup| |repeating| |traceMatrix| |reduceLODE| - |linearlyDependentOverZ?| |type| |rightRemainder| - |commutativeEquality| |e02adf| |f04qaf| |setPredicates| - |beauzamyBound| |fortranCarriageReturn| |real?| |colorFunction| - |myDegree| |hermite| |normFactors| |LazardQuotient2| |conditionP| - |computeCycleEntry| |cAcosh| |rank| |f02aff| |imagj| |rightLcm| - |fractRagits| |aLinear| |dimension| |segment| |initiallyReduced?| - |findCycle| |integers| |extractIfCan| |setMaxPoints| |OMwrite| - |lexGroebner| |lastSubResultantEuclidean| |varselect| |schema| - |removeSinhSq| |generalizedContinuumHypothesisAssumed?| |leftNorm| - |f02bjf| |noKaratsuba| |mathieu24| |pToHdmp| |monic?| |euler| - |possiblyInfinite?| |eyeDistance| |OMputEndAttr| |OMunhandledSymbol| - |epilogue| |iflist2Result| |pole?| |rationalIfCan| |clip| |fill!| - |userOrdered?| |lfextendedint| |sub| |s17ahf| |deepestInitial| - |groebner| |coshIfCan| |zero?| |dimensionsOf| |OMsupportsSymbol?| - |algSplitSimple| |rischDE| |iFTable| |cons| |airyBi| |lazy?| |iisin| - |tableau| |power!| |firstNumer| |dihedralGroup| |partialNumerators| - |doubleComplex?| |lists| |collectUnder| |linearPart| |s14aaf| - |euclideanGroebner| |nlde| |virtualDegree| |oddlambert| |aQuadratic| - |createPrimitiveElement| |inverseLaplace| |sort| |factorGroebnerBasis| - |unitVector| |leadingTerm| |radPoly| |internalLastSubResultant| - |tanNa| |makeTerm| |lyndon?| |upperCase?| |representationType| - |definingInequation| |stopMusserTrials| |unvectorise| |directSum| - |mesh| |parametersOf| |primextintfrac| |viewDeltaXDefault| - |arrayStack| |redpps| |generalLambert| |points| |palgint| |droot| - |stoseInvertible?| |nextPrimitiveNormalPoly| |primlimitedint| - |exprToGenUPS| |setOfMinN| |source| |univariate?| |primeFrobenius| - |getOperator| |selectODEIVPRoutines| |numberOfImproperPartitions| - |vedf2vef| |rational?| |float?| |besselJ| |iicot| |belong?| - |precision| |denomRicDE| |partitions| |random| |rightGcd| - |expandPower| |sechIfCan| |recoverAfterFail| |mr| |OMputApp| - |viewWriteDefault| |e02ajf| |factorset| |froot| |remainder| - |createNormalElement| |OMreadStr| |specialTrigs| |e02akf| - |rightCharacteristicPolynomial| |null| |parseString| |f04maf| - |OMmakeConn| |lflimitedint| |s13adf| |f01qdf| |s18dcf| |f02ajf| |case| - |andOperands| |contractSolve| |prefixRagits| |algDsolve| - |completeHermite| |bright| |symbolTable| |digamma| |parent| - |uniform01| |Zero| |mirror| |symmetricPower| |KrullNumber| |sts2stst| - |semiSubResultantGcdEuclidean1| |tanSum| |brillhartTrials| - |kroneckerDelta| |checkForZero| |pseudoDivide| |rk4| |One| - |complexZeros| |linearAssociatedExp| |universe| - |branchPointAtInfinity?| |taylorRep| |pushFortranOutputStack| - |ramified?| |swapColumns!| |ridHack1| |opeval| |changeMeasure| - |nthCoef| |popFortranOutputStack| |stosePrepareSubResAlgo| |rspace| - |varList| |inf| |s15adf| |OMgetEndApp| |internalSubPolSet?| |innerint| - |curveColor| |gbasis| |e01sef| |makingStats?| |mindegTerm| |fmecg| - |outputAsFortran| |lambert| |exprToUPS| |sizeMultiplication| |palgRDE| - |explogs2trigs| |constantRight| |tRange| |readIfCan!| |d03edf| - |leftDivide| |bezoutDiscriminant| |iprint| |categories| |parametric?| - |coefficients| |rootRadius| |constantLeft| |compiledFunction| - |currentCategoryFrame| |selectsecond| |nextColeman| |key| - |var1StepsDefault| |changeBase| |elt| |generalizedEigenvectors| - |explicitlyFinite?| |critB| |ScanRoman| |outputMeasure| |divideIfCan!| - |fortranReal| |superscript| |pmintegrate| |getCurve| |palgint0| - |numberOfComputedEntries| |zeroSquareMatrix| |prem| |filename| - |clearTheFTable| |innerEigenvectors| |sequences| |exQuo| - |integerIfCan| |trueEqual| |palgRDE0| GE |mainKernel| - |genericRightMinimalPolynomial| |setPoly| |subresultantVector| |prime| - |not?| |controlPanel| |digit| |useEisensteinCriterion| - |insertionSort!| GT |any| |computeCycleLength| |operation| |quickSort| - |computeBasis| |overbar| |redmat| |parse| |iiasinh| |groebner?| - |ef2edf| |coefChoose| LE |viewThetaDefault| |cSech| |paren| - |semiDiscriminantEuclidean| |closeComponent| |algintegrate| - |primPartElseUnitCanonical| |zeroDimPrimary?| |lfextlimint| LT |label| - |diff| |outputList| |possiblyNewVariety?| |twoFactor| - |createNormalPoly| |probablyZeroDim?| |s21bcf| |variationOfParameters| - |charthRoot| |signatureAst| |complex| |transcendentalDecompose| - |numerators| |option?| |e02baf| |or?| |OMopenFile| - |extendedSubResultantGcd| |reciprocalPolynomial| |ran| |curryRight| - |basis| |getMeasure| |printStatement| |f02fjf| - |semiDegreeSubResultantEuclidean| |makeFR| |normal01| |sincos| - |digit?| |identity| |setProperties!| |fullDisplay| |goodnessOfFit| - |birth| |lquo| |routines| |quasiMonic?| |returnTypeOf| |iifact| - |primextendedint| |f07aef| |plus| |OMputEndObject| - |numberOfPrimitivePoly| |vector| |firstSubsetGray| |drawComplex| - |trunc| |fortranDoubleComplex| |keys| |var1Steps| |innerSolve1| - |distFact| |perspective| |numberOfMonomials| |differentiate| - |limitedint| |iiacos| |generic?| UP2UTS |doubleRank| |bivariate?| - |lowerCase?| |credPol| |currentEnv| |cycleRagits| |lfintegrate| - |measure| |quote| |coleman| |groebSolve| |normalizedDivide| |basicSet| - |iiacsc| |pdf2df| |e01baf| |monomRDEsys| |newLine| |imports| |s20acf| - |lazyPremWithDefault| |realEigenvalues| |times| |OMputEndBVar| - |lowerCase!| |minIndex| |decimal| |c06eaf| |argscript| |search| - |meshFun2Var| |index| |f01brf| |univariateSolve| |RittWuCompare| - |invmultisect| |unravel| |fillPascalTriangle| |bandedHessian| - |addPoint| |readable?| |shallowExpand| |setCondition!| - |normalizeIfCan| |quotientByP| |isMult| |s14abf| |simplifyLog| - |graphStates| |option| |call| |predicates| |symFunc| |squareFree| - |basisOfNucleus| |numericalIntegration| |subscript| |iidprod| |arity| - |iicsc| |stiffnessAndStabilityFactor| |appendPoint| |conjug| - |stopTable!| |list| |monom| |makeop| |pair| |pascalTriangle| |back| - |number?| |complex?| |complement| |pow| |car| |SturmHabichtSequence| - |satisfy?| |rquo| |constDsolve| |basisOfCentroid| |prinshINFO| - |coerceL| |singularitiesOf| |pushdown| |diophantineSystem| |cdr| - |internalZeroSetSplit| |declare| |setEmpty!| |shallowCopy| - |lfinfieldint| |testModulus| |stopTableGcd!| |arg1| |common| - |anfactor| |nextPrime| |setDifference| |e02ddf| |close!| - |solveLinearlyOverQ| |checkPrecision| |tab| |fractRadix| - |HermiteIntegrate| |changeWeightLevel| |arg2| |function| - |setIntersection| |setOrder| |nthFactor| |yCoord| |prevPrime| - |weighted| |max| |cyclotomic| |outputFloating| |exponent| |untab| - |cartesian| |addBadValue| |reify| |setUnion| |morphism| |ignore?| - |identitySquareMatrix| |rightRank| |numberOfVariables| |cCsch| - |rightTrim| |leaves| |conditions| |apply| |pseudoQuotient| - |extractPoint| |listOfLists| |associative?| |numberOfFactors| - |critMonD1| |colorDef| |bat1| |viewpoint| |leftTrim| |abs| |iiacosh| - |iiGamma| |perfectSqrt| |clearTheIFTable| |OMclose| - |linearAssociatedLog| |brillhartIrreducible?| |LiePoly| |e04ucf| - |trapezoidalo| |principalIdeal| |size| |getButtonValue| |pureLex| - |intermediateResultsIF| |conditionsForIdempotents| |e02dcf| - |toseSquareFreePart| |reseed| |cAtan| |s19abf| |idealiser| - |extractIndex| |lintgcd| |extendedEuclidean| |cRationalPower| |nodes| - |log| |trace2PowMod| |explicitEntries?| |jacobian| |sylvesterSequence| - |rules| |split!| |polarCoordinates| |expandLog| |internalIntegrate| - |numFunEvals| |makeSketch| |polynomialZeros| |simpson| |first| - |increasePrecision| |clipSurface| |listexp| |rangePascalTriangle| - |messagePrint| |factorSquareFreeByRecursion| |inverseIntegralMatrix| - |qfactor| |pattern| |rest| |extensionDegree| |var2Steps| |s14baf| - |pushucoef| |normalizedAssociate| |rule| |Lazard| - |stoseInternalLastSubResultant| |reorder| |key?| |substitute| |f02aef| - |setLabelValue| |createMultiplicationTable| |setPrologue!| - |numberOfOperations| |makeCos| |submod| |polyRDE| |removeDuplicates| - |hasHi| |OMputSymbol| |reduceByQuasiMonic| |modTree| |OMputVariable| - |certainlySubVariety?| |stripCommentsAndBlanks| - |integralBasisAtInfinity| |zeroSetSplitIntoTriangularSystems| |e04naf| - |torsionIfCan| |expenseOfEvaluationIF| |polygon| |bombieriNorm| - |OMopenString| |insertRoot!| |exprex| |stoseInvertibleSetreg| |f04mcf| - |/\\| |lcm| |elliptic| |changeVar| |relerror| |message| - |constantCoefficientRicDE| |decompose| |d02kef| |rightScalarTimes!| - |\\/| |OMgetApp| |presuper| |chainSubResultants| |squareMatrix| - |resetNew| |addMatchRestricted| |selectFiniteRoutines| |id| |rowEch| - |showAllElements| |RemainderList| |append| |principal?| |f2st| - |errorKind| |toroidal| |trigs| |permanent| |exprHasLogarithmicWeights| - |writable?| |gcd| |startTable!| |maxrank| |showTheSymbolTable| - |palgLODE0| |s21baf| |table| |inverse| |f01ref| |hasoln| |false| - |iiasec| |discriminantEuclidean| |infRittWu?| |se2rfi| |fixPredicate| - |setProperty!| |new| |pomopo!| |removeSquaresIfCan| |isOp| - |extractSplittingLeaf| |rotatey| |pdf2ef| |f01rcf| |setvalue!| - |polygamma| |character?| |cup| |symmetricDifference| |curry| |stFuncN| - |alphabetic?| |s17dgf| |mindeg| |printInfo| |setAttributeButtonStep| - |test| |lowerPolynomial| |LiePolyIfCan| |bivariateSLPEBR| - |subResultantGcd| |zero| |clearFortranOutputStack| |deepestTail| - |comp| |shufflein| |invertIfCan| |#| |getMultiplicationMatrix| - |distribute| |palglimint0| |infieldIntegrate| |quoted?| |inc| |entry?| - |cyclicGroup| |putColorInfo| |setMaxPoints3D| |endOfFile?| |OMgetType| - |createThreeSpace| |And| |generalizedEigenvector| |laplacian| - |composite| |hessian| |factorOfDegree| |rootOfIrreduciblePoly| - |OMgetBVar| |direction| |open?| |Or| |root?| |binaryFunction| - |addPointLast| |lazyIntegrate| |twist| |e02bcf| |OMencodingUnknown| - |rCoord| |symmetricTensors| |Not| |sqfree| |rootsOf| |imagJ| |remove| - |stack| |polyPart| |factorials| |multisect| |removeZeroes| - |changeName| |getBadValues| |bitLength| |mkcomm| |leftRemainder| - |normalizeAtInfinity| |pdct| |prod| |zeroDimensional?| - |quasiMonicPolynomials| |last| |resultantReduit| |weights| - |shiftRight| |tanintegrate| ~= |partialFraction| |nthRootIfCan| - |assoc| |left| |balancedBinaryTree| |UnVectorise| |zeroSetSplit| - |e04dgf| |characteristicSet| |saturate| |f01mcf| |coerce| |csc2sin| - |right| |composites| |cycleElt| |term?| |separant| |double?| - |construct| RF2UTS |intPatternMatch| |pseudoRemainder| |slex| - |setProperties| |reducedDiscriminant| |elRow1!| |bandedJacobian| - |LyndonWordsList| |trivialIdeal?| |roughBasicSet| |lfunc| - |cyclotomicDecomposition| |rational| |divisor| |s18acf| - |symmetricSquare| |SFunction| |rightFactorIfCan| |ravel| |aromberg| - |systemSizeIF| |vertConcat| |leftScalarTimes!| |d01bbf| |Lazard2| - |reshape| |assign| |inRadical?| |cAsec| |testDim| |updateStatus!| ** - |read!| |integralAtInfinity?| |inverseColeman| |central?| |tubeRadius| - |lllip| |square?| |dominantTerm| |outputForm| |rootKerSimp| |log2| - |semiIndiceSubResultantEuclidean| |toScale| |useEisensteinCriterion?| - |internalDecompose| |sign| |duplicates| |bfEntry| - |unprotectedRemoveRedundantFactors| |rootBound| EQ |edf2efi| - |useNagFunctions| |ffactor| |ptFunc| |mainForm| |bfKeys| |charClass| - |e02dff| |subresultantSequence| |rightUnit| |pade| |d01gbf| - |maxPoints| |d01gaf| |ranges| |rightRecip| |makeFloatFunction| - |subNode?| |generic| |indices| |normalDeriv| |normalized?| |nthRoot| - |squareTop| |root| |f04jgf| |printTypes| |c06ecf| |readLine!| - |deleteProperty!| |updatD| |flatten| |e01bhf| |radix| |acosIfCan| - |symbol| |sn| |matrix| |s20adf| |numericalOptimization| |externalList| - |denominators| |trigs2explogs| |finiteBound| |headReduce| - |OMgetVariable| |expression| |reopen!| |rightFactorCandidate| - |countable?| |zoom| |generalizedContinuumHypothesisAssumed| |bits| - |coerceImages| |rk4f| |chiSquare| |integer| |totalGroebner| - |splitLinear| |tryFunctionalDecomposition| |gradient| |permutation| - |s17acf| |groebnerIdeal| |reducedQPowers| |quasiAlgebraicSet| - |relativeApprox| |complexExpand| |recip| |compound?| |showTheFTable| - |enumerate| |isQuotient| |evaluate| |nextItem| |constant?| |signature| - |integer?| |cTan| |one?| |hash| |axesColorDefault| |e04mbf| |typeList| - |mergeFactors| |singleFactorBound| |compose| - |noncommutativeJordanAlgebra?| |cn| |count| |cPower| - |unrankImproperPartitions1| |extractClosed| |makeMulti| |power| - |meshPar2Var| |createPrimitiveNormalPoly| - |semiResultantReduitEuclidean| |exactQuotient!| |not| |systemCommand| - |check| |genericLeftNorm| |gramschmidt| |fortranDouble| |midpoint| - |f04axf| |cschIfCan| |round| |newSubProgram| |scale| |expPot| - |vconcat| |cyclicEqual?| |fixedPointExquo| |mpsode| |bezoutMatrix| - |dioSolve| |gcdPrimitive| |double| |generalizedInverse| |freeOf?| - |minimalPolynomial| |computeInt| |complexElementary| |mkAnswer| |nor| - |height| |quadratic| |makeViewport3D| |bumptab| |kmax| |normal| - |characteristicPolynomial| |reduced?| |tubeRadiusDefault| - |quasiRegular| |iisinh| |fprindINFO| |computePowers| |triangulate| - |outerProduct| |fortranLiteralLine| |leader| |d01aqf| |associates?| - |csubst| |cyclotomicFactorization| |rarrow| |rightMinimalPolynomial| - |mapExponents| |e02ahf| |floor| |OMgetObject| |even?| |subset?| - |rootPower| |df2mf| |restorePrecision| |algebraicSort| |coth2tanh| - |initials| |directory| |dflist| |mapExpon| |medialSet| - |partialQuotients| |sumOfKthPowerDivisors| |overlap| |doubleResultant| - |optAttributes| |iisqrt3| |fractionFreeGauss!| |rightDivide| |point?| - |leadingSupport| |monomialIntPoly| |iomode| |jacobiIdentity?| |cSin| - |internalInfRittWu?| |highCommonTerms| |getProperty| |euclideanSize| - |cCot| |repeating?| |palgextint| |nothing| |approxSqrt| |makeUnit| - |const| |declare!| |LyndonCoordinates| |primeFactor| |column| - |extractBottom!| |OMputFloat| |fortranLinkerArgs| |sort!| |laguerre| - |cond| |high| |cyclePartition| |rightOne| |setScreenResolution3D| - |cycle| |rename!| |basisOfMiddleNucleus| |coordinate| |norm| |brace| - |karatsuba| |factorPolynomial| |symmetricRemainder| |c06gsf| - |powerSum| |getlo| |replace| |integral?| |OMReadError?| |normalForm| - |position!| |aQuartic| |f04adf| |leastMonomial| |linears| - |stoseInvertibleSet| |f02abf| |box| |cyclicParents| |lineColorDefault| - |sec2cos| |dot| |c05pbf| |difference| |basisOfRightNucleus| - |createIrreduciblePoly| |lastSubResultantElseSplit| |rowEchLocal| - |viewport2D| |stop| |cSec| |failed| |zag| |f04mbf| |wordInGenerators| - |exprHasAlgebraicWeight| |argument| |graphImage| |randomLC| - |mainDefiningPolynomial| |space| |value| |impliesOperands| |nthExpon| - |coordinates| |tracePowMod| |rightRankPolynomial| |plus!| |sqfrFactor| - |inHallBasis?| |iitanh| |mvar| |ldf2vmf| |associator| - |purelyTranscendental?| |unexpand| |karatsubaDivide| - |jordanAdmissible?| |coerceListOfPairs| |decomposeFunc| |deepExpand| - |overset?| |stoseInvertibleSetsqfreg| |intChoose| |whatInfinity| - |makeResult| |bernoulliB| |vectorise| |cyclic?| |monicDivide| - |choosemon| |monicRightDivide| |f02aaf| |ParCond| |complexForm| - |permutations| |airyAi| |sech2cosh| |lazyVariations| |exponential| - |quotedOperators| |wrregime| |isTimes| |more?| |critT| |remove!| |or| - |bounds| |categoryFrame| |getPickedPoints| |length| - |removeRedundantFactors| |integral| |primitivePart| |hex| - |initializeGroupForWordProblem| |exactQuotient| |c06fpf| - |rootDirectory| |scripts| |isExpt| |laurentRep| |powers| |Hausdorff| - |multiple?| |zeroDimPrime?| |var2StepsDefault| |s15aef| - |halfExtendedSubResultantGcd2| |linearAssociatedOrder| |presub| - |hMonic| |create3Space| |removeConstantTerm| |primintfldpoly| |maxint| - |tubePoints| |cosh2sech| |e04ycf| |OMgetEndAtp| |bezoutResultant| - |explicitlyEmpty?| |closed?| |integralRepresents| - |rewriteSetByReducingWithParticularGenerators| |lazyResidueClass| - |extractTop!| |generator| |getGoodPrime| |enqueue!| - |doubleFloatFormat| |setnext!| |f07fdf| |dictionary| |cfirst| - |diagonalProduct| |lprop| |scalarTypeOf| |makeGraphImage| - |exponentialOrder| |OMgetInteger| |rotatex| |useSingleFactorBound?| - |delay| |leftUnits| |leftLcm| |argumentListOf| |iicoth| |pol| - |leadingBasisTerm| |shrinkable| |getExplanations| |safetyMargin| - |mesh?| |reverse!| |asinhIfCan| |OMread| |d02gbf| |setlast!| - |associatedSystem| |ParCondList| |basisOfCommutingElements| - |sturmVariationsOf| |linearDependenceOverZ| |nthFractionalTerm| - |radicalSimplify| |lieAlgebra?| |fibonacci| |scopes| |denominator| - |less?| |cSinh| |BumInSepFFE| |processTemplate| |exp1| |horizConcat| - |fi2df| |ideal| |setClipValue| |stoseInvertible?reg| - |multiplyCoefficients| |d02bhf| |style| |mapUnivariateIfCan| - |pushNewContour| |edf2fi| |nextSubsetGray| |problemPoints| - |atrapezoidal| |sinh2csch| |radicalEigenvectors| |addMatch| |e02bdf| - |solveInField| |outputAsTex| |cAsin| |makeprod| |bat| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record| + |Union| |zeroOf| |rootsOf| |makeSketch| |inrootof| |droot| |iroot| |size?| + |eq?| |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit| |ratDenom| + |ratPoly| |rootPower| |rootProduct| |rootSimp| |rootKerSimp| |leftRank| + |rightRank| |doubleRank| |weakBiRank| |biRank| |basisOfCommutingElements| + |basisOfLeftAnnihilator| |basisOfRightAnnihilator| |basisOfLeftNucleus| + |basisOfRightNucleus| |basisOfMiddleNucleus| |basisOfNucleus| |basisOfCenter| + |basisOfLeftNucloid| |basisOfRightNucloid| |basisOfCentroid| + |radicalOfLeftTraceForm| |showTypeInOutput| |obj| |dom| |objectOf| |domainOf| + |any| |applyRules| |localUnquote| |setColumn!| |setRow!| |oneDimensionalArray| + |associatedSystem| |uncouplingMatrices| |associatedEquations| |arrayStack| + |setButtonValue| |setAttributeButtonStep| |resetAttributeButtons| + |getButtonValue| |decrease| |increase| |morphism| |balancedFactorisation| + |mapDown!| |mapUp!| |setleaves!| |balancedBinaryTree| |sylvesterMatrix| + |bezoutMatrix| |bezoutResultant| |bezoutDiscriminant| |bfEntry| |bfKeys| + |inspect| |extract!| |bag| |binding| |position!| |test| |setProperties| + |setProperty| |deleteProperty!| |has?| |input| |comparison| |equality| |nary?| + |unary?| |nullary?| |arity| |properties| |derivative| |constantOperator| + |constantOpIfCan| |integerBound| |setright!| |setleft!| + |brillhartIrreducible?| |brillhartTrials| |noLinearFactor?| |insertRoot!| + |binarySearchTree| |nor| |nand| |node| |binaryTournament| |binaryTree| + |bitior| |bitand| |byte| |subtractIfCan| |setPosition| + |generalizedContinuumHypothesisAssumed| + |generalizedContinuumHypothesisAssumed?| |countable?| |Aleph| |unravel| + |ravel| |leviCivitaSymbol| |kroneckerDelta| |reindex| |kind| |alphanumeric| + |alphabetic| |hexDigit| |digit| |charClass| |alphanumeric?| |lowerCase?| + |upperCase?| |alphabetic?| |hexDigit?| |digit?| |escape| |char| |ord| + |mkIntegral| |radPoly| |rootPoly| |goodPoint| |chvar| |removeDuplicates| + |find| |e| |clipParametric| |clipWithRanges| |numberOfHues| |blue| |green| + |yellow| |red| |iifact| |iibinom| |iiperm| |iipow| |iidsum| |iidprod| |ipow| + |factorial| |multinomial| |permutation| |stirling1| |stirling2| |summation| + |factorials| |mkcomm| |polarCoordinates| |complex| |imaginary| |solid| + |solid?| |denominators| |numerators| |convergents| |approximants| + |reducedForm| |partialQuotients| |partialDenominators| |partialNumerators| + |reducedContinuedFraction| |push| |bindings| |cartesian| |polar| |cylindrical| + |spherical| |parabolic| |parabolicCylindrical| |paraboloidal| + |ellipticCylindrical| |prolateSpheroidal| |oblateSpheroidal| |bipolar| + |bipolarCylindrical| |toroidal| |conical| |modTree| |multiEuclideanTree| + |complexZeros| |divisorCascade| |graeffe| |pleskenSplit| + |reciprocalPolynomial| |rootRadius| |schwerpunkt| |setErrorBound| + |startPolynomial| |cycleElt| |computeCycleLength| |computeCycleEntry| + |arguments| |constructorName| |coerceP| |powerSum| |elementary| |alternating| + |cyclic| |dihedral| |cap| |cup| |wreath| |SFunction| |skewSFunction| + |cyclotomicDecomposition| |cyclotomicFactorization| |rangeIsFinite| + |functionIsContinuousAtEndPoints| |functionIsOscillatory| |changeName| + |exprHasWeightCosWXorSinWX| |exprHasAlgebraicWeight| + |exprHasLogarithmicWeights| |combineFeatureCompatibility| |sparsityIF| + |stiffnessAndStabilityFactor| |stiffnessAndStabilityOfODEIF| |systemSizeIF| + |expenseOfEvaluationIF| |accuracyIF| |intermediateResultsIF| + |subscriptedVariables| |central?| |elliptic?| |doubleResultant| |distdfact| + |separateDegrees| |trace2PowMod| |tracePowMod| |irreducible?| |decimal| + |innerint| |exteriorDifferential| |totalDifferential| |homogeneous?| + |leadingBasisTerm| |ignore?| |computeInt| |checkForZero| |doubleFloatFormat| + |logGamma| |hypergeometric0F1| |rotatez| |rotatey| |rotatex| |identity| + |dictionary| |dioSolve| |directProduct| |newLine| |copies| |say| |sayLength| + |setnext!| |setprevious!| |next| |previous| |datalist| + |shanksDiscLogAlgorithm| |showSummary| |reflect| |reify| |separant| |initial| + |leader| |isobaric?| |weights| |differentialVariables| |extractBottom!| + |extractTop!| |insertBottom!| |insertTop!| |bottom!| |top!| |dequeue| + |makeObject| |recolor| |drawComplex| |drawComplexVectorField| |setRealSteps| + |setImagSteps| |setClipValue| |draw| |option?| |range| |colorFunction| + |curveColor| |pointColor| |clip| |clipBoolean| |style| |toScale| + |pointColorPalette| |curveColorPalette| |var1Steps| |var2Steps| |space| + |tubePoints| |tubeRadius| |option| |weight| |makeVariable| |finiteBound| + |sortConstraints| |sumOfSquares| |splitLinear| |simpleBounds?| |linearMatrix| + |linearPart| |nonLinearPart| |quadratic?| |changeNameToObjf| |optAttributes| + |Nul| |exponents| |iisqrt2| |iisqrt3| |iiexp| |iilog| |iisin| |iicos| |iitan| + |iicot| |iisec| |iicsc| |iiasin| |iiacos| |iiatan| |iiacot| |iiasec| |iiacsc| + |iisinh| |iicosh| |iitanh| |iicoth| |iisech| |iicsch| |iiasinh| |iiacosh| + |iiatanh| |iiacoth| |iiasech| |iiacsch| |specialTrigs| |localReal?| + |rischNormalize| |realElementary| |validExponential| |rootNormalize| |tanQ| + |callForm?| |getIdentifier| |getConstant| |type| |select!| |delete!| |sn| |cn| + |dn| |sncndn| |qsetelt!| |categoryFrame| |currentEnv| |setProperties!| + |getProperties| |setProperty!| |getProperty| |scopes| |eigenvalues| + |eigenvector| |generalizedEigenvector| |generalizedEigenvectors| + |eigenvectors| |factorAndSplit| |rightOne| |leftOne| |rightZero| |leftZero| + |swap| |error| |minPoly| |freeOf?| |operators| |tower| |kernels| |mainKernel| + |distribute| |subst| |functionIsFracPolynomial?| |problemPoints| |zerosOf| + |singularitiesOf| |polynomialZeros| |f2df| |ef2edf| |ocf2ocdf| |socf2socdf| + |df2fi| |edf2fi| |edf2df| |expenseOfEvaluation| |numberOfOperations| |edf2efi| + |dfRange| |dflist| |df2mf| |ldf2vmf| |edf2ef| |vedf2vef| |df2st| |f2st| + |ldf2lst| |sdf2lst| |getlo| |gethi| |outputMeasure| |measure2Result| + |att2Result| |iflist2Result| |pdf2ef| |pdf2df| |df2ef| |fi2df| |mat| |neglist| + |multiEuclidean| |extendedEuclidean| |euclideanSize| |sizeLess?| + |simplifyPower| |number?| |seriesSolve| |constantToUnaryFunction| |tubePlot| + |exponentialOrder| |completeEval| |lowerPolynomial| |raisePolynomial| + |normalDeriv| |ran| |highCommonTerms| |mapCoef| |nthCoef| |binomThmExpt| + |pomopo!| |mapExponents| |linearAssociatedLog| |linearAssociatedOrder| + |linearAssociatedExp| |createNormalElement| |setLabelValue| |getCode| + |printCode| |code| |operation| |common| |printStatement| |save| |stop| |block| + |cond| |returns| |call| |comment| |continue| |goto| |repeatUntilLoop| + |whileLoop| |forLoop| |sin?| |zeroVector| |zeroSquareMatrix| + |identitySquareMatrix| |lSpaceBasis| |finiteBasis| |principal?| |divisor| + |useNagFunctions| |rationalPoints| |nonSingularModel| |algSplitSimple| + |hyperelliptic| |elliptic| |integralDerivationMatrix| |integralRepresents| + |integralCoordinates| |yCoordinates| |inverseIntegralMatrixAtInfinity| + |integralMatrixAtInfinity| |inverseIntegralMatrix| |integralMatrix| + |reduceBasisAtInfinity| |normalizeAtInfinity| |complementaryBasis| |integral?| + |integralAtInfinity?| |integralBasisAtInfinity| |ramified?| + |ramifiedAtInfinity?| |singular?| |singularAtInfinity?| |branchPoint?| + |branchPointAtInfinity?| |rationalPoint?| |absolutelyIrreducible?| |genus| + |getZechTable| |createZechTable| |createMultiplicationTable| + |createMultiplicationMatrix| |createLowComplexityTable| + |createLowComplexityNormalBasis| |representationType| |createPrimitiveElement| + |tableForDiscreteLogarithm| |factorsOfCyclicGroupSize| |sizeMultiplication| + |getMultiplicationMatrix| |getMultiplicationTable| |primitive?| + |numberOfIrreduciblePoly| |numberOfPrimitivePoly| |numberOfNormalPoly| + |createIrreduciblePoly| |createPrimitivePoly| |createNormalPoly| + |createNormalPrimitivePoly| |createPrimitiveNormalPoly| |nextIrreduciblePoly| + |nextPrimitivePoly| |nextNormalPoly| |nextNormalPrimitivePoly| + |nextPrimitiveNormalPoly| |leastAffineMultiple| |reducedQPowers| + |rootOfIrreduciblePoly| |write!| |read!| |iomode| |close!| |reopen!| |open| + |rightUnit| |leftUnit| |rightMinimalPolynomial| |leftMinimalPolynomial| + |associatorDependence| |lieAlgebra?| |jordanAlgebra?| + |noncommutativeJordanAlgebra?| |jordanAdmissible?| |lieAdmissible?| + |jacobiIdentity?| |powerAssociative?| |alternative?| |flexible?| + |rightAlternative?| |leftAlternative?| |antiAssociative?| |associative?| + |antiCommutative?| |commutative?| |rightCharacteristicPolynomial| + |leftCharacteristicPolynomial| |rightNorm| |leftNorm| |rightTrace| |leftTrace| + |someBasis| |sort!| |copyInto!| |sorted?| |LiePoly| |quickSort| |heapSort| + |shellSort| |outputSpacing| |outputGeneral| |outputFixed| |outputFloating| + |exp1| |log10| |log2| |rationalApproximation| |relerror| |complexSolve| + |complexRoots| |realRoots| |leadingTerm| |writable?| |readable?| |exists?| + |extension| |directory| |filename| |shallowExpand| |deepExpand| + |clearFortranOutputStack| |showFortranOutputStack| |popFortranOutputStack| + |pushFortranOutputStack| |topFortranOutputStack| |setFormula!| |formula| + |linkToFortran| |setLegalFortranSourceExtensions| |fracPart| |polyPart| + |fullPartialFraction| |primeFrobenius| |discreteLog| |decreasePrecision| + |increasePrecision| |bits| |unitNormalize| |unit| |flagFactor| |sqfrFactor| + |primeFactor| |nthFlag| |nthExponent| |irreducibleFactor| |nilFactor| + |regularRepresentation| |traceMatrix| |randomLC| |minimize| |module| + |rightRegularRepresentation| |leftRegularRepresentation| |rightTraceMatrix| + |leftTraceMatrix| |rightDiscriminant| |leftDiscriminant| |represents| + |mergeFactors| |isMult| |applyQuote| |ground| |ground?| |exprToXXP| + |exprToUPS| |exprToGenUPS| |localAbs| |universe| |complement| |cardinality| + |internalIntegrate0| |makeCos| |makeSin| |iiGamma| |iiabs| |bringDown| + |newReduc| |logical?| |character?| |doubleComplex?| |complex?| |double?| + |ffactor| |qfactor| |UP2ifCan| |anfactor| |fortranCharacter| + |fortranDoubleComplex| |fortranComplex| |fortranLogical| |fortranInteger| + |fortranDouble| |fortranReal| |external?| |scalarTypeOf| + |fortranCarriageReturn| |fortranLiteral| |fortranLiteralLine| + |processTemplate| |makeFR| |musserTrials| |stopMusserTrials| |numberOfFactors| + |modularFactor| |useSingleFactorBound?| |useSingleFactorBound| + |useEisensteinCriterion?| |useEisensteinCriterion| |eisensteinIrreducible?| + |tryFunctionalDecomposition?| |tryFunctionalDecomposition| |btwFact| + |beauzamyBound| |bombieriNorm| |rootBound| |singleFactorBound| |quadraticNorm| + |infinityNorm| |scaleRoots| |shiftRoots| |degreePartition| |factorOfDegree| + |factorsOfDegree| |pascalTriangle| |rangePascalTriangle| |sizePascalTriangle| + |fillPascalTriangle| |safeCeiling| |safeFloor| |safetyMargin| |sumSquares| + |euclideanNormalForm| |euclideanGroebner| |factorGroebnerBasis| + |groebnerFactorize| |credPol| |redPol| |gbasis| |critT| |critM| |critB| + |critBonD| |critMTonD1| |critMonD1| |redPo| |hMonic| |updatF| |sPol| |updatD| + |minGbasis| |lepol| |prinshINFO| |prindINFO| |fprindINFO| |prinpolINFO| + |prinb| |critpOrder| |makeCrit| |virtualDegree| |lcm| + |conditionsForIdempotents| |genericRightDiscriminant| |genericRightTraceForm| + |genericLeftDiscriminant| |genericLeftTraceForm| |genericRightNorm| + |genericRightTrace| |genericRightMinimalPolynomial| |rightRankPolynomial| + |genericLeftNorm| |genericLeftTrace| |genericLeftMinimalPolynomial| + |leftRankPolynomial| |generic| |rightUnits| |leftUnits| |compBound| |tablePow| + |solveid| |testModulus| |HenselLift| |completeHensel| |multMonom| |build| + |leadingIndex| |leadingExponent| |GospersMethod| |nextSubsetGray| + |firstSubsetGray| |clipPointsDefault| |drawToScale| |adaptive| |figureUnits| + |putColorInfo| |appendPoint| |component| |ranges| |pointLists| + |makeGraphImage| |graphImage| |groebSolve| |testDim| |genericPosition| |lfunc| + |inHallBasis?| |reorder| |parameters| |headAst| |heap| |gcdprim| |gcdcofact| + |gcdcofactprim| |lintgcd| |hex| |parts| |count| |every?| |any?| |map!| |host| + |trueEqual| |factorList| |listConjugateBases| |matrixGcd| |divideIfCan!| + |leastPower| |idealiser| |idealiserMatrix| |moduleSum| |mapUnivariate| + |mapUnivariateIfCan| |mapMatrixIfCan| |mapBivariate| |fullDisplay| + |relationsIdeal| |saturate| |groebner?| |groebnerIdeal| |ideal| |leadingIdeal| + |backOldPos| |generalPosition| |quotient| |zeroDim?| |inRadical?| |in?| + |element?| |zeroDimPrime?| |zeroDimPrimary?| |radical| |primaryDecomp| + |contract| |leadingSupport| |shrinkable| |physicalLength!| |physicalLength| + |flexibleArray| |elseBranch| |thenBranch| |generalizedInverse| |imports| + |sequence| |iterationVar| |readBytes!| |readByteIfCan!| |setFieldInfo| |pol| + |xn| |dAndcExp| |repSq| |expPot| |qPot| |lookup| |normal?| |basis| + |normalElement| |minimalPolynomial| |increment| |incrementBy| |charpol| + |solve1| |innerEigenvectors| |compile| |declare| |parseString| |unparse| + |flatten| |lambda| |binary| |packageCall| |interpret| |innerSolve1| + |innerSolve| |makeEq| |modularGcdPrimitive| |modularGcd| |reduction| + |signAround| |invmod| |powmod| |mulmod| |submod| |addmod| |mask| |dec| |inc| + |symmetricRemainder| |positiveRemainder| |bit?| |algint| |algintegrate| + |palgintegrate| |palginfieldint| |bitLength| |bitCoef| |bitTruth| |contains?| + |inf| |qinterval| |interval| |unit?| |associates?| |unitCanonical| + |unitNormal| |lfextendedint| |lflimitedint| |lfinfieldint| |lfintegrate| + |lfextlimint| |BasicMethod| |PollardSmallFactor| |showTheFTable| + |clearTheFTable| |fTable| |showAttributes| |entry| |palgint0| |palgextint0| + |palglimint0| |palgRDE0| |palgLODE0| |chineseRemainder| |divisors| |eulerPhi| + |fibonacci| |harmonic| |jacobi| |moebiusMu| |numberOfDivisors| |sumOfDivisors| + |sumOfKthPowerDivisors| |HermiteIntegrate| |palgint| |palgextint| |palglimint| + |palgRDE| |palgLODE| |splitConstant| |pmComplexintegrate| |pmintegrate| + |infieldint| |extendedint| |limitedint| |integerIfCan| |internalIntegrate| + |infieldIntegrate| |limitedIntegrate| |extendedIntegrate| |varselect| |kmax| + |ksec| |vark| |removeConstantTerm| |mkPrim| |intPatternMatch| |primintegrate| + |expintegrate| |tanintegrate| |primextendedint| |expextendedint| + |primlimitedint| |explimitedint| |primextintfrac| |primlimintfrac| + |primintfldpoly| |expintfldpoly| |monomialIntegrate| |monomialIntPoly| + |inverseLaplace| |iprint| |elem?| |notelem| |logpart| |ratpart| |mkAnswer| + |perfectNthPower?| |perfectNthRoot| |approxNthRoot| |perfectSquare?| + |perfectSqrt| |approxSqrt| |generateIrredPoly| |complexExpand| + |complexIntegrate| |dimensionOfIrreducibleRepresentation| + |irreducibleRepresentation| |checkRur| |cAcsch| |cAsech| |cAcoth| |cAtanh| + |cAcosh| |cAsinh| |cCsch| |cSech| |cCoth| |cTanh| |cCosh| |cSinh| |cAcsc| + |cAsec| |cAcot| |cAtan| |cAcos| |cAsin| |cCsc| |cSec| |cCot| |cTan| |cCos| + |cSin| |cLog| |cExp| |cRationalPower| |cPower| |seriesToOutputForm| |iCompose| + |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| GF2FG FG2F F2FG + |explogs2trigs| |trigs2explogs| |swap!| |fill!| |minIndex| |maxIndex| |entry?| + |indices| |index?| |entries| |categories| |search| |key?| |symbolIfCan| + |kernel| |argument| |constantKernel| |constantIfCan| |kovacic| |true| + |unknown| |false| |laplace| |trailingCoefficient| |normalizeIfCan| |polCase| + |distFact| |identification| |LyndonCoordinates| |LyndonBasis| + |zeroDimensional?| |fglmIfCan| |groebner| |lexTriangular| + |squareFreeLexTriangular| |belong?| |erf| |dilog| |li| |Ci| |Si| |Ei| + |linGenPos| |groebgen| |totolex| |minPol| |computeBasis| |coord| |anticoord| + |intcompBasis| |choosemon| |transform| |pack!| |library| |complexLimit| + |limit| |linearlyDependent?| |linearDependence| |solveLinear| |reducedSystem| + |setDifference| |setIntersection| |setUnion| |append| |null| |nil| + |substitute| |duplicates?| |mapGen| |mapExpon| |commutativeEquality| + |leftMult| |rightMult| |makeUnit| |reverse!| |reverse| |makeMulti| |makeTerm| + |listOfMonoms| |insert| |delete| |symmetricSquare| |factor1| + |symmetricProduct| |symmetricPower| |directSum| + |solveLinearPolynomialEquationByFractions| |hasSolution?| |linSolve| + |LyndonWordsList| |LyndonWordsList1| |lyndonIfCan| |lyndon| |lyndon?| + |numberOfComputedEntries| |rst| |frst| |lazyEvaluate| |lazy?| + |explicitlyEmpty?| |explicitEntries?| |matrixDimensions| |matrixConcat3D| + |setelt!| |plus| |identityMatrix| |zeroMatrix| |iter| |arg1| |arg2| |comp| + |mappingAst| |nullary| |fixedPoint| |id| |recur| |const| |curry| |diag| + |curryRight| |curryLeft| |constantRight| |constantLeft| |twist| + |setsubMatrix!| |subMatrix| |swapColumns!| |swapRows!| |vertConcat| + |horizConcat| |squareTop| |elRow1!| |elRow2!| |elColumn2!| + |fractionFreeGauss!| |invertIfCan| |copy!| |plus!| |minus!| |leftScalarTimes!| + |rightScalarTimes!| |times!| |power!| |nothing| |gradient| |divergence| + |laplacian| |hessian| |bandedHessian| |jacobian| |bandedJacobian| |duplicates| + |removeDuplicates!| |linears| |ddFact| |separateFactors| |exptMod| + |meshPar2Var| |meshFun2Var| |meshPar1Var| |ptFunc| |minimumExponent| + |maximumExponent| |precision| |mantissa| |rowEch| |rowEchLocal| + |rowEchelonLocal| |normalizedDivide| |maxint| |binaryFunction| + |makeFloatFunction| |function| |makeRecord| |unaryFunction| |compiledFunction| + |corrPoly| |lifting| |lifting1| |exprex| |coerceL| |coerceS| |frobenius| + |computePowers| |pow| |An| |UnVectorise| |Vectorise| |setPoly| |index| + |exponent| |exQuo| |moebius| |rightRecip| |leftRecip| |leftPower| |rightPower| + |derivationCoordinates| |generator| |one?| |splitSquarefree| |normalDenom| + |reshape| |totalfract| |pushdterm| |pushucoef| |pushuconst| + |numberOfMonomials| |members| |multiset| |systemCommand| |mergeDifference| + |squareFreePrim| |compdegd| |univcase| |consnewpol| |nsqfree| |intChoose| + |coefChoose| |myDegree| |normDeriv2| |plenaryPower| |c02aff| |c02agf| |c05adf| + |c05nbf| |c05pbf| |c06eaf| |c06ebf| |c06ecf| |c06ekf| |c06fpf| |c06fqf| + |c06frf| |c06fuf| |c06gbf| |c06gcf| |c06gqf| |c06gsf| |d01ajf| |d01akf| + |d01alf| |d01amf| |d01anf| |d01apf| |d01aqf| |d01asf| |d01bbf| |d01fcf| + |d01gaf| |d01gbf| |d02bbf| |d02bhf| |d02cjf| |d02ejf| |d02gaf| |d02gbf| + |d02kef| |d02raf| |d03edf| |d03eef| |d03faf| |e01baf| |e01bef| |e01bff| + |e01bgf| |e01bhf| |e01daf| |e01saf| |e01sbf| |e01sef| |e01sff| |e02adf| + |e02aef| |e02agf| |e02ahf| |e02ajf| |e02akf| |e02baf| |e02bbf| |e02bcf| + |e02bdf| |e02bef| |e02daf| |e02dcf| |e02ddf| |e02def| |e02dff| |e02gaf| + |e02zaf| |e04dgf| |e04fdf| |e04gcf| |e04jaf| |e04mbf| |e04naf| |e04ucf| + |e04ycf| |f01brf| |f01bsf| |f01maf| |f01mcf| |f01qcf| |f01qdf| |f01qef| + |f01rcf| |f01rdf| |f01ref| |f02aaf| |f02abf| |f02adf| |f02aef| |f02aff| + |f02agf| |f02ajf| |f02akf| |f02awf| |f02axf| |f02bbf| |f02bjf| |f02fjf| + |f02wef| |f02xef| |f04adf| |f04arf| |f04asf| |f04atf| |f04axf| |f04faf| + |f04jgf| |f04maf| |f04mbf| |f04mcf| |f04qaf| |f07adf| |f07aef| |f07fdf| + |f07fef| |s01eaf| |s13aaf| |s13acf| |s13adf| |s14aaf| |s14abf| |s14baf| + |s15adf| |s15aef| |s17acf| |s17adf| |s17aef| |s17aff| |s17agf| |s17ahf| + |s17ajf| |s17akf| |s17dcf| |s17def| |s17dgf| |s17dhf| |s17dlf| |s18acf| + |s18adf| |s18aef| |s18aff| |s18dcf| |s18def| |s19aaf| |s19abf| |s19acf| + |s19adf| |s20acf| |s20adf| |s21baf| |s21bbf| |s21bcf| |s21bdf| + |fortranCompilerName| |fortranLinkerArgs| |aspFilename| |dimensionsOf| + |checkPrecision| |restorePrecision| |antiCommutator| |commutator| |associator| + |complexEigenvalues| |complexEigenvectors| |shift| |normalizedAssociate| + |normalize| |outputArgs| |normInvertible?| |normFactors| |npcoef| |listexp| + |characteristicPolynomial| |realEigenvalues| |realEigenvectors| + |halfExtendedResultant2| |halfExtendedResultant1| |extendedResultant| + |subResultantsChain| |lazyPseudoQuotient| |lazyPseudoRemainder| |bernoulliB| + |eulerE| |numeric| |complexNumeric| |numericIfCan| |complexNumericIfCan| + |FormatArabic| |ScanArabic| |FormatRoman| |ScanRoman| |ScanFloatIgnoreSpaces| + |ScanFloatIgnoreSpacesIfCan| |numericalIntegration| |rk4| |rk4a| |rk4qc| + |rk4f| |aromberg| |asimpson| |atrapezoidal| |romberg| |simpson| |trapezoidal| + |rombergo| |simpsono| |trapezoidalo| |sup| |inv| |imagE| |imagk| |imagj| + |imagi| |octon| |ODESolve| |constDsolve| |showTheIFTable| |clearTheIFTable| + |keys| |iFTable| |showIntensityFunctions| |expint| |diff| |algDsolve| + |denomLODE| |indicialEquations| |indicialEquation| |denomRicDE| + |leadingCoefficientRicDE| |constantCoefficientRicDE| |changeVar| |ratDsolve| + |indicialEquationAtInfinity| |reduceLODE| |singRicDE| |polyRicDE| |ricDsolve| + |triangulate| |solveInField| |wronskianMatrix| |variationOfParameters| + |factors| |nthFactor| |nthExpon| |overlap| |hcrf| |hclf| |lexico| |OMmakeConn| + |OMcloseConn| |OMconnInDevice| |OMconnOutDevice| |OMconnectTCP| |OMbindTCP| + |OMopenFile| |OMopenString| |OMclose| |OMsetEncoding| |OMputApp| |OMputAtp| + |OMputAttr| |OMputBind| |OMputBVar| |OMputError| |OMputObject| |OMputEndApp| + |OMputEndAtp| |OMputEndAttr| |OMputEndBind| |OMputEndBVar| |OMputEndError| + |OMputEndObject| |OMputInteger| |OMputFloat| |OMputVariable| |OMputString| + |OMputSymbol| |OMgetApp| |OMgetAtp| |OMgetAttr| |OMgetBind| |OMgetBVar| + |OMgetError| |OMgetObject| |OMgetEndApp| |OMgetEndAtp| |OMgetEndAttr| + |OMgetEndBind| |OMgetEndBVar| |OMgetEndError| |OMgetEndObject| |OMgetInteger| + |OMgetFloat| |OMgetVariable| |OMgetString| |OMgetSymbol| |OMgetType| + |OMencodingBinary| |OMencodingSGML| |OMencodingXML| |OMencodingUnknown| + |omError| |errorInfo| |errorKind| |OMReadError?| |OMUnknownSymbol?| + |OMUnknownCD?| |OMParseError?| |OMwrite| |po| |op| |OMread| |OMreadFile| + |OMreadStr| |OMlistCDs| |OMlistSymbols| |OMsupportsCD?| |OMsupportsSymbol?| + |OMunhandledSymbol| |OMreceive| |OMsend| |OMserve| |infinity| |makeop| + |opeval| |evaluateInverse| |evaluate| |conjug| |adjoint| |getDatabase| + |numericalOptimization| |optimize| |goodnessOfFit| |whatInfinity| |infinite?| + |finite?| |minusInfinity| |plusInfinity| |pureLex| |totalLex| |reverseLex| + |leftLcm| |rightExtendedGcd| |rightGcd| |rightExactQuotient| |rightRemainder| + |rightQuotient| |rightLcm| |leftExtendedGcd| |leftGcd| |leftExactQuotient| + |leftRemainder| |leftQuotient| |times| |apply| |monicLeftDivide| + |monicRightDivide| |leftDivide| |rightDivide| |hermiteH| |laguerreL| + |legendreP| |outputList| |writeBytes!| |writeByteIfCan!| |quo| |rem| |div| >= + > ~= |blankSeparate| |semicolonSeparate| |commaSeparate| |pile| |paren| + |bracket| |prod| |overlabel| |overbar| |prime| |quote| |supersub| |presuper| + |presub| |super| |sub| |rarrow| |assign| |slash| |over| |zag| |box| |label| + |infix?| |postfix| |infix| |prefix| |vconcat| |hconcat| |rspace| |vspace| + |hspace| |superHeight| |subHeight| |height| |width| |messagePrint| |message| + |padecf| |pade| |root| |quotientByP| |moduloP| |modulus| |digits| + |continuedFraction| |pair| |light| |pastel| |bright| |dim| |dark| + |getSyntaxFormsFromFile| |surface| |coordinate| |partitions| |conjugates| + |shuffle| |shufflein| |sequences| |permutations| |lists| |atoms| |makeResult| + |is?| |Is| |addMatchRestricted| |insertMatch| |addMatch| |getMatch| |failed| + |failed?| |optpair| |getBadValues| |resetBadValues| |hasTopPredicate?| + |topPredicate| |setTopPredicate| |patternVariable| |withPredicates| + |setPredicates| |predicates| |hasPredicate?| |optional?| |multiple?| + |generic?| |quoted?| |inR?| |isList| |isQuotient| |isOp| |Zero| |satisfy?| + |addBadValue| |badValues| |retractable?| |ListOfTerms| |One| |PDESolve| + |leftFactor| |rightFactorCandidate| |measure| D |ptree| |coerceImages| + |fixedPoints| |odd?| |even?| |numberOfCycles| |cyclePartition| + |coerceListOfPairs| |coercePreimagesImages| |listRepresentation| |permanent| + |cycles| |cycle| |initializeGroupForWordProblem| <= < |movedPoints| + |wordInGenerators| |wordInStrongGenerators| |orbits| |orbit| + |permutationGroup| |wordsForStrongGenerators| |strongGenerators| |base| + |generators| |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion| + |factorByRecursion| |factorSquareFreeByRecursion| |randomR| |factorSFBRlcUnit| + |charthRoot| |conditionP| |solveLinearPolynomialEquation| + |factorSquareFreePolynomial| |factorPolynomial| |squareFreePolynomial| + |gcdPolynomial| |torsion?| |torsionIfCan| |getGoodPrime| |badNum| |mix| + |doubleDisc| |polyred| |padicFraction| |padicallyExpand| + |numberOfFractionalTerms| |nthFractionalTerm| |firstNumer| |firstDenom| + |compactFraction| |partialFraction| |gcdPrimitive| |symmetricGroup| + |alternatingGroup| |abelianGroup| |cyclicGroup| |dihedralGroup| |mathieu11| + |mathieu12| |mathieu22| |mathieu23| |mathieu24| |janko2| |rubiksGroup| + |youngGroup| |lexGroebner| |totalGroebner| |expressIdealMember| + |principalIdeal| |LagrangeInterpolation| |psolve| |wrregime| |rdregime| + |bsolve| |dmp2rfi| |se2rfi| |pr2dmp| |hasoln| |ParCondList| |redpps| |B1solve| + |factorset| |maxrank| |minrank| |minset| |nextSublist| |overset?| |ParCond| + |redmat| |regime| |sqfree| |inconsistent?| |debug| |numFunEvals| |setAdaptive| + |adaptive?| |setScreenResolution| |screenResolution| |setMaxPoints| + |maxPoints| |setMinPoints| |minPoints| |parametric?| |plotPolar| |debug3D| + |numFunEvals3D| |setAdaptive3D| |adaptive3D?| |setScreenResolution3D| + |screenResolution3D| |setMaxPoints3D| |maxPoints3D| |setMinPoints3D| + |minPoints3D| |tValues| |tRange| |plot| |pointPlot| |calcRanges| |assert| + |optional| |multiple| |fixPredicate| |patternMatch| |patternMatchTimes| + |bernoulli| |chebyshevT| |chebyshevU| |cyclotomic| |euler| |fixedDivisor| + |laguerre| |legendre| |dmpToHdmp| |hdmpToDmp| |pToHdmp| |hdmpToP| |dmpToP| + |pToDmp| |sylvesterSequence| |sturmSequence| |boundOfCauchy| + |sturmVariationsOf| |lazyVariations| |content| |primitiveMonomials| + |totalDegree| |minimumDegree| |monomials| |isPlus| |isTimes| |isExpt| + |isPower| |rroot| |qroot| |froot| |nthr| |port| |firstUncouplingMatrix| + |integral| |primitiveElement| |nextPrime| |prevPrime| |primes| |print| + |selectsecond| |selectfirst| |makeprod| |property| |equivOperands| |equiv?| + |impliesOperands| |implies?| |orOperands| |or?| |andOperands| |and?| + |notOperand| |not?| |variable?| |term| |term?| |equiv| |implies| |or| |and| + |merge!| |resultantEuclidean| |semiResultantEuclidean2| + |semiResultantEuclidean1| |indiceSubResultant| |indiceSubResultantEuclidean| + |semiIndiceSubResultantEuclidean| |degreeSubResultant| + |degreeSubResultantEuclidean| |semiDegreeSubResultantEuclidean| + |lastSubResultantEuclidean| |semiLastSubResultantEuclidean| + |subResultantGcdEuclidean| |semiSubResultantGcdEuclidean2| + |semiSubResultantGcdEuclidean1| |discriminantEuclidean| + |semiDiscriminantEuclidean| |chainSubResultants| |schema| |resultantReduit| + |resultantReduitEuclidean| |semiResultantReduitEuclidean| |divide| |Lazard| + |Lazard2| |nextsousResultant2| |resultantnaif| |resultantEuclideannaif| + |semiResultantEuclideannaif| |pdct| |powers| |partition| |complete| |pole?| + |monomial| |leadingMonomial| |zRange| |yRange| |xRange| |listBranches| + |triangular?| |rewriteIdealWithRemainder| |rewriteIdealWithHeadRemainder| + |remainder| |headRemainder| |roughUnitIdeal?| |roughEqualIdeals?| + |roughSubIdeal?| |roughBase?| |trivialIdeal?| |sort| |collectUpper| |collect| + |collectUnder| |mainVariable?| |mainVariables| |removeSquaresIfCan| + |unprotectedRemoveRedundantFactors| |removeRedundantFactors| + |certainlySubVariety?| |possiblyNewVariety?| |probablyZeroDim?| + |selectPolynomials| |selectOrPolynomials| |selectAndPolynomials| + |quasiMonicPolynomials| |univariate?| |univariatePolynomials| |linear?| + |linearPolynomials| |bivariate?| |bivariatePolynomials| + |removeRoughlyRedundantFactorsInPols| |removeRoughlyRedundantFactorsInPol| + |interReduce| |roughBasicSet| |crushedSet| + |rewriteSetByReducingWithParticularGenerators| + |rewriteIdealWithQuasiMonicGenerators| |squareFreeFactors| + |univariatePolynomialsGcds| |removeRoughlyRedundantFactorsInContents| + |removeRedundantFactorsInContents| |removeRedundantFactorsInPols| + |irreducibleFactors| |lazyIrreducibleFactors| + |removeIrreducibleRedundantFactors| |normalForm| |changeBase| + |companionBlocks| |xCoord| |yCoord| |zCoord| |rCoord| |thetaCoord| |phiCoord| + |color| |hue| |shade| |nthRootIfCan| |expIfCan| |logIfCan| |sinIfCan| + |cosIfCan| |tanIfCan| |cotIfCan| |secIfCan| |cscIfCan| |asinIfCan| |acosIfCan| + |atanIfCan| |acotIfCan| |asecIfCan| |acscIfCan| |sinhIfCan| |coshIfCan| + |tanhIfCan| |cothIfCan| |sechIfCan| |cschIfCan| |asinhIfCan| |acoshIfCan| + |atanhIfCan| |acothIfCan| |asechIfCan| |acschIfCan| |pushdown| |pushup| + |reducedDiscriminant| |idealSimplify| |definingInequation| |definingEquations| + |setStatus| |quasiAlgebraicSet| |radicalSimplify| |random| |denominator| + |numerator| |denom| |numer| |quadraticForm| |back| |front| |rotate!| + |dequeue!| |enqueue!| |quatern| |imagK| |imagJ| |imagI| |conjugate| |queue| + |nthRoot| |fractRadix| |wholeRadix| |cycleRagits| |prefixRagits| |fractRagits| + |wholeRagits| |radix| |randnum| |reseed| |seed| |rational| |rational?| + |rationalIfCan| |setvalue!| |setchildren!| |node?| |child?| |distance| + |leaves| |nodes| |rename| |rename!| |mainValue| |mainDefiningPolynomial| + |mainForm| |sqrt| |rischDE| |rischDEsys| |monomRDE| |baseRDE| |polyRDE| + |monomRDEsys| |baseRDEsys| |weighted| |rdHack1| |operator| |midpoint| + |midpoints| |realZeros| |mainCharacterization| |algebraicOf| |ReduceOrder| = + |setref| |deref| |ref| |radicalEigenvectors| |radicalEigenvector| + |radicalEigenvalues| |eigenMatrix| |normalise| |gramschmidt| + |orthonormalBasis| |antisymmetricTensors| |createGenericMatrix| + |symmetricTensors| |tensorProduct| |permutationRepresentation| + |completeEchelonBasis| |createRandomElement| |cyclicSubmodule| + |standardBasisOfCyclicSubmodule| |areEquivalent?| |isAbsolutelyIrreducible?| + |meatAxe| |scanOneDimSubspaces| |double| |expt| |lift| |showArrayValues| + |showScalarValues| |solveRetract| |variables| |mainVariable| |univariate| + |multivariate| |uniform01| |normal01| |exponential1| |chiSquare1| |normal| + |exponential| |chiSquare| F |t| |factorFraction| |uniform| |binomial| + |poisson| |geometric| |ridHack1| |interpolate| |nullSpace| |nullity| |rank| + |rowEchelon| |column| |row| |qelt| |ncols| |nrows| |maxColIndex| |minColIndex| + |maxRowIndex| |minRowIndex| |antisymmetric?| |symmetric?| |diagonal?| + |square?| |matrix| |rectangularMatrix| |characteristic| |round| |fractionPart| + |wholePart| |floor| |ceiling| |norm| |mightHaveRoots| |refine| |middle| |size| + |right| |left| |roman| |recoverAfterFail| |showTheRoutinesTable| + |deleteRoutine!| |getExplanations| |getMeasure| |changeMeasure| + |changeThreshhold| |selectMultiDimensionalRoutines| |selectNonFiniteRoutines| + |selectSumOfSquaresRoutines| |selectFiniteRoutines| |selectODEIVPRoutines| + |selectPDERoutines| |selectOptimizationRoutines| |selectIntegrationRoutines| + |routines| |mainSquareFreePart| |mainPrimitivePart| |mainContent| + |primitivePart!| |gcd| |nextsubResultant2| |LazardQuotient2| |LazardQuotient| + |subResultantChain| |halfExtendedSubResultantGcd2| + |halfExtendedSubResultantGcd1| |extendedSubResultantGcd| |exactQuotient!| + |exactQuotient| |primPartElseUnitCanonical!| |primPartElseUnitCanonical| + |retract| |retractIfCan| |lazyResidueClass| |monicModulo| |lazyPseudoDivide| + |lazyPremWithDefault| |lazyPquo| |lazyPrem| |pquo| |prem| |supRittWu?| + |RittWuCompare| |mainMonomials| |mainCoefficients| |leastMonomial| + |mainMonomial| |quasiMonic?| |monic?| |leadingCoefficient| |deepestInitial| + |iteratedInitials| |deepestTail| |head| |mdeg| |mvar| |iterators| + |relativeApprox| |rootOf| |allRootsOf| |definingPolynomial| |positive?| + |negative?| |zero?| |augment| |lastSubResultant| |lastSubResultantElseSplit| + |invertibleSet| |invertible?| |invertibleElseSplit?| + |purelyAlgebraicLeadingMonomial?| |algebraicCoefficients?| + |purelyTranscendental?| |purelyAlgebraic?| |prepareSubResAlgo| + |internalLastSubResultant| |integralLastSubResultant| |toseLastSubResultant| + |toseInvertible?| |toseInvertibleSet| |toseSquareFreePart| |expression| + |quotedOperators| |pattern| |suchThat| |rule| |rules| |ruleset| |rur| |create| + |clearCache| |cache| |enterInCache| |currentCategoryFrame| |currentScope| + |pushNewContour| |findBinding| |contours| |structuralConstants| |coordinates| + |bounds| |equation| |incr| |high| |low| |hi| |lo| BY |body| |union| |subset?| + |symmetricDifference| |difference| |intersect| |set| |brace| |part?| |latex| + |hash| |delta| |member?| |enumerate| |setOfMinN| |elements| + |replaceKthElement| |incrementKthElement| |cdr| |car| |expr| |float| |integer| + |symbol| |destruct| |float?| |integer?| |symbol?| |string?| |list?| |pair?| + |atom?| |null?| |eq| |fortran| |startTable!| |stopTable!| |supDimElseRittWu?| + |algebraicSort| |moreAlgebraic?| |subTriSet?| |subPolSet?| + |internalSubPolSet?| |internalInfRittWu?| |internalSubQuasiComponent?| + |subQuasiComponent?| |removeSuperfluousQuasiComponents| |subCase?| + |removeSuperfluousCases| |prepareDecompose| |branchIfCan| |startTableGcd!| + |stopTableGcd!| |startTableInvSet!| |stopTableInvSet!| + |stosePrepareSubResAlgo| |stoseInternalLastSubResultant| + |stoseIntegralLastSubResultant| |stoseLastSubResultant| + |stoseInvertible?sqfreg| |stoseInvertibleSetsqfreg| |stoseInvertible?reg| + |stoseInvertibleSetreg| |stoseInvertible?| |stoseInvertibleSet| + |stoseSquareFreePart| |coleman| |inverseColeman| |listYoungTableaus| + |makeYoungTableau| |nextColeman| |nextLatticePermutation| |nextPartition| + |numberOfImproperPartitions| |subSet| |unrankImproperPartitions0| + |unrankImproperPartitions1| |subresultantSequence| |SturmHabichtSequence| + |SturmHabichtCoefficients| |SturmHabicht| |countRealRoots| + |SturmHabichtMultiple| |countRealRootsMultiple| |source| |target| |signature| + |signatureAst| |Or| |And| |Not| |xor| |not| |min| |max| ~ |/\\| |\\/| |depth| + |top| |pop!| |push!| |minordet| |determinant| |diagonalProduct| |trace| + |diagonal| |diagonalMatrix| |scalarMatrix| |hermite| |completeHermite| |smith| + |completeSmith| |diophantineSystem| |csubst| |particularSolution| |mapSolve| + |linear| |quadratic| |cubic| |quartic| |aLinear| |aQuadratic| |aCubic| + |aQuartic| |radicalSolve| |radicalRoots| |contractSolve| |decomposeFunc| + |unvectorise| |bubbleSort!| |insertionSort!| |check| |objects| |lprop| + |llprop| |lllp| |lllip| |lp| |mesh?| |mesh| |polygon?| |polygon| + |closedCurve?| |closedCurve| |curve?| |curve| |point?| |enterPointData| + |composites| |components| |numberOfComposites| |numberOfComponents| + |create3Space| |parse| |outputAsFortran| |outputAsScript| |outputAsTex| |abs| + |Beta| |digamma| |polygamma| |Gamma| |besselJ| |besselY| |besselI| |besselK| + |airyAi| |airyBi| |subNode?| |infLex?| |setEmpty!| |setStatus!| + |setCondition!| |setValue!| |copy| |status| |value| |empty?| |splitNodeOf!| + |remove!| |remove| |subNodeOf?| |nodeOf?| |result| |conditions| + |updateStatus!| |extractSplittingLeaf| |squareMatrix| |transpose| |rightTrim| + |leftTrim| |trim| |split| |position| |replace| |match?| |match| |substring?| + |suffix?| |prefix?| |upperCase!| |upperCase| |lowerCase!| |lowerCase| + |KrullNumber| |numberOfVariables| |algebraicDecompose| + |transcendentalDecompose| |internalDecompose| |decompose| |upDateBranches| + |printInfo| |preprocess| |internalZeroSetSplit| |internalAugment| |stack| + |possiblyInfinite?| |explicitlyFinite?| |nextItem| |init| |infiniteProduct| + |evenInfiniteProduct| |oddInfiniteProduct| |generalInfiniteProduct| + |filterUntil| |filterWhile| |generate| |showAll?| |showAllElements| |output| + |cons| |delay| |findCycle| |repeating?| |repeating| |exquo| |recip| |integers| + |oddintegers| |int| |mapmult| |deriv| |gderiv| |compose| |addiag| + |lazyIntegrate| |nlde| |powern| |mapdiv| |lazyGintegrate| |power| |sincos| + |sinhcosh| |asin| |acos| |atan| |acot| |asec| |acsc| |sinh| |cosh| |tanh| + |coth| |sech| |csch| |asinh| |acosh| |atanh| |acoth| |asech| |acsch| + |subresultantVector| |primitivePart| |pointData| |parent| |level| + |extractProperty| |extractClosed| |extractIndex| |extractPoint| |traverse| + |defineProperty| |closeComponent| |modifyPoint| |addPointLast| |addPoint2| + |addPoint| |merge| |deepCopy| |shallowCopy| |numberOfChildren| |children| + |child| |birth| |internal?| |root?| |leaf?| |rhs| |lhs| |construct| + |predicate| |sum| |outputForm| NOT AND EQ OR GE LE GT LT |sample| |list| + |string| |argscript| |superscript| |subscript| |script| |scripts| |scripted?| + |name| |resetNew| |symFunc| |symbolTableOf| |argumentListOf| |returnTypeOf| + |printHeader| |returnType!| |argumentList!| |endSubProgram| + |currentSubProgram| |newSubProgram| |clearTheSymbolTable| |showTheSymbolTable| + |symbolTable| |printTypes| |newTypeLists| |typeLists| |externalList| + |typeList| |parametersOf| |fortranTypeOf| |declare!| |empty| |case| + |compound?| |getOperands| |getOperator| |nil?| |buildSyntax| |autoCoerce| + |solve| |triangularSystems| |rootDirectory| |hostPlatform| + |nativeModuleExtension| |loadNativeModule| |bumprow| |bumptab| |bumptab1| + |untab| |bat1| |bat| |tab1| |tab| |lex| |slex| |inverse| |maxrow| |mr| + |tableau| |listOfLists| |tanSum| |tanAn| |tanNa| |table| |initTable!| + |printInfo!| |startStats!| |printStats!| |clearTable!| |usingTable?| + |printingInfo?| |makingStats?| |extractIfCan| |insert!| |interpretString| + |stripCommentsAndBlanks| |setPrologue!| |setTex!| |setEpilogue!| |prologue| + |new| |tex| |epilogue| |display| |endOfFile?| |readIfCan!| |readLineIfCan!| + |readLine!| |writeLine!| |sign| |nonQsign| |direction| |createThreeSpace| |pi| + |cyclicParents| |cyclicEqual?| |cyclicEntries| |cyclicCopy| |tree| |cyclic?| + |cos| |cot| |csc| |sec| |sin| |tan| |complexNormalize| |complexElementary| + |trigs| |real| |imag| |real?| |complexForm| |UpTriBddDenomInv| + |LowTriBddDenomInv| |simplify| |htrigs| |simplifyExp| |simplifyLog| + |expandPower| |expandLog| |cos2sec| |cosh2sech| |cot2trig| |coth2trigh| + |csc2sin| |csch2sinh| |sec2cos| |sech2cosh| |sin2csc| |sinh2csch| |tan2trig| + |tanh2trigh| |tan2cot| |tanh2coth| |cot2tan| |coth2tanh| |removeCosSq| + |removeSinSq| |removeCoshSq| |removeSinhSq| |expandTrigProducts| |fintegrate| + |coefficient| |coHeight| |extendIfCan| |algebraicVariables| + |zeroSetSplitIntoTriangularSystems| |zeroSetSplit| |reduceByQuasiMonic| + |collectQuasiMonic| |removeZero| |initiallyReduce| |headReduce| + |stronglyReduce| |rewriteSetWithReduction| |autoReduced?| |initiallyReduced?| + |headReduced?| |stronglyReduced?| |reduced?| |normalized?| |quasiComponent| + |initials| |basicSet| |infRittWu?| |getCurve| |listLoops| |closed?| |open?| + |setClosed| |tube| |point| |unitVector| |cosSinInfo| |loopPoints| |select| + |generalTwoFactor| |generalSqFr| |twoFactor| |setOrder| |getOrder| |less?| + |userOrdered?| |largest| |more?| |setVariableOrder| |getVariableOrder| + |resetVariableOrder| |prime?| |rationalFunction| |taylorIfCan| |taylor| + |removeZeroes| |taylorRep| |factor| |factorSquareFree| |henselFact| |hasHi| + |segment| SEGMENT |fmecg| |commonDenominator| |clearDenominator| + |splitDenominator| |monicRightFactorIfCan| |rightFactorIfCan| + |leftFactorIfCan| |monicDecomposeIfCan| |monicCompleteDecompose| |divideIfCan| + |noKaratsuba| |karatsubaOnce| |karatsuba| |separate| |pseudoDivide| + |pseudoQuotient| |composite| |subResultantGcd| |resultant| |discriminant| + |pseudoRemainder| |shiftLeft| |shiftRight| |karatsubaDivide| |monicDivide| + |divideExponents| |unmakeSUP| |makeSUP| |vectorise| |eval| |extend| + |approximate| |truncate| |order| |center| |terms| |squareFreePart| + |BumInSepFFE| |multiplyExponents| |laurentIfCan| |laurent| |laurentRep| + |rationalPower| |puiseux| |dominantTerm| |limitPlus| |split!| |setlast!| + |setrest!| |setelt| |setfirst!| |cycleSplit!| |concat!| |cycleTail| + |cycleLength| |cycleEntry| |third| |second| |tail| |last| |rest| |elt| |first| + |concat| |invmultisect| |multisect| |revert| |generalLambert| |evenlambert| + |oddlambert| |lambert| |lagrange| |differentiate| |univariatePolynomial| + |integrate| ** |polynomial| |multiplyCoefficients| |quoByVar| |coefficients| + |series| |stFunc1| |stFunc2| |stFuncN| |fixedPointExquo| |ode1| |ode2| |ode| + |mpsode| UP2UTS UTS2UP LODO2FUN RF2UTS |variable| |magnitude| |length| |cross| + |outerProduct| |dot| - |zero| + |vector| |scan| |reduce| |graphCurves| + |drawCurves| |update| |show| |scale| |connect| |region| |points| |units| + |getGraph| |putGraph| |graphs| |graphStates| |graphState| |makeViewport2D| + |viewport2D| |getPickedPoints| |key| |close| |write| |colorDef| |reset| + |intensity| |lighting| |clipSurface| |showClipRegion| |showRegion| + |hitherPlane| |eyeDistance| |perspective| |translate| |zoom| |rotate| + |drawStyle| |outlineRender| |diagonals| |axes| |controlPanel| |viewpoint| + |dimensions| |title| |resize| |move| |options| |modifyPointData| |subspace| + |makeViewport3D| |viewport3D| |viewDeltaYDefault| |viewDeltaXDefault| + |viewZoomDefault| |viewPhiDefault| |viewThetaDefault| |pointColorDefault| + |lineColorDefault| |axesColorDefault| |unitsColorDefault| |pointSizeDefault| + |viewPosDefault| |viewSizeDefault| |viewDefaults| |viewWriteDefault| + |viewWriteAvailable| |var1StepsDefault| |var2StepsDefault| |tubePointsDefault| + |tubeRadiusDefault| |void| |dimension| |crest| |cfirst| |sts2stst| |clikeUniv| + |weierstrass| |qqq| |integralBasis| |localIntegralBasis| |qualifier| + |mainExpression| |condition| |changeWeightLevel| |characteristicSerie| + |characteristicSet| |medialSet| |Hausdorff| |Frobenius| |transcendenceDegree| + |extensionDegree| |inGroundField?| |transcendent?| |algebraic?| |varList| |sh| + |mirror| |monomial?| |monom| |rquo| |lquo| |mindegTerm| |log| |exp| |product| + |LiePolyIfCan| |trunc| |degree| / |quasiRegular| |quasiRegular?| |constant| + |constant?| |coef| |mindeg| |maxdeg| |#| |coerce| |map| |reductum| * + |RemainderList| |unexpand| |expand| Y |triangSolve| |univariateSolve| + |realSolve| |positiveSolve| |squareFree| |convert| |linearlyDependentOverZ?| + |linearDependenceOverZ| |solveLinearlyOverQ| |nil| |infinite| + |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| + |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|)
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(-170)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-170)) ((-101) -1536 (|has| |#2| (-1066)) (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-769)) (|has| |#2| (-703)) (|has| |#2| (-361)) (|has| |#2| (-356)) (|has| |#2| (-170)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -1536 (|has| |#2| (-1018)) (|has| |#2| (-356)) (|has| |#2| (-170))) ((-111 $ $) |has| |#2| (-170)) ((-130) -1536 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-769)) (|has| |#2| (-356)) (|has| |#2| (-170)) (|has| |#2| (-130))) ((-593 (-834)) -1536 (|has| |#2| (-1066)) (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-769)) (|has| |#2| (-703)) (|has| |#2| (-361)) (|has| |#2| (-356)) (|has| |#2| (-170)) (|has| |#2| (-593 (-834))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-593 (-1225 |#2|)) . T) ((-170) |has| |#2| (-170)) ((-225 |#2|) |has| |#2| (-1018)) ((-227) -12 (|has| |#2| (-227)) (|has| |#2| (-1018))) ((-279 #0=(-549) |#2|) . T) ((-281 #0# |#2|) . T) ((-302 |#2|) -12 (|has| |#2| (-302 |#2|)) (|has| |#2| (-1066))) ((-361) |has| |#2| (-361)) ((-370 |#2|) |has| |#2| (-1018)) ((-404 |#2|) |has| |#2| (-1066)) ((-481 |#2|) . T) ((-584 #0# |#2|) . T) ((-505 |#2| |#2|) -12 (|has| |#2| (-302 |#2|)) (|has| |#2| (-1066))) ((-624 |#2|) -1536 (|has| |#2| (-1018)) (|has| |#2| (-356)) (|has| |#2| (-170))) ((-624 $) -1536 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-170))) ((-617 (-549)) -12 (|has| |#2| (-617 (-549))) (|has| |#2| (-1018))) ((-617 |#2|) |has| |#2| (-1018)) ((-694 |#2|) -1536 (|has| |#2| (-356)) (|has| |#2| (-170))) ((-703) -1536 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-703)) (|has| |#2| (-170))) ((-767) |has| |#2| (-821)) ((-768) -1536 (|has| |#2| (-821)) (|has| |#2| (-769))) ((-769) |has| |#2| (-769)) ((-770) -1536 (|has| |#2| (-821)) (|has| |#2| (-769))) ((-771) -1536 (|has| |#2| (-821)) (|has| |#2| (-769))) ((-821) |has| |#2| (-821)) ((-823) -1536 (|has| |#2| (-821)) (|has| |#2| (-769))) ((-871 (-1142)) -12 (|has| |#2| (-871 (-1142))) (|has| |#2| (-1018))) ((-1009 (-400 (-549))) -12 (|has| |#2| (-1009 (-400 (-549)))) (|has| |#2| (-1066))) ((-1009 (-549)) -12 (|has| |#2| (-1009 (-549))) (|has| |#2| (-1066))) ((-1009 |#2|) |has| |#2| (-1066)) ((-1024 |#2|) -1536 (|has| |#2| (-1018)) (|has| |#2| (-356)) (|has| |#2| (-170))) ((-1024 $) |has| |#2| (-170)) ((-1018) -1536 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-170))) ((-1025) -1536 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-170))) ((-1078) -1536 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-703)) (|has| |#2| (-170))) ((-1066) -1536 (|has| |#2| (-1066)) (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-769)) (|has| |#2| (-703)) (|has| |#2| (-361)) (|has| |#2| (-356)) (|has| |#2| (-170)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1179) . T) ((-1232 |#2|) |has| |#2| (-356))) -((-3076 (((-234 |#1| |#3|) (-1 |#3| |#2| |#3|) (-234 |#1| |#2|) |#3|) 21)) (-2558 ((|#3| (-1 |#3| |#2| |#3|) (-234 |#1| |#2|) |#3|) 23)) (-2796 (((-234 |#1| |#3|) (-1 |#3| |#2|) (-234 |#1| |#2|)) 18))) -(((-233 |#1| |#2| |#3|) (-10 -7 (-15 -3076 ((-234 |#1| |#3|) (-1 |#3| |#2| |#3|) (-234 |#1| |#2|) |#3|)) (-15 -2558 (|#3| (-1 |#3| |#2| |#3|) (-234 |#1| |#2|) |#3|)) (-15 -2796 ((-234 |#1| |#3|) (-1 |#3| |#2|) (-234 |#1| |#2|)))) (-747) (-1179) (-1179)) (T -233)) -((-2796 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-234 *5 *6)) (-14 *5 (-747)) (-4 *6 (-1179)) (-4 *7 (-1179)) (-5 *2 (-234 *5 *7)) (-5 *1 (-233 *5 *6 *7)))) (-2558 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-234 *5 *6)) (-14 *5 (-747)) (-4 *6 (-1179)) (-4 *2 (-1179)) (-5 *1 (-233 *5 *6 *2)))) (-3076 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-234 *6 *7)) (-14 *6 (-747)) (-4 *7 (-1179)) (-4 *5 (-1179)) (-5 *2 (-234 *6 *5)) (-5 *1 (-233 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-38 |#2|) |has| |#2| (-170)) ((-101) -3874 (|has| |#2| (-1067)) (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-769)) (|has| |#2| (-703)) (|has| |#2| (-361)) (|has| |#2| (-356)) (|has| |#2| (-170)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3874 (|has| |#2| (-1018)) (|has| |#2| (-356)) (|has| |#2| (-170))) ((-111 $ $) |has| |#2| (-170)) ((-130) -3874 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-769)) (|has| |#2| (-356)) (|has| |#2| (-170)) (|has| |#2| (-130))) ((-593 (-835)) -3874 (|has| |#2| (-1067)) (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-769)) (|has| |#2| (-703)) (|has| |#2| (-361)) (|has| |#2| (-356)) (|has| |#2| (-170)) (|has| |#2| (-593 (-835))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-593 (-1224 |#2|)) . T) ((-170) |has| |#2| (-170)) ((-225 |#2|) |has| |#2| (-1018)) ((-227) -12 (|has| |#2| (-227)) (|has| |#2| (-1018))) ((-279 #1=(-535) |#2|) . T) ((-281 #1# |#2|) . T) ((-302 |#2|) -12 (|has| |#2| (-302 |#2|)) (|has| |#2| (-1067))) ((-361) |has| |#2| (-361)) ((-370 |#2|) |has| |#2| (-1018)) ((-405 |#2|) |has| |#2| (-1067)) ((-481 |#2|) . T) ((-584 #1# |#2|) . T) ((-505 |#2| |#2|) -12 (|has| |#2| (-302 |#2|)) (|has| |#2| (-1067))) ((-624 |#2|) -3874 (|has| |#2| (-1018)) (|has| |#2| (-356)) (|has| |#2| (-170))) ((-624 $) -3874 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-170))) ((-617 (-535)) -12 (|has| |#2| (-617 (-535))) (|has| |#2| (-1018))) ((-617 |#2|) |has| |#2| (-1018)) ((-694 |#2|) -3874 (|has| |#2| (-356)) (|has| |#2| (-170))) ((-703) -3874 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-703)) (|has| |#2| (-170))) ((-767) |has| |#2| (-821)) ((-768) -3874 (|has| |#2| (-821)) (|has| |#2| (-769))) ((-769) |has| |#2| (-769)) ((-770) -3874 (|has| |#2| (-821)) (|has| |#2| (-769))) ((-773) -3874 (|has| |#2| (-821)) (|has| |#2| (-769))) ((-821) |has| |#2| (-821)) ((-823) -3874 (|has| |#2| (-821)) (|has| |#2| (-769))) ((-871 (-1142)) -12 (|has| |#2| (-871 (-1142))) (|has| |#2| (-1018))) ((-1009 (-400 (-535))) -12 (|has| |#2| (-1009 (-400 (-535)))) (|has| |#2| (-1067))) ((-1009 (-535)) -12 (|has| |#2| (-1009 (-535))) (|has| |#2| (-1067))) ((-1009 |#2|) |has| |#2| (-1067)) ((-1024 |#2|) -3874 (|has| |#2| (-1018)) (|has| |#2| (-356)) (|has| |#2| (-170))) ((-1024 $) |has| |#2| (-170)) ((-1018) -3874 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-170))) ((-1025) -3874 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-170))) ((-1078) -3874 (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-703)) (|has| |#2| (-170))) ((-1067) -3874 (|has| |#2| (-1067)) (|has| |#2| (-1018)) (|has| |#2| (-821)) (|has| |#2| (-769)) (|has| |#2| (-703)) (|has| |#2| (-361)) (|has| |#2| (-356)) (|has| |#2| (-170)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1178) . T) ((-1232 |#2|) |has| |#2| (-356))) +((-2887 (((-112) $ $) NIL (|has| |#2| (-1067)))) (-3522 (((-112) $) NIL (|has| |#2| (-130)))) (-4053 (($ (-890)) 56 (|has| |#2| (-1018)))) (-2296 (((-1230) $ (-535) (-535)) NIL (|has| $ (-6 -4337)))) (-2724 (($ $ $) 60 (|has| |#2| (-769)))) (-1363 (((-3 $ "failed") $ $) 49 (|has| |#2| (-130)))) (-1264 (((-112) $ (-747)) 17)) (-3454 (((-747)) NIL (|has| |#2| (-361)))) (-3969 (((-535) $) NIL (|has| |#2| (-821)))) (-4130 ((|#2| $ (-535) |#2|) NIL (|has| $ (-6 -4337)))) (-3879 (($) NIL T CONST)) (-3491 (((-3 (-535) #1="failed") $) NIL (-12 (|has| |#2| (-1009 (-535))) (|has| |#2| (-1067)))) (((-3 (-400 (-535)) #1#) $) NIL (-12 (|has| |#2| (-1009 (-400 (-535)))) (|has| |#2| (-1067)))) (((-3 |#2| #1#) $) 29 (|has| |#2| (-1067)))) (-3490 (((-535) $) NIL (-12 (|has| |#2| (-1009 (-535))) (|has| |#2| (-1067)))) (((-400 (-535)) $) NIL (-12 (|has| |#2| (-1009 (-400 (-535)))) (|has| |#2| (-1067)))) ((|#2| $) 27 (|has| |#2| (-1067)))) (-2353 (((-665 (-535)) (-665 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #1=(-400 (-535))) |has| |#1| (-38 (-400 (-535)))) ((-38 |#1|) |has| |#1| (-170)) ((-38 $) -3874 (|has| |#1| (-881)) (|has| |#1| (-542)) (|has| |#1| (-444))) ((-101) . T) ((-111 #1# #1#) |has| |#1| (-38 (-400 (-535)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3874 (|has| |#1| (-881)) (|has| |#1| (-542)) (|has| |#1| (-444)) (|has| |#1| (-170))) ((-130) . T) ((-143) |has| |#1| (-143)) ((-145) |has| |#1| (-145)) ((-593 (-835)) . 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T) ((-617 (-535)) |has| |#1| (-617 (-535))) ((-617 |#1|) . T) ((-694 #1#) |has| |#1| (-38 (-400 (-535)))) ((-694 |#1|) |has| |#1| (-170)) ((-694 $) -3874 (|has| |#1| (-881)) (|has| |#1| (-542)) (|has| |#1| (-444))) ((-703) . T) ((-823) |has| |#1| (-823)) ((-871 |#3|) . T) ((-857 (-371)) -12 (|has| |#1| (-857 (-371))) (|has| |#3| (-857 (-371)))) ((-857 (-535)) -12 (|has| |#1| (-857 (-535))) (|has| |#3| (-857 (-535)))) ((-921 |#1| |#2| |#3|) . T) ((-881) |has| |#1| (-881)) ((-1009 (-400 (-535))) |has| |#1| (-1009 (-400 (-535)))) ((-1009 (-535)) |has| |#1| (-1009 (-535))) ((-1009 |#1|) . T) ((-1009 |#3|) . T) ((-1024 #1#) |has| |#1| (-38 (-400 (-535)))) ((-1024 |#1|) . T) ((-1024 $) -3874 (|has| |#1| (-881)) (|has| |#1| (-542)) (|has| |#1| (-444)) (|has| |#1| (-170))) ((-1018) . T) ((-1025) . T) ((-1078) . T) ((-1067) . T) ((-1183) |has| |#1| (-881))) +((-2887 (((-112) $ $) NIL)) (-3576 (((-1124) $) NIL)) (-3515 (((-618 (-1101)) $) 13)) (-3577 (((-1086) $) NIL)) (-4300 (((-835) $) 24) (((-1147) $) NIL) (($ (-1147)) NIL)) (-3567 (((-1101) $) 15)) (-3375 (((-112) $ $) NIL))) +(((-1033) (-13 (-1049) (-10 -8 (-15 -3515 ((-618 (-1101)) $)) (-15 -3567 ((-1101) $))))) (T -1033)) +((-3515 (*1 *2 *1) (-12 (-5 *2 (-618 (-1101))) (-5 *1 (-1033)))) (-3567 (*1 *2 *1) (-12 (-5 *2 (-1101)) (-5 *1 (-1033))))) +(-13 (-1049) (-10 -8 (-15 -3515 ((-618 (-1101)) $)) (-15 -3567 ((-1101) $)))) +((-3522 (((-112) |#3| $) 13)) (-3517 (((-3 $ "failed") |#3| (-890)) 23)) (-3804 (((-3 |#3| "failed") |#3| $) 38)) (-3520 (((-112) |#3| $) 16)) (-3521 (((-112) |#3| $) 14))) +(((-1034 |#1| |#2| |#3|) (-10 -8 (-15 -3517 ((-3 |#1| "failed") |#3| (-890))) (-15 -3804 ((-3 |#3| "failed") |#3| |#1|)) (-15 -3520 ((-112) |#3| |#1|)) (-15 -3521 ((-112) |#3| |#1|)) (-15 -3522 ((-112) |#3| |#1|))) (-1035 |#2| |#3|) (-13 (-821) (-356)) (-1200 |#2|)) (T -1034)) +NIL +(-10 -8 (-15 -3517 ((-3 |#1| "failed") |#3| (-890))) (-15 -3804 ((-3 |#3| "failed") |#3| |#1|)) (-15 -3520 ((-112) |#3| |#1|)) (-15 -3521 ((-112) |#3| |#1|)) (-15 -3522 ((-112) |#3| |#1|))) +((-2887 (((-112) $ $) 7)) (-3522 (((-112) |#2| $) 21)) (-3969 (((-535) |#2| $) 22)) (-3517 (((-3 $ "failed") |#2| (-890)) 15)) (-3516 ((|#1| |#2| $ |#1|) 13)) (-3804 (((-3 |#2| "failed") |#2| $) 18)) (-3520 (((-112) |#2| $) 19)) (-3521 (((-112) |#2| $) 20)) (-3576 (((-1124) $) 9)) (-3577 (((-1086) $) 10)) (-3519 ((|#2| $) 17)) (-4300 (((-835) $) 11)) (-4112 ((|#1| |#2| $ |#1|) 14)) (-3518 (((-618 $) |#2|) 16)) (-3375 (((-112) $ $) 6))) +(((-1035 |#1| |#2|) (-138) (-13 (-821) (-356)) (-1200 |t#1|)) (T -1035)) +((-3969 (*1 *2 *3 *1) (-12 (-4 *1 (-1035 *4 *3)) (-4 *4 (-13 (-821) (-356))) (-4 *3 (-1200 *4)) (-5 *2 (-535)))) (-3522 (*1 *2 *3 *1) (-12 (-4 *1 (-1035 *4 *3)) (-4 *4 (-13 (-821) (-356))) (-4 *3 (-1200 *4)) (-5 *2 (-112)))) (-3521 (*1 *2 *3 *1) (-12 (-4 *1 (-1035 *4 *3)) (-4 *4 (-13 (-821) (-356))) (-4 *3 (-1200 *4)) (-5 *2 (-112)))) (-3520 (*1 *2 *3 *1) (-12 (-4 *1 (-1035 *4 *3)) (-4 *4 (-13 (-821) (-356))) (-4 *3 (-1200 *4)) (-5 *2 (-112)))) (-3804 (*1 *2 *2 *1) (|partial| -12 (-4 *1 (-1035 *3 *2)) (-4 *3 (-13 (-821) (-356))) (-4 *2 (-1200 *3)))) (-3519 (*1 *2 *1) (-12 (-4 *1 (-1035 *3 *2)) (-4 *3 (-13 (-821) (-356))) (-4 *2 (-1200 *3)))) (-3518 (*1 *2 *3) (-12 (-4 *4 (-13 (-821) (-356))) (-4 *3 (-1200 *4)) (-5 *2 (-618 *1)) (-4 *1 (-1035 *4 *3)))) (-3517 (*1 *1 *2 *3) (|partial| -12 (-5 *3 (-890)) (-4 *4 (-13 (-821) (-356))) (-4 *1 (-1035 *4 *2)) (-4 *2 (-1200 *4)))) (-4112 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1035 *2 *3)) (-4 *2 (-13 (-821) (-356))) (-4 *3 (-1200 *2)))) (-3516 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1035 *2 *3)) (-4 *2 (-13 (-821) (-356))) (-4 *3 (-1200 *2))))) +(-13 (-1067) (-10 -8 (-15 -3969 ((-535) |t#2| $)) (-15 -3522 ((-112) |t#2| $)) (-15 -3521 ((-112) |t#2| $)) (-15 -3520 ((-112) |t#2| $)) (-15 -3804 ((-3 |t#2| "failed") |t#2| $)) (-15 -3519 (|t#2| $)) (-15 -3518 ((-618 $) |t#2|)) (-15 -3517 ((-3 $ "failed") |t#2| (-890))) (-15 -4112 (|t#1| |t#2| $ |t#1|)) (-15 -3516 (|t#1| |t#2| $ |t#1|)))) +(((-101) . T) ((-593 (-835)) . T) ((-1067) . T)) +((-3778 (((-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))) (-618 |#4|) (-618 |#5|) (-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))) (-2 (|:| |done| (-618 |#5|)) (|:| |todo| (-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))))) (-747)) 96)) (-3775 (((-2 (|:| |done| (-618 |#5|)) (|:| |todo| (-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))))) |#4| |#5|) 57) (((-2 (|:| |done| (-618 |#5|)) (|:| |todo| (-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))))) |#4| |#5| (-747)) 56)) (-3779 (((-1230) (-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))) (-747)) 87)) (-3773 (((-747) (-618 |#4|) (-618 |#5|)) 27)) (-3776 (((-2 (|:| |done| (-618 |#5|)) (|:| |todo| (-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))))) |#4| |#5|) 59) (((-2 (|:| |done| (-618 |#5|)) (|:| |todo| (-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))))) |#4| |#5| (-747)) 58) (((-2 (|:| |done| (-618 |#5|)) (|:| |todo| (-618 (-2 (|:| |val| (-618 |#4|)) (|:| -1655 |#5|))))) |#4| |#5| (-747) (-112)) 60)) (-3777 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T) ((-170) -1536 (|has| |#1| (-541)) (|has| |#1| (-356)) (|has| |#1| (-170))) ((-594 (-219)) -12 (|has| |#1| (-356)) (|has| |#2| (-993))) ((-594 (-372)) -12 (|has| |#1| (-356)) (|has| |#2| (-993))) ((-594 (-525)) -12 (|has| |#1| (-356)) (|has| |#2| (-594 (-525)))) ((-594 (-863 (-372))) -12 (|has| |#1| (-356)) (|has| |#2| (-594 (-863 (-372))))) ((-594 (-863 (-549))) -12 (|has| |#1| (-356)) (|has| |#2| (-594 (-863 (-549))))) ((-225 |#2|) |has| |#1| (-356)) ((-227) -1536 (-12 (|has| |#1| (-356)) (|has| |#2| (-227))) (|has| |#1| (-15 * (|#1| (-549) |#1|)))) ((-237) |has| |#1| (-356)) ((-277) |has| |#1| (-38 (-400 (-549)))) ((-279 |#2| $) -12 (|has| |#1| (-356)) (|has| |#2| (-279 |#2| |#2|))) ((-279 $ $) |has| (-549) (-1078)) ((-283) -1536 (|has| |#1| (-541)) (|has| |#1| (-356))) ((-300) |has| |#1| (-356)) ((-302 |#2|) -12 (|has| |#1| (-356)) (|has| |#2| (-302 |#2|))) ((-356) |has| |#1| (-356)) ((-331 |#2|) |has| |#1| (-356)) ((-370 |#2|) |has| |#1| (-356)) ((-393 |#2|) |has| |#1| (-356)) ((-444) |has| |#1| (-356)) ((-484) |has| |#1| (-38 (-400 (-549)))) ((-505 (-1142) |#2|) -12 (|has| |#1| (-356)) (|has| |#2| (-505 (-1142) |#2|))) ((-505 |#2| |#2|) -12 (|has| |#1| (-356)) (|has| |#2| (-302 |#2|))) ((-541) -1536 (|has| |#1| (-541)) (|has| |#1| (-356))) ((-624 #1#) -1536 (|has| |#1| (-356)) (|has| |#1| (-38 (-400 (-549))))) ((-624 |#1|) . T) ((-624 |#2|) |has| |#1| (-356)) ((-624 $) . T) ((-617 (-549)) -12 (|has| |#1| (-356)) (|has| |#2| (-617 (-549)))) ((-617 |#2|) |has| |#1| (-356)) ((-694 #1#) -1536 (|has| |#1| (-356)) (|has| |#1| (-38 (-400 (-549))))) ((-694 |#1|) |has| |#1| (-170)) ((-694 |#2|) |has| |#1| (-356)) ((-694 $) -1536 (|has| |#1| (-541)) (|has| |#1| (-356))) ((-703) . T) ((-767) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-768) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-770) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-771) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-796) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-821) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-823) -1536 (-12 (|has| |#1| (-356)) (|has| |#2| (-823))) (-12 (|has| |#1| (-356)) (|has| |#2| (-796)))) ((-871 (-1142)) -1536 (-12 (|has| |#1| (-356)) (|has| |#2| (-871 (-1142)))) (-12 (|has| |#1| (-15 * (|#1| (-549) |#1|))) (|has| |#1| (-871 (-1142))))) ((-857 (-372)) -12 (|has| |#1| (-356)) (|has| |#2| (-857 (-372)))) ((-857 (-549)) -12 (|has| |#1| (-356)) (|has| |#2| (-857 (-549)))) ((-855 |#2|) |has| |#1| (-356)) ((-880) -12 (|has| |#1| (-356)) (|has| |#2| (-880))) ((-944 |#1| #0# (-1048)) . T) ((-891) |has| |#1| (-356)) ((-963 |#2|) |has| |#1| (-356)) ((-973) |has| |#1| (-38 (-400 (-549)))) ((-993) -12 (|has| |#1| (-356)) (|has| |#2| (-993))) ((-1009 (-400 (-549))) -12 (|has| |#1| (-356)) (|has| |#2| (-1009 (-549)))) ((-1009 (-549)) -12 (|has| |#1| (-356)) (|has| |#2| (-1009 (-549)))) ((-1009 (-1142)) -12 (|has| |#1| (-356)) (|has| |#2| (-1009 (-1142)))) ((-1009 |#2|) . T) ((-1024 #1#) -1536 (|has| |#1| (-356)) (|has| |#1| (-38 (-400 (-549))))) ((-1024 |#1|) . T) ((-1024 |#2|) |has| |#1| (-356)) ((-1024 $) -1536 (|has| |#1| (-541)) (|has| |#1| (-356)) (|has| |#1| (-170))) ((-1018) . T) ((-1025) . T) ((-1078) . T) ((-1066) . T) ((-1117) -12 (|has| |#1| (-356)) (|has| |#2| (-1117))) ((-1164) |has| |#1| (-38 (-400 (-549)))) ((-1167) |has| |#1| (-38 (-400 (-549)))) ((-1179) |has| |#1| (-356)) ((-1183) |has| |#1| (-356)) ((-1185 |#1|) . T) ((-1203 |#1| #0#) . 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T) ((-279 (-400 $) (-400 $)) |has| |#1| (-541)) ((-279 |#1| |#1|) . T) ((-279 $ $) . T) ((-283) -1536 (|has| |#1| (-880)) (|has| |#1| (-541)) (|has| |#1| (-444)) (|has| |#1| (-356))) ((-300) |has| |#1| (-356)) ((-302 $) . T) ((-319 |#1| #0#) . T) ((-370 |#1|) . T) ((-404 |#1|) . T) ((-444) -1536 (|has| |#1| (-880)) (|has| |#1| (-444)) (|has| |#1| (-356))) ((-505 #2=(-1048) |#1|) . T) ((-505 #2# $) . T) ((-505 $ $) . T) ((-541) -1536 (|has| |#1| (-880)) (|has| |#1| (-541)) (|has| |#1| (-444)) (|has| |#1| (-356))) ((-624 #1#) |has| |#1| (-38 (-400 (-549)))) ((-624 |#1|) . T) ((-624 $) . T) ((-617 (-549)) |has| |#1| (-617 (-549))) ((-617 |#1|) . T) ((-694 #1#) |has| |#1| (-38 (-400 (-549)))) ((-694 |#1|) |has| |#1| (-170)) ((-694 $) -1536 (|has| |#1| (-880)) (|has| |#1| (-541)) (|has| |#1| (-444)) (|has| |#1| (-356))) ((-703) . T) ((-823) |has| |#1| (-823)) ((-871 #2#) . 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T) ((-23) . T) ((-47 |#1| #1=(-535)) . T) ((-25) . T) ((-38 #2=(-400 (-535))) -3874 (|has| |#1| (-356)) (|has| |#1| (-38 (-400 (-535))))) ((-38 |#1|) |has| |#1| (-170)) ((-38 |#2|) |has| |#1| (-356)) ((-38 $) -3874 (|has| |#1| (-542)) (|has| |#1| (-356))) ((-35) |has| |#1| (-38 (-400 (-535)))) ((-94) |has| |#1| (-38 (-400 (-535)))) ((-101) . T) ((-111 #2# #2#) -3874 (|has| |#1| (-356)) (|has| |#1| (-38 (-400 (-535))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-356)) ((-111 $ $) -3874 (|has| |#1| (-542)) (|has| |#1| (-356)) (|has| |#1| (-170))) ((-130) . T) ((-143) -3874 (-12 (|has| |#1| (-356)) (|has| |#2| (-143))) (|has| |#1| (-143))) ((-145) -3874 (-12 (|has| |#1| (-356)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-593 (-835)) . T) ((-170) -3874 (|has| |#1| (-542)) (|has| |#1| (-356)) (|has| |#1| (-170))) ((-594 (-219)) -12 (|has| |#1| (-356)) (|has| |#2| (-991))) ((-594 (-371)) -12 (|has| |#1| (-356)) (|has| |#2| (-991))) ((-594 (-524)) -12 (|has| |#1| (-356)) (|has| |#2| (-594 (-524)))) ((-594 (-861 (-371))) -12 (|has| |#1| (-356)) (|has| |#2| (-594 (-861 (-371))))) ((-594 (-861 (-535))) -12 (|has| |#1| (-356)) (|has| |#2| (-594 (-861 (-535))))) ((-225 |#2|) |has| |#1| (-356)) ((-227) -3874 (|has| |#1| (-15 * (|#1| (-535) |#1|))) (-12 (|has| |#1| (-356)) (|has| |#2| (-227)))) ((-237) |has| |#1| (-356)) ((-277) |has| |#1| (-38 (-400 (-535)))) ((-279 |#2| $) -12 (|has| |#1| (-356)) (|has| |#2| (-279 |#2| |#2|))) ((-279 $ $) |has| (-535) (-1078)) ((-283) -3874 (|has| |#1| (-542)) (|has| |#1| (-356))) ((-300) |has| |#1| (-356)) ((-302 |#2|) -12 (|has| |#1| (-356)) (|has| |#2| (-302 |#2|))) ((-356) |has| |#1| (-356)) ((-331 |#2|) |has| |#1| (-356)) ((-370 |#2|) |has| |#1| (-356)) ((-393 |#2|) |has| |#1| (-356)) ((-444) |has| |#1| (-356)) ((-484) |has| |#1| (-38 (-400 (-535)))) ((-505 (-1142) |#2|) -12 (|has| |#1| (-356)) (|has| |#2| (-505 (-1142) |#2|))) ((-505 |#2| |#2|) -12 (|has| |#1| (-356)) (|has| |#2| (-302 |#2|))) ((-542) -3874 (|has| |#1| (-542)) (|has| |#1| (-356))) ((-624 #2#) -3874 (|has| |#1| (-356)) (|has| |#1| (-38 (-400 (-535))))) ((-624 |#1|) . T) ((-624 |#2|) |has| |#1| (-356)) ((-624 $) . T) ((-617 (-535)) -12 (|has| |#1| (-356)) (|has| |#2| (-617 (-535)))) ((-617 |#2|) |has| |#1| (-356)) ((-694 #2#) -3874 (|has| |#1| (-356)) (|has| |#1| (-38 (-400 (-535))))) ((-694 |#1|) |has| |#1| (-170)) ((-694 |#2|) |has| |#1| (-356)) ((-694 $) -3874 (|has| |#1| (-542)) (|has| |#1| (-356))) ((-703) . T) ((-767) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-768) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-770) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-773) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-796) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-821) -12 (|has| |#1| (-356)) (|has| |#2| (-796))) ((-823) -3874 (-12 (|has| |#1| (-356)) (|has| |#2| (-823))) (-12 (|has| |#1| (-356)) (|has| |#2| (-796)))) ((-871 (-1142)) -3874 (-12 (|has| |#1| (-871 (-1142))) (|has| |#1| (-15 * (|#1| (-535) |#1|)))) (-12 (|has| |#1| (-356)) (|has| |#2| (-871 (-1142))))) ((-857 (-371)) -12 (|has| |#1| (-356)) (|has| |#2| (-857 (-371)))) ((-857 (-535)) -12 (|has| |#1| (-356)) (|has| |#2| (-857 (-535)))) ((-855 |#2|) |has| |#1| (-356)) ((-881) -12 (|has| |#1| (-356)) (|has| |#2| (-881))) ((-944 |#1| #1# (-1048)) . T) ((-892) |has| |#1| (-356)) ((-962 |#2|) |has| |#1| (-356)) ((-973) |has| |#1| (-38 (-400 (-535)))) ((-991) -12 (|has| |#1| (-356)) (|has| |#2| (-991))) ((-1009 (-400 (-535))) -12 (|has| |#1| (-356)) (|has| |#2| (-1009 (-535)))) ((-1009 (-535)) -12 (|has| |#1| (-356)) (|has| |#2| (-1009 (-535)))) ((-1009 (-1142)) -12 (|has| |#1| (-356)) (|has| |#2| (-1009 (-1142)))) ((-1009 |#2|) . T) ((-1024 #2#) -3874 (|has| |#1| (-356)) (|has| |#1| (-38 (-400 (-535))))) ((-1024 |#1|) . T) ((-1024 |#2|) |has| |#1| (-356)) ((-1024 $) -3874 (|has| |#1| (-542)) (|has| |#1| (-356)) (|has| |#1| (-170))) ((-1018) . T) ((-1025) . T) ((-1078) . T) ((-1067) . T) ((-1117) -12 (|has| |#1| (-356)) (|has| |#2| (-1117))) ((-1164) |has| |#1| (-38 (-400 (-535)))) ((-1167) |has| |#1| (-38 (-400 (-535)))) ((-1178) |has| |#1| (-356)) ((-1183) |has| |#1| (-356)) ((-1186 |#1|) . T) ((-1203 |#1| #1#) . 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"TSETCAT" 2889457 NIL TSETCAT (NIL T T T T) -9 NIL 2890988) (-1171 2874733 2876331 2878222 "TSETCAT-" 2878227 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1170 2868996 2869842 2870784 "TRMANIP" 2873869 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1169 2868437 2868500 2868663 "TRIMAT" 2868928 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1168 2866233 2866470 2866834 "TRIGMNIP" 2868186 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1167 2865753 2865866 2865896 "TRIGCAT" 2866109 T TRIGCAT (NIL) -9 NIL NIL) (-1166 2865422 2865501 2865642 "TRIGCAT-" 2865647 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1165 2862321 2864282 2864562 "TREE" 2865177 NIL TREE (NIL T) -8 NIL NIL) (-1164 2861595 2862123 2862153 "TRANFUN" 2862188 T TRANFUN (NIL) -9 NIL 2862254) (-1163 2860874 2861065 2861345 "TRANFUN-" 2861350 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1162 2860678 2860710 2860771 "TOPSP" 2860835 T TOPSP (NIL) -7 NIL NIL) (-1161 2860026 2860141 2860295 "TOOLSIGN" 2860559 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1160 2858687 2859203 2859442 "TEXTFILE" 2859809 T TEXTFILE (NIL) -8 NIL NIL) (-1159 2856552 2857066 2857504 "TEX" 2858271 T TEX (NIL) -8 NIL NIL) (-1158 2856333 2856364 2856436 "TEX1" 2856515 NIL TEX1 (NIL T) -7 NIL NIL) (-1157 2855981 2856044 2856134 "TEMUTL" 2856265 T TEMUTL (NIL) -7 NIL NIL) (-1156 2854135 2854415 2854740 "TBCMPPK" 2855704 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1155 2846023 2852295 2852351 "TBAGG" 2852751 NIL TBAGG (NIL T T) -9 NIL 2852962) (-1154 2841093 2842581 2844335 "TBAGG-" 2844340 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1153 2840477 2840584 2840729 "TANEXP" 2840982 NIL TANEXP (NIL T) -7 NIL NIL) (-1152 2833978 2840334 2840427 "TABLE" 2840432 NIL TABLE (NIL T T) -8 NIL NIL) (-1151 2833390 2833489 2833627 "TABLEAU" 2833875 NIL TABLEAU (NIL T) -8 NIL NIL) (-1150 2827998 2829218 2830466 "TABLBUMP" 2832176 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1149 2827426 2827526 2827654 "SYSTEM" 2827892 T SYSTEM (NIL) -7 NIL NIL) (-1148 2823889 2824584 2825367 "SYSSOLP" 2826677 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1147 2820181 2820888 2821622 "SYNTAX" 2823177 T SYNTAX (NIL) -8 NIL NIL) (-1146 2817339 2817941 2818573 "SYMTAB" 2819571 T SYMTAB (NIL) -8 NIL NIL) (-1145 2812588 2813490 2814473 "SYMS" 2816378 T SYMS (NIL) -8 NIL NIL) (-1144 2809860 2812046 2812276 "SYMPOLY" 2812393 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1143 2809377 2809452 2809575 "SYMFUNC" 2809772 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1142 2805354 2806614 2807436 "SYMBOL" 2808577 T SYMBOL (NIL) -8 NIL NIL) (-1141 2798893 2800582 2802302 "SWITCH" 2803656 T SWITCH (NIL) -8 NIL NIL) (-1140 2792163 2797714 2798017 "SUTS" 2798648 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1139 2784132 2791278 2791560 "SUPXS" 2791939 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1138 2775661 2783750 2783876 "SUP" 2784041 NIL SUP (NIL T) -8 NIL NIL) (-1137 2774820 2774947 2775164 "SUPFRACF" 2775529 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1136 2774441 2774500 2774613 "SUP2" 2774755 NIL SUP2 (NIL T T) -7 NIL NIL) (-1135 2772854 2773128 2773491 "SUMRF" 2774140 NIL SUMRF (NIL T) -7 NIL NIL) (-1134 2772168 2772234 2772433 "SUMFS" 2772775 NIL SUMFS (NIL T T) -7 NIL NIL) (-1133 2756177 2771345 2771596 "SULS" 2771975 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1132 2755806 2755999 2756069 "SUCHTAST" 2756129 T SUCHTAST (NIL) -8 NIL NIL) (-1131 2755128 2755331 2755471 "SUCH" 2755714 NIL SUCH (NIL T T) -8 NIL NIL) (-1130 2749022 2750034 2750993 "SUBSPACE" 2754216 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1129 2748452 2748542 2748706 "SUBRESP" 2748910 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1128 2741821 2743117 2744428 "STTF" 2747188 NIL STTF (NIL T) -7 NIL NIL) (-1127 2735994 2737114 2738261 "STTFNC" 2740721 NIL STTFNC (NIL T) -7 NIL NIL) (-1126 2727309 2729176 2730970 "STTAYLOR" 2734235 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1125 2720553 2727173 2727256 "STRTBL" 2727261 NIL STRTBL (NIL T) -8 NIL NIL) (-1124 2715944 2720508 2720539 "STRING" 2720544 T STRING (NIL) -8 NIL NIL) (-1123 2710832 2715317 2715347 "STRICAT" 2715406 T STRICAT (NIL) -9 NIL 2715468) (-1122 2703545 2708355 2708975 "STREAM" 2710247 NIL STREAM (NIL T) -8 NIL NIL) (-1121 2703055 2703132 2703276 "STREAM3" 2703462 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1120 2702037 2702220 2702455 "STREAM2" 2702868 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1119 2701725 2701777 2701870 "STREAM1" 2701979 NIL STREAM1 (NIL T) -7 NIL NIL) (-1118 2700741 2700922 2701153 "STINPROD" 2701541 NIL STINPROD (NIL T) -7 NIL NIL) (-1117 2700319 2700503 2700533 "STEP" 2700613 T STEP (NIL) -9 NIL 2700691) (-1116 2693862 2700218 2700295 "STBL" 2700300 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1115 2689037 2693084 2693127 "STAGG" 2693280 NIL STAGG (NIL T) -9 NIL 2693369) (-1114 2686739 2687341 2688213 "STAGG-" 2688218 NIL STAGG- (NIL T T) -8 NIL NIL) (-1113 2684934 2686509 2686601 "STACK" 2686682 NIL STACK (NIL T) -8 NIL NIL) (-1112 2677659 2683075 2683531 "SREGSET" 2684564 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1111 2670085 2671453 2672966 "SRDCMPK" 2676265 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1110 2663052 2667525 2667555 "SRAGG" 2668858 T SRAGG (NIL) -9 NIL 2669466) (-1109 2662069 2662324 2662703 "SRAGG-" 2662708 NIL SRAGG- (NIL T) -8 NIL NIL) (-1108 2656555 2660984 2661412 "SQMATRIX" 2661688 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1107 2650307 2653275 2654001 "SPLTREE" 2655901 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1106 2646297 2646963 2647609 "SPLNODE" 2649733 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1105 2645344 2645577 2645607 "SPFCAT" 2646051 T SPFCAT (NIL) -9 NIL NIL) (-1104 2644081 2644291 2644555 "SPECOUT" 2645102 T SPECOUT (NIL) -7 NIL NIL) (-1103 2635770 2637514 2637544 "SPADXPT" 2641936 T SPADXPT (NIL) -9 NIL 2643970) (-1102 2635531 2635571 2635640 "SPADPRSR" 2635723 T SPADPRSR (NIL) -7 NIL NIL) (-1101 2633714 2635486 2635517 "SPADAST" 2635522 T SPADAST (NIL) -8 NIL NIL) (-1100 2625685 2627432 2627475 "SPACEC" 2631848 NIL SPACEC (NIL T) -9 NIL 2633664) (-1099 2623856 2625617 2625666 "SPACE3" 2625671 NIL SPACE3 (NIL T) -8 NIL NIL) (-1098 2622608 2622779 2623070 "SORTPAK" 2623661 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1097 2620658 2620961 2621380 "SOLVETRA" 2622272 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1096 2619669 2619891 2620165 "SOLVESER" 2620431 NIL SOLVESER (NIL T) -7 NIL NIL) (-1095 2614889 2615770 2616772 "SOLVERAD" 2618721 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1094 2610704 2611313 2612042 "SOLVEFOR" 2614256 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1093 2605001 2610053 2610150 "SNTSCAT" 2610155 NIL SNTSCAT (NIL T T T T) -9 NIL 2610225) (-1092 2599144 2603324 2603715 "SMTS" 2604691 NIL SMTS (NIL T T T) -8 NIL NIL) (-1091 2593594 2599032 2599109 "SMP" 2599114 NIL SMP (NIL T T) -8 NIL NIL) (-1090 2591753 2592054 2592452 "SMITH" 2593291 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1089 2584736 2588891 2588994 "SMATCAT" 2590345 NIL SMATCAT (NIL NIL T T T) -9 NIL 2590895) (-1088 2581676 2582499 2583677 "SMATCAT-" 2583682 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1087 2579389 2580912 2580955 "SKAGG" 2581216 NIL SKAGG (NIL T) -9 NIL 2581351) (-1086 2575505 2578493 2578771 "SINT" 2579133 T SINT (NIL) -8 NIL NIL) (-1085 2575277 2575315 2575381 "SIMPAN" 2575461 T SIMPAN (NIL) -7 NIL NIL) (-1084 2574584 2574812 2574952 "SIG" 2575159 T SIG (NIL) -8 NIL NIL) (-1083 2573422 2573643 2573918 "SIGNRF" 2574343 NIL SIGNRF (NIL T) -7 NIL NIL) (-1082 2572227 2572378 2572669 "SIGNEF" 2573251 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1081 2571560 2571810 2571934 "SIGAST" 2572125 T SIGAST (NIL) -8 NIL NIL) (-1080 2569250 2569704 2570210 "SHP" 2571101 NIL SHP (NIL T NIL) -7 NIL NIL) (-1079 2563156 2569151 2569227 "SHDP" 2569232 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1078 2562755 2562921 2562951 "SGROUP" 2563044 T SGROUP (NIL) -9 NIL 2563106) (-1077 2562613 2562639 2562712 "SGROUP-" 2562717 NIL SGROUP- (NIL T) -8 NIL NIL) (-1076 2559449 2560146 2560869 "SGCF" 2561912 T SGCF (NIL) -7 NIL NIL) (-1075 2553844 2558896 2558993 "SFRTCAT" 2558998 NIL SFRTCAT (NIL T T T T) -9 NIL 2559037) (-1074 2547268 2548283 2549419 "SFRGCD" 2552827 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1073 2540396 2541467 2542653 "SFQCMPK" 2546201 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1072 2540018 2540107 2540217 "SFORT" 2540337 NIL SFORT (NIL T T) -8 NIL NIL) (-1071 2539163 2539858 2539979 "SEXOF" 2539984 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1070 2538297 2539044 2539112 "SEX" 2539117 T SEX (NIL) -8 NIL NIL) (-1069 2533073 2533762 2533857 "SEXCAT" 2537628 NIL SEXCAT (NIL T T T T T) -9 NIL 2538247) (-1068 2530253 2533007 2533055 "SET" 2533060 NIL SET (NIL T) -8 NIL NIL) (-1067 2528504 2528966 2529271 "SETMN" 2529994 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1066 2528110 2528236 2528266 "SETCAT" 2528383 T SETCAT (NIL) -9 NIL 2528468) (-1065 2527890 2527942 2528041 "SETCAT-" 2528046 NIL SETCAT- (NIL T) -8 NIL NIL) (-1064 2524277 2526351 2526394 "SETAGG" 2527264 NIL SETAGG (NIL T) -9 NIL 2527604) (-1063 2523735 2523851 2524088 "SETAGG-" 2524093 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1062 2523205 2523431 2523532 "SEQAST" 2523656 T SEQAST (NIL) -8 NIL NIL) (-1061 2522409 2522702 2522763 "SEGXCAT" 2523049 NIL SEGXCAT (NIL T T) -9 NIL 2523169) (-1060 2521465 2522075 2522257 "SEG" 2522262 NIL SEG (NIL T) -8 NIL NIL) (-1059 2520372 2520585 2520628 "SEGCAT" 2521210 NIL SEGCAT (NIL T) -9 NIL 2521448) (-1058 2519421 2519751 2519951 "SEGBIND" 2520207 NIL SEGBIND (NIL T) -8 NIL NIL) (-1057 2519042 2519101 2519214 "SEGBIND2" 2519356 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1056 2518643 2518843 2518920 "SEGAST" 2518987 T SEGAST (NIL) -8 NIL NIL) (-1055 2517862 2517988 2518192 "SEG2" 2518487 NIL SEG2 (NIL T T) -7 NIL NIL) (-1054 2517299 2517797 2517844 "SDVAR" 2517849 NIL SDVAR (NIL T) -8 NIL NIL) (-1053 2509589 2517069 2517199 "SDPOL" 2517204 NIL SDPOL (NIL T) -8 NIL NIL) (-1052 2508182 2508448 2508767 "SCPKG" 2509304 NIL SCPKG (NIL T) -7 NIL NIL) (-1051 2507318 2507498 2507698 "SCOPE" 2508004 T SCOPE (NIL) -8 NIL NIL) (-1050 2506539 2506672 2506851 "SCACHE" 2507173 NIL SCACHE (NIL T) -7 NIL NIL) (-1049 2506248 2506408 2506438 "SASTCAT" 2506443 T SASTCAT (NIL) -9 NIL 2506456) (-1048 2505687 2506008 2506093 "SAOS" 2506185 T SAOS (NIL) -8 NIL NIL) (-1047 2505252 2505287 2505460 "SAERFFC" 2505646 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1046 2499226 2505149 2505229 "SAE" 2505234 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1045 2498819 2498854 2499013 "SAEFACT" 2499185 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1044 2497140 2497454 2497855 "RURPK" 2498485 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1043 2495776 2496055 2496367 "RULESET" 2496974 NIL RULESET (NIL T T T) -8 NIL NIL) (-1042 2492963 2493466 2493931 "RULE" 2495457 NIL RULE (NIL T T T) -8 NIL NIL) (-1041 2492602 2492757 2492840 "RULECOLD" 2492915 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1040 2492100 2492319 2492413 "RSTRCAST" 2492530 T RSTRCAST (NIL) -8 NIL NIL) (-1039 2486949 2487743 2488663 "RSETGCD" 2491299 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1038 2476206 2481258 2481355 "RSETCAT" 2485474 NIL RSETCAT (NIL T T T T) -9 NIL 2486571) (-1037 2474133 2474672 2475496 "RSETCAT-" 2475501 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1036 2466520 2467895 2469415 "RSDCMPK" 2472732 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1035 2464525 2464966 2465040 "RRCC" 2466126 NIL RRCC (NIL T T) -9 NIL 2466470) (-1034 2463876 2464050 2464329 "RRCC-" 2464334 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1033 2463346 2463572 2463673 "RPTAST" 2463797 T RPTAST (NIL) -8 NIL NIL) (-1032 2437574 2447159 2447226 "RPOLCAT" 2457890 NIL RPOLCAT (NIL T T T) -9 NIL 2461049) (-1031 2429074 2431412 2434534 "RPOLCAT-" 2434539 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1030 2420121 2427285 2427767 "ROUTINE" 2428614 T ROUTINE (NIL) -8 NIL NIL) (-1029 2416879 2419672 2419821 "ROMAN" 2419994 T ROMAN (NIL) -8 NIL NIL) (-1028 2415154 2415739 2415999 "ROIRC" 2416684 NIL ROIRC (NIL T T) -8 NIL NIL) (-1027 2411605 2413844 2413874 "RNS" 2414178 T RNS (NIL) -9 NIL 2414450) (-1026 2410114 2410497 2411031 "RNS-" 2411106 NIL RNS- (NIL T) -8 NIL NIL) (-1025 2409563 2409945 2409975 "RNG" 2409980 T RNG (NIL) -9 NIL 2410001) (-1024 2408955 2409317 2409360 "RMODULE" 2409422 NIL RMODULE (NIL T) -9 NIL 2409464) (-1023 2407791 2407885 2408221 "RMCAT2" 2408856 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1022 2404496 2406965 2407290 "RMATRIX" 2407525 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1021 2397438 2399672 2399787 "RMATCAT" 2403146 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2404128) (-1020 2396813 2396960 2397267 "RMATCAT-" 2397272 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1019 2396380 2396455 2396583 "RINTERP" 2396732 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1018 2395468 2395988 2396018 "RING" 2396130 T RING (NIL) -9 NIL 2396225) (-1017 2395260 2395304 2395401 "RING-" 2395406 NIL RING- (NIL T) -8 NIL NIL) (-1016 2394101 2394338 2394596 "RIDIST" 2395024 T RIDIST (NIL) -7 NIL NIL) (-1015 2385417 2393569 2393775 "RGCHAIN" 2393949 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1014 2382411 2383025 2383695 "RF" 2384781 NIL RF (NIL T) -7 NIL NIL) (-1013 2382057 2382120 2382223 "RFFACTOR" 2382342 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1012 2381782 2381817 2381914 "RFFACT" 2382016 NIL RFFACT (NIL T) -7 NIL NIL) (-1011 2379899 2380263 2380645 "RFDIST" 2381422 T RFDIST (NIL) -7 NIL NIL) (-1010 2379352 2379444 2379607 "RETSOL" 2379801 NIL RETSOL (NIL T T) -7 NIL NIL) (-1009 2378940 2379020 2379063 "RETRACT" 2379256 NIL RETRACT (NIL T) -9 NIL NIL) (-1008 2378789 2378814 2378901 "RETRACT-" 2378906 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1007 2378418 2378611 2378681 "RETAST" 2378741 T RETAST (NIL) -8 NIL NIL) (-1006 2371272 2378071 2378198 "RESULT" 2378313 T RESULT (NIL) -8 NIL NIL) (-1005 2369898 2370541 2370740 "RESRING" 2371175 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1004 2369534 2369583 2369681 "RESLATC" 2369835 NIL RESLATC (NIL T) -7 NIL NIL) (-1003 2369240 2369274 2369381 "REPSQ" 2369493 NIL REPSQ (NIL T) -7 NIL NIL) (-1002 2366662 2367242 2367844 "REP" 2368660 T REP (NIL) -7 NIL NIL) (-1001 2366360 2366394 2366505 "REPDB" 2366621 NIL REPDB (NIL T) -7 NIL NIL) (-1000 2360270 2361649 2362872 "REP2" 2365172 NIL REP2 (NIL T) -7 NIL NIL) (-999 2356662 2357343 2358149 "REP1" 2359497 NIL REP1 (NIL T) -7 NIL NIL) (-998 2349400 2354815 2355269 "REGSET" 2356292 NIL REGSET (NIL T T T T) -8 NIL NIL) (-997 2348221 2348556 2348804 "REF" 2349185 NIL REF (NIL T) -8 NIL NIL) (-996 2347602 2347705 2347870 "REDORDER" 2348105 NIL REDORDER (NIL T T) -7 NIL NIL) (-995 2343622 2346830 2347053 "RECLOS" 2347431 NIL RECLOS (NIL T) -8 NIL NIL) (-994 2342679 2342860 2343073 "REALSOLV" 2343429 T REALSOLV (NIL) -7 NIL NIL) (-993 2342527 2342568 2342596 "REAL" 2342601 T REAL (NIL) -9 NIL 2342636) (-992 2339018 2339820 2340702 "REAL0Q" 2341692 NIL REAL0Q (NIL T) -7 NIL NIL) (-991 2334629 2335617 2336676 "REAL0" 2337999 NIL REAL0 (NIL T) -7 NIL NIL) (-990 2334131 2334350 2334442 "RDUCEAST" 2334557 T RDUCEAST (NIL) -8 NIL NIL) (-989 2333539 2333611 2333816 "RDIV" 2334053 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-988 2332612 2332786 2332997 "RDIST" 2333361 NIL RDIST (NIL T) -7 NIL NIL) (-987 2331213 2331500 2331870 "RDETRS" 2332320 NIL RDETRS (NIL T T) -7 NIL NIL) (-986 2329030 2329484 2330020 "RDETR" 2330755 NIL RDETR (NIL T T) -7 NIL NIL) (-985 2327644 2327922 2328324 "RDEEFS" 2328746 NIL RDEEFS (NIL T T) -7 NIL NIL) (-984 2326142 2326448 2326878 "RDEEF" 2327332 NIL RDEEF (NIL T T) -7 NIL NIL) (-983 2320479 2323350 2323378 "RCFIELD" 2324655 T RCFIELD (NIL) -9 NIL 2325385) (-982 2318548 2319052 2319745 "RCFIELD-" 2319818 NIL RCFIELD- (NIL T) -8 NIL NIL) (-981 2314879 2316664 2316705 "RCAGG" 2317776 NIL RCAGG (NIL T) -9 NIL 2318241) (-980 2314510 2314604 2314764 "RCAGG-" 2314769 NIL RCAGG- (NIL T T) -8 NIL NIL) (-979 2313850 2313962 2314125 "RATRET" 2314394 NIL RATRET (NIL T) -7 NIL NIL) (-978 2313407 2313474 2313593 "RATFACT" 2313778 NIL RATFACT (NIL T) -7 NIL NIL) (-977 2312722 2312842 2312992 "RANDSRC" 2313277 T RANDSRC (NIL) -7 NIL NIL) (-976 2312459 2312503 2312574 "RADUTIL" 2312671 T RADUTIL (NIL) -7 NIL NIL) (-975 2305524 2311202 2311519 "RADIX" 2312174 NIL RADIX (NIL NIL) -8 NIL NIL) (-974 2297180 2305368 2305496 "RADFF" 2305501 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-973 2296832 2296907 2296935 "RADCAT" 2297092 T RADCAT (NIL) -9 NIL NIL) (-972 2296617 2296665 2296762 "RADCAT-" 2296767 NIL RADCAT- (NIL T) -8 NIL NIL) (-971 2294768 2296392 2296481 "QUEUE" 2296561 NIL QUEUE (NIL T) -8 NIL NIL) (-970 2291344 2294705 2294750 "QUAT" 2294755 NIL QUAT (NIL T) -8 NIL NIL) (-969 2290982 2291025 2291152 "QUATCT2" 2291295 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-968 2284842 2288143 2288183 "QUATCAT" 2288963 NIL QUATCAT (NIL T) -9 NIL 2289729) (-967 2280986 2282023 2283410 "QUATCAT-" 2283504 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-966 2278506 2280070 2280111 "QUAGG" 2280486 NIL QUAGG (NIL T) -9 NIL 2280661) (-965 2278138 2278331 2278399 "QQUTAST" 2278458 T QQUTAST (NIL) -8 NIL NIL) (-964 2277063 2277536 2277708 "QFORM" 2278010 NIL QFORM (NIL NIL T) -8 NIL NIL) (-963 2268396 2273599 2273639 "QFCAT" 2274297 NIL QFCAT (NIL T) -9 NIL 2275296) (-962 2263968 2265169 2266760 "QFCAT-" 2266854 NIL QFCAT- (NIL T T) -8 NIL NIL) (-961 2263606 2263649 2263776 "QFCAT2" 2263919 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-960 2263066 2263176 2263306 "QEQUAT" 2263496 T QEQUAT (NIL) -8 NIL NIL) (-959 2256214 2257285 2258469 "QCMPACK" 2261999 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-958 2253790 2254211 2254639 "QALGSET" 2255869 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-957 2253035 2253209 2253441 "QALGSET2" 2253610 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-956 2251726 2251949 2252266 "PWFFINTB" 2252808 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-955 2249908 2250076 2250430 "PUSHVAR" 2251540 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-954 2245826 2246880 2246921 "PTRANFN" 2248805 NIL PTRANFN (NIL T) -9 NIL NIL) (-953 2244228 2244519 2244841 "PTPACK" 2245537 NIL PTPACK (NIL T) -7 NIL NIL) (-952 2243860 2243917 2244026 "PTFUNC2" 2244165 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-951 2238326 2242671 2242712 "PTCAT" 2243085 NIL PTCAT (NIL T) -9 NIL 2243247) (-950 2237984 2238019 2238143 "PSQFR" 2238285 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-949 2236579 2236877 2237211 "PSEUDLIN" 2237682 NIL 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1950577 1951635 "OREPCAT-" 1951640 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-823 1948972 1949244 1949272 "ORDSET" 1949581 T ORDSET (NIL) -9 NIL 1949745) (-822 1948491 1948613 1948806 "ORDSET-" 1948811 NIL ORDSET- (NIL T) -8 NIL NIL) (-821 1947145 1947902 1947930 "ORDRING" 1948132 T ORDRING (NIL) -9 NIL 1948257) (-820 1946790 1946884 1947028 "ORDRING-" 1947033 NIL ORDRING- (NIL T) -8 NIL NIL) (-819 1946196 1946633 1946661 "ORDMON" 1946666 T ORDMON (NIL) -9 NIL 1946687) (-818 1945358 1945505 1945700 "ORDFUNS" 1946045 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-817 1944869 1945228 1945256 "ORDFIN" 1945261 T ORDFIN (NIL) -9 NIL 1945282) (-816 1941461 1943455 1943864 "ORDCOMP" 1944493 NIL ORDCOMP (NIL T) -8 NIL NIL) (-815 1940727 1940854 1941040 "ORDCOMP2" 1941321 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-814 1937234 1938117 1938954 "OPTPROB" 1939910 T OPTPROB (NIL) -8 NIL NIL) (-813 1934036 1934675 1935379 "OPTPACK" 1936550 T OPTPACK (NIL) -7 NIL NIL) (-812 1931749 1932489 1932517 "OPTCAT" 1933336 T 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NIL NIL) (-798 1908569 1909754 1910925 "OMDEV" 1913523 T OMDEV (NIL) -8 NIL NIL) (-797 1907638 1907809 1908003 "OMCONN" 1908395 T OMCONN (NIL) -8 NIL NIL) (-796 1906294 1907236 1907264 "OINTDOM" 1907269 T OINTDOM (NIL) -9 NIL 1907290) (-795 1902100 1903284 1904000 "OFMONOID" 1905610 NIL OFMONOID (NIL T) -8 NIL NIL) (-794 1901538 1902037 1902082 "ODVAR" 1902087 NIL ODVAR (NIL T) -8 NIL NIL) (-793 1898748 1901035 1901220 "ODR" 1901413 NIL ODR (NIL T T NIL) -8 NIL NIL) (-792 1891092 1898524 1898650 "ODPOL" 1898655 NIL ODPOL (NIL T) -8 NIL NIL) (-791 1884968 1890964 1891069 "ODP" 1891074 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-790 1883734 1883949 1884224 "ODETOOLS" 1884742 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-789 1880703 1881359 1882075 "ODESYS" 1883067 NIL ODESYS (NIL T T) -7 NIL NIL) (-788 1875585 1876493 1877518 "ODERTRIC" 1879778 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-787 1875011 1875093 1875287 "ODERED" 1875497 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-786 1871899 1872447 1873124 "ODERAT" 1874434 NIL ODERAT (NIL T T) -7 NIL NIL) (-785 1868859 1869323 1869920 "ODEPRRIC" 1871428 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-784 1866728 1867297 1867806 "ODEPROB" 1868370 T ODEPROB (NIL) -8 NIL NIL) (-783 1863250 1863733 1864380 "ODEPRIM" 1866207 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-782 1862499 1862601 1862861 "ODEPAL" 1863142 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-781 1858661 1859452 1860316 "ODEPACK" 1861655 T ODEPACK (NIL) -7 NIL NIL) (-780 1857694 1857801 1858030 "ODEINT" 1858550 NIL ODEINT (NIL T T) -7 NIL NIL) (-779 1851795 1853220 1854667 "ODEIFTBL" 1856267 T ODEIFTBL (NIL) -8 NIL NIL) (-778 1847130 1847916 1848875 "ODEEF" 1850954 NIL ODEEF (NIL T T) -7 NIL NIL) (-777 1846465 1846554 1846784 "ODECONST" 1847035 NIL ODECONST (NIL T T T) -7 NIL NIL) (-776 1844616 1845251 1845279 "ODECAT" 1845884 T ODECAT (NIL) -9 NIL 1846415) (-775 1841523 1844328 1844447 "OCT" 1844529 NIL OCT (NIL T) -8 NIL NIL) (-774 1841161 1841204 1841331 "OCTCT2" 1841474 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-773 1836022 1838422 1838462 "OC" 1839559 NIL OC (NIL T) -9 NIL 1840417) (-772 1833249 1833997 1834987 "OC-" 1835081 NIL OC- (NIL T T) -8 NIL NIL) (-771 1832627 1833069 1833097 "OCAMON" 1833102 T OCAMON (NIL) -9 NIL 1833123) (-770 1832184 1832499 1832527 "OASGP" 1832532 T OASGP (NIL) -9 NIL 1832552) (-769 1831471 1831934 1831962 "OAMONS" 1832002 T OAMONS (NIL) -9 NIL 1832045) (-768 1830911 1831318 1831346 "OAMON" 1831351 T OAMON (NIL) -9 NIL 1831371) (-767 1830215 1830707 1830735 "OAGROUP" 1830740 T OAGROUP (NIL) -9 NIL 1830760) (-766 1829905 1829955 1830043 "NUMTUBE" 1830159 NIL NUMTUBE (NIL T) -7 NIL NIL) (-765 1823478 1824996 1826532 "NUMQUAD" 1828389 T NUMQUAD (NIL) -7 NIL NIL) (-764 1819234 1820222 1821247 "NUMODE" 1822473 T NUMODE (NIL) -7 NIL NIL) (-763 1816615 1817469 1817497 "NUMINT" 1818420 T NUMINT (NIL) -9 NIL 1819184) (-762 1815563 1815760 1815978 "NUMFMT" 1816417 T NUMFMT (NIL) -7 NIL NIL) (-761 1801922 1804867 1807399 "NUMERIC" 1813070 NIL NUMERIC (NIL T) -7 NIL NIL) (-760 1796319 1801371 1801466 "NTSCAT" 1801471 NIL NTSCAT (NIL T T T T) -9 NIL 1801510) (-759 1795513 1795678 1795871 "NTPOLFN" 1796158 NIL NTPOLFN (NIL T) -7 NIL NIL) (-758 1783353 1792338 1793150 "NSUP" 1794734 NIL NSUP (NIL T) -8 NIL NIL) (-757 1782985 1783042 1783151 "NSUP2" 1783290 NIL NSUP2 (NIL T T) -7 NIL NIL) (-756 1772982 1782759 1782892 "NSMP" 1782897 NIL NSMP (NIL T T) -8 NIL NIL) (-755 1771414 1771715 1772072 "NREP" 1772670 NIL NREP (NIL T) -7 NIL NIL) (-754 1770005 1770257 1770615 "NPCOEF" 1771157 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-753 1769071 1769186 1769402 "NORMRETR" 1769886 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-752 1767112 1767402 1767811 "NORMPK" 1768779 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-751 1766797 1766825 1766949 "NORMMA" 1767078 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-750 1766624 1766754 1766783 "NONE" 1766788 T NONE (NIL) -8 NIL NIL) (-749 1766413 1766442 1766511 "NONE1" 1766588 NIL NONE1 (NIL T) -7 NIL NIL) (-748 1765896 1765958 1766144 "NODE1" 1766345 NIL NODE1 (NIL T T) -7 NIL NIL) (-747 1764236 1765059 1765314 "NNI" 1765661 T NNI (NIL) -8 NIL NIL) (-746 1762656 1762969 1763333 "NLINSOL" 1763904 NIL NLINSOL (NIL T) -7 NIL NIL) (-745 1758823 1759791 1760713 "NIPROB" 1761754 T NIPROB (NIL) -8 NIL NIL) (-744 1757580 1757814 1758116 "NFINTBAS" 1758585 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-743 1756288 1756519 1756800 "NCODIV" 1757348 NIL NCODIV (NIL T T) -7 NIL NIL) (-742 1756050 1756087 1756162 "NCNTFRAC" 1756245 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-741 1754230 1754594 1755014 "NCEP" 1755675 NIL NCEP (NIL T) -7 NIL NIL) (-740 1753141 1753880 1753908 "NASRING" 1754018 T NASRING (NIL) -9 NIL 1754092) (-739 1752936 1752980 1753074 "NASRING-" 1753079 NIL NASRING- (NIL T) -8 NIL NIL) (-738 1752089 1752588 1752616 "NARNG" 1752733 T NARNG (NIL) -9 NIL 1752824) (-737 1751781 1751848 1751982 "NARNG-" 1751987 NIL NARNG- (NIL T) -8 NIL NIL) (-736 1750660 1750867 1751102 "NAGSP" 1751566 T NAGSP (NIL) -7 NIL NIL) (-735 1741932 1743616 1745289 "NAGS" 1749007 T NAGS (NIL) -7 NIL NIL) (-734 1740480 1740788 1741119 "NAGF07" 1741621 T NAGF07 (NIL) -7 NIL NIL) (-733 1735018 1736309 1737616 "NAGF04" 1739193 T NAGF04 (NIL) -7 NIL NIL) (-732 1727986 1729600 1731233 "NAGF02" 1733405 T NAGF02 (NIL) -7 NIL NIL) (-731 1723210 1724310 1725427 "NAGF01" 1726889 T NAGF01 (NIL) -7 NIL NIL) (-730 1716838 1718404 1719989 "NAGE04" 1721645 T NAGE04 (NIL) -7 NIL NIL) (-729 1708007 1710128 1712258 "NAGE02" 1714728 T NAGE02 (NIL) -7 NIL NIL) (-728 1703960 1704907 1705871 "NAGE01" 1707063 T NAGE01 (NIL) -7 NIL NIL) (-727 1701755 1702289 1702847 "NAGD03" 1703422 T NAGD03 (NIL) -7 NIL NIL) (-726 1693505 1695433 1697387 "NAGD02" 1699821 T NAGD02 (NIL) -7 NIL NIL) (-725 1687316 1688741 1690181 "NAGD01" 1692085 T NAGD01 (NIL) -7 NIL NIL) (-724 1683525 1684347 1685184 "NAGC06" 1686499 T NAGC06 (NIL) -7 NIL NIL) (-723 1681990 1682322 1682678 "NAGC05" 1683189 T NAGC05 (NIL) -7 NIL NIL) (-722 1681366 1681485 1681629 "NAGC02" 1681866 T NAGC02 (NIL) -7 NIL NIL) (-721 1680426 1680983 1681023 "NAALG" 1681102 NIL NAALG (NIL T) -9 NIL 1681163) (-720 1680261 1680290 1680380 "NAALG-" 1680385 NIL NAALG- (NIL T T) -8 NIL NIL) (-719 1674211 1675319 1676506 "MULTSQFR" 1679157 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-718 1673530 1673605 1673789 "MULTFACT" 1674123 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-717 1666753 1670618 1670671 "MTSCAT" 1671741 NIL MTSCAT (NIL T T) -9 NIL 1672255) (-716 1666465 1666519 1666611 "MTHING" 1666693 NIL MTHING (NIL T) -7 NIL NIL) (-715 1666257 1666290 1666350 "MSYSCMD" 1666425 T MSYSCMD (NIL) -7 NIL NIL) (-714 1662369 1665012 1665332 "MSET" 1665970 NIL MSET (NIL T) -8 NIL NIL) (-713 1659464 1661930 1661971 "MSETAGG" 1661976 NIL MSETAGG (NIL T) -9 NIL 1662010) (-712 1655347 1656843 1657588 "MRING" 1658764 NIL MRING (NIL T T) -8 NIL NIL) (-711 1654913 1654980 1655111 "MRF2" 1655274 NIL MRF2 (NIL T T T) -7 NIL NIL) (-710 1654531 1654566 1654710 "MRATFAC" 1654872 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-709 1652143 1652438 1652869 "MPRFF" 1654236 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-708 1646203 1651997 1652094 "MPOLY" 1652099 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-707 1645693 1645728 1645936 "MPCPF" 1646162 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-706 1645207 1645250 1645434 "MPC3" 1645644 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-705 1644402 1644483 1644704 "MPC2" 1645122 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-704 1642703 1643040 1643430 "MONOTOOL" 1644062 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-703 1641954 1642245 1642273 "MONOID" 1642492 T MONOID (NIL) -9 NIL 1642639) (-702 1641500 1641619 1641800 "MONOID-" 1641805 NIL MONOID- (NIL T) -8 NIL NIL) (-701 1632550 1638456 1638515 "MONOGEN" 1639189 NIL MONOGEN (NIL T T) -9 NIL 1639645) (-700 1629768 1630503 1631503 "MONOGEN-" 1631622 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-699 1628627 1629047 1629075 "MONADWU" 1629467 T MONADWU (NIL) -9 NIL 1629705) (-698 1627999 1628158 1628406 "MONADWU-" 1628411 NIL MONADWU- (NIL T) -8 NIL NIL) (-697 1627384 1627602 1627630 "MONAD" 1627837 T MONAD (NIL) -9 NIL 1627949) (-696 1627069 1627147 1627279 "MONAD-" 1627284 NIL MONAD- (NIL T) -8 NIL NIL) (-695 1625385 1625982 1626261 "MOEBIUS" 1626822 NIL MOEBIUS (NIL T) -8 NIL NIL) (-694 1624777 1625155 1625195 "MODULE" 1625200 NIL MODULE (NIL T) -9 NIL 1625226) (-693 1624345 1624441 1624631 "MODULE-" 1624636 NIL MODULE- (NIL T T) -8 NIL NIL) (-692 1622060 1622709 1623036 "MODRING" 1624169 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-691 1619046 1620165 1620686 "MODOP" 1621589 NIL MODOP (NIL T T) -8 NIL NIL) (-690 1617233 1617685 1618026 "MODMONOM" 1618845 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-689 1606941 1615425 1615848 "MODMON" 1616861 NIL MODMON (NIL T T) -8 NIL NIL) (-688 1604132 1605785 1606061 "MODFIELD" 1606816 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-687 1603136 1603413 1603603 "MMLFORM" 1603962 T MMLFORM (NIL) -8 NIL NIL) (-686 1602662 1602705 1602884 "MMAP" 1603087 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-685 1600931 1601664 1601705 "MLO" 1602128 NIL MLO (NIL T) -9 NIL 1602370) (-684 1598298 1598813 1599415 "MLIFT" 1600412 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-683 1597689 1597773 1597927 "MKUCFUNC" 1598209 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-682 1597288 1597358 1597481 "MKRECORD" 1597612 NIL MKRECORD (NIL T T) -7 NIL NIL) (-681 1596336 1596497 1596725 "MKFUNC" 1597099 NIL MKFUNC (NIL T) -7 NIL NIL) (-680 1595724 1595828 1595984 "MKFLCFN" 1596219 NIL MKFLCFN (NIL T) -7 NIL NIL) (-679 1595150 1595517 1595606 "MKCHSET" 1595668 NIL MKCHSET (NIL T) -8 NIL NIL) (-678 1594427 1594529 1594714 "MKBCFUNC" 1595043 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-677 1591169 1593981 1594117 "MINT" 1594311 T MINT (NIL) -8 NIL NIL) (-676 1589981 1590224 1590501 "MHROWRED" 1590924 NIL MHROWRED (NIL T) -7 NIL NIL) (-675 1585407 1588516 1588921 "MFLOAT" 1589596 T MFLOAT (NIL) -8 NIL NIL) (-674 1584764 1584840 1585011 "MFINFACT" 1585319 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-673 1581079 1581927 1582811 "MESH" 1583900 T MESH (NIL) -7 NIL NIL) (-672 1579469 1579781 1580134 "MDDFACT" 1580766 NIL MDDFACT (NIL T) -7 NIL NIL) (-671 1576311 1578628 1578669 "MDAGG" 1578924 NIL MDAGG (NIL T) -9 NIL 1579067) (-670 1566091 1575604 1575811 "MCMPLX" 1576124 T MCMPLX (NIL) -8 NIL NIL) (-669 1565232 1565378 1565578 "MCDEN" 1565940 NIL MCDEN (NIL T T) -7 NIL NIL) (-668 1563122 1563392 1563772 "MCALCFN" 1564962 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-667 1562033 1562206 1562447 "MAYBE" 1562920 NIL MAYBE (NIL T) -8 NIL NIL) (-666 1559645 1560168 1560730 "MATSTOR" 1561504 NIL MATSTOR (NIL T) -7 NIL NIL) (-665 1555651 1559017 1559265 "MATRIX" 1559430 NIL MATRIX (NIL T) -8 NIL NIL) (-664 1551420 1552124 1552860 "MATLIN" 1555008 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-663 1541574 1544712 1544789 "MATCAT" 1549669 NIL MATCAT (NIL T T T) -9 NIL 1551086) (-662 1537938 1538951 1540307 "MATCAT-" 1540312 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-661 1536532 1536685 1537018 "MATCAT2" 1537773 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-660 1534644 1534968 1535352 "MAPPKG3" 1536207 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-659 1533625 1533798 1534020 "MAPPKG2" 1534468 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-658 1532124 1532408 1532735 "MAPPKG1" 1533331 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-657 1531230 1531530 1531707 "MAPPAST" 1531967 T MAPPAST (NIL) -8 NIL NIL) (-656 1530841 1530899 1531022 "MAPHACK3" 1531166 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-655 1530433 1530494 1530608 "MAPHACK2" 1530773 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-654 1529871 1529974 1530116 "MAPHACK1" 1530324 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-653 1527977 1528571 1528875 "MAGMA" 1529599 NIL MAGMA (NIL T) -8 NIL NIL) (-652 1527483 1527701 1527792 "MACROAST" 1527906 T MACROAST (NIL) -8 NIL NIL) (-651 1523950 1525722 1526183 "M3D" 1527055 NIL M3D (NIL T) -8 NIL NIL) (-650 1518105 1522320 1522361 "LZSTAGG" 1523143 NIL LZSTAGG (NIL T) -9 NIL 1523438) (-649 1514078 1515236 1516693 "LZSTAGG-" 1516698 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-648 1511192 1511969 1512456 "LWORD" 1513623 NIL LWORD (NIL T) -8 NIL NIL) (-647 1510795 1510996 1511071 "LSTAST" 1511137 T LSTAST (NIL) -8 NIL NIL) (-646 1503996 1510566 1510700 "LSQM" 1510705 NIL LSQM (NIL NIL T) -8 NIL NIL) (-645 1503220 1503359 1503587 "LSPP" 1503851 NIL LSPP (NIL T T T T) -7 NIL NIL) (-644 1501032 1501333 1501789 "LSMP" 1502909 NIL LSMP (NIL T T T T) -7 NIL NIL) (-643 1497811 1498485 1499215 "LSMP1" 1500334 NIL LSMP1 (NIL T) -7 NIL NIL) (-642 1491737 1496979 1497020 "LSAGG" 1497082 NIL LSAGG (NIL T) -9 NIL 1497160) (-641 1488432 1489356 1490569 "LSAGG-" 1490574 NIL LSAGG- (NIL T T) -8 NIL NIL) (-640 1486058 1487576 1487825 "LPOLY" 1488227 NIL LPOLY (NIL T T) -8 NIL NIL) (-639 1485640 1485725 1485848 "LPEFRAC" 1485967 NIL LPEFRAC (NIL T) -7 NIL NIL) (-638 1483987 1484734 1484987 "LO" 1485472 NIL LO (NIL T T T) -8 NIL NIL) (-637 1483639 1483751 1483779 "LOGIC" 1483890 T LOGIC (NIL) -9 NIL 1483971) (-636 1483501 1483524 1483595 "LOGIC-" 1483600 NIL LOGIC- (NIL T) -8 NIL NIL) (-635 1482694 1482834 1483027 "LODOOPS" 1483357 NIL LODOOPS (NIL T T) -7 NIL NIL) (-634 1480152 1482610 1482676 "LODO" 1482681 NIL LODO (NIL T NIL) -8 NIL NIL) (-633 1478690 1478925 1479278 "LODOF" 1479899 NIL LODOF (NIL T T) -7 NIL NIL) (-632 1475133 1477530 1477571 "LODOCAT" 1478009 NIL LODOCAT (NIL T) -9 NIL 1478220) (-631 1474866 1474924 1475051 "LODOCAT-" 1475056 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-630 1472221 1474707 1474825 "LODO2" 1474830 NIL LODO2 (NIL T T) -8 NIL NIL) (-629 1469691 1472158 1472203 "LODO1" 1472208 NIL LODO1 (NIL T) -8 NIL NIL) (-628 1468551 1468716 1469028 "LODEEF" 1469514 NIL LODEEF (NIL T T T) -7 NIL NIL) (-627 1463837 1466681 1466722 "LNAGG" 1467669 NIL LNAGG (NIL T) -9 NIL 1468113) (-626 1462984 1463198 1463540 "LNAGG-" 1463545 NIL LNAGG- (NIL T T) -8 NIL NIL) (-625 1459147 1459909 1460548 "LMOPS" 1462399 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-624 1458542 1458904 1458945 "LMODULE" 1459006 NIL LMODULE (NIL T) -9 NIL 1459048) (-623 1455788 1458187 1458310 "LMDICT" 1458452 NIL LMDICT (NIL T) -8 NIL NIL) (-622 1455514 1455696 1455756 "LITERAL" 1455761 NIL LITERAL (NIL T) -8 NIL NIL) (-621 1448741 1454460 1454758 "LIST" 1455249 NIL LIST (NIL T) -8 NIL NIL) (-620 1448266 1448340 1448479 "LIST3" 1448661 NIL LIST3 (NIL T T T) -7 NIL NIL) (-619 1447273 1447451 1447679 "LIST2" 1448084 NIL LIST2 (NIL T T) -7 NIL NIL) (-618 1445407 1445719 1446118 "LIST2MAP" 1446920 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-617 1444157 1444793 1444834 "LINEXP" 1445089 NIL LINEXP (NIL T) -9 NIL 1445238) (-616 1442804 1443064 1443361 "LINDEP" 1443909 NIL LINDEP (NIL T T) -7 NIL NIL) (-615 1439571 1440290 1441067 "LIMITRF" 1442059 NIL LIMITRF (NIL T) -7 NIL NIL) (-614 1437847 1438142 1438558 "LIMITPS" 1439266 NIL LIMITPS (NIL T T) -7 NIL NIL) (-613 1432302 1437358 1437586 "LIE" 1437668 NIL LIE (NIL T T) -8 NIL NIL) (-612 1431351 1431794 1431834 "LIECAT" 1431974 NIL LIECAT (NIL T) -9 NIL 1432125) (-611 1431192 1431219 1431307 "LIECAT-" 1431312 NIL LIECAT- (NIL T T) -8 NIL NIL) (-610 1423804 1430641 1430806 "LIB" 1431047 T LIB (NIL) -8 NIL NIL) (-609 1419441 1420322 1421257 "LGROBP" 1422921 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-608 1417307 1417581 1417943 "LF" 1419162 NIL LF (NIL T T) -7 NIL NIL) (-607 1416147 1416839 1416867 "LFCAT" 1417074 T LFCAT (NIL) -9 NIL 1417213) (-606 1413051 1413679 1414367 "LEXTRIPK" 1415511 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-605 1409822 1410621 1411124 "LEXP" 1412631 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-604 1409325 1409543 1409635 "LETAST" 1409750 T LETAST (NIL) -8 NIL NIL) (-603 1407723 1408036 1408437 "LEADCDET" 1409007 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-602 1406913 1406987 1407216 "LAZM3PK" 1407644 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-601 1401869 1404990 1405528 "LAUPOL" 1406425 NIL LAUPOL (NIL T T) -8 NIL NIL) (-600 1401434 1401478 1401646 "LAPLACE" 1401819 NIL LAPLACE (NIL T T) -7 NIL NIL) (-599 1399408 1400535 1400786 "LA" 1401267 NIL LA (NIL T T T) -8 NIL NIL) (-598 1398509 1399059 1399100 "LALG" 1399162 NIL LALG (NIL T) -9 NIL 1399221) (-597 1398223 1398282 1398418 "LALG-" 1398423 NIL LALG- (NIL T T) -8 NIL NIL) (-596 1397023 1397440 1397669 "KTVLOGIC" 1398014 T KTVLOGIC (NIL) -8 NIL NIL) (-595 1395927 1396114 1396413 "KOVACIC" 1396823 NIL KOVACIC (NIL T T) -7 NIL NIL) (-594 1395762 1395786 1395827 "KONVERT" 1395889 NIL KONVERT (NIL T) -9 NIL NIL) (-593 1395597 1395621 1395662 "KOERCE" 1395724 NIL KOERCE (NIL T) -9 NIL NIL) (-592 1393331 1394091 1394484 "KERNEL" 1395236 NIL KERNEL (NIL T) -8 NIL NIL) (-591 1392833 1392914 1393044 "KERNEL2" 1393245 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-590 1386684 1391372 1391426 "KDAGG" 1391803 NIL KDAGG (NIL T T) -9 NIL 1392009) (-589 1386213 1386337 1386542 "KDAGG-" 1386547 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-588 1379388 1385874 1386029 "KAFILE" 1386091 NIL KAFILE (NIL T) -8 NIL NIL) (-587 1373843 1378899 1379127 "JORDAN" 1379209 NIL JORDAN (NIL T T) -8 NIL NIL) (-586 1373249 1373492 1373613 "JOINAST" 1373742 T JOINAST (NIL) -8 NIL NIL) (-585 1372978 1373037 1373124 "JAVACODE" 1373182 T JAVACODE (NIL) -8 NIL NIL) (-584 1369277 1371183 1371237 "IXAGG" 1372166 NIL IXAGG (NIL T T) -9 NIL 1372625) (-583 1368196 1368502 1368921 "IXAGG-" 1368926 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-582 1363776 1368118 1368177 "IVECTOR" 1368182 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-581 1362542 1362779 1363045 "ITUPLE" 1363543 NIL ITUPLE (NIL T) -8 NIL NIL) (-580 1360978 1361155 1361461 "ITRIGMNP" 1362364 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-579 1359723 1359927 1360210 "ITFUN3" 1360754 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-578 1359355 1359412 1359521 "ITFUN2" 1359660 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-577 1357192 1358217 1358516 "ITAYLOR" 1359089 NIL ITAYLOR (NIL T) -8 NIL NIL) (-576 1346186 1351338 1352498 "ISUPS" 1356065 NIL ISUPS (NIL T) -8 NIL NIL) (-575 1345290 1345430 1345666 "ISUMP" 1346033 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-574 1340554 1345091 1345170 "ISTRING" 1345243 NIL ISTRING (NIL NIL) -8 NIL NIL) (-573 1340057 1340275 1340367 "ISAST" 1340482 T ISAST (NIL) -8 NIL NIL) (-572 1339267 1339348 1339564 "IRURPK" 1339971 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-571 1338203 1338404 1338644 "IRSN" 1339047 T IRSN (NIL) -7 NIL NIL) (-570 1336232 1336587 1337023 "IRRF2F" 1337841 NIL IRRF2F (NIL T) -7 NIL NIL) (-569 1335979 1336017 1336093 "IRREDFFX" 1336188 NIL IRREDFFX (NIL T) -7 NIL NIL) (-568 1334594 1334853 1335152 "IROOT" 1335712 NIL IROOT (NIL T) -7 NIL NIL) (-567 1331226 1332278 1332970 "IR" 1333934 NIL IR (NIL T) -8 NIL NIL) (-566 1328839 1329334 1329900 "IR2" 1330704 NIL IR2 (NIL T T) -7 NIL NIL) (-565 1327911 1328024 1328245 "IR2F" 1328722 NIL IR2F (NIL T T) -7 NIL NIL) (-564 1327702 1327736 1327796 "IPRNTPK" 1327871 T IPRNTPK (NIL) -7 NIL NIL) (-563 1324321 1327591 1327660 "IPF" 1327665 NIL IPF (NIL NIL) -8 NIL NIL) (-562 1322684 1324246 1324303 "IPADIC" 1324308 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-561 1322448 1322588 1322616 "IOBCON" 1322621 T IOBCON (NIL) -9 NIL 1322642) (-560 1321945 1322003 1322193 "INVLAPLA" 1322384 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-559 1311594 1313947 1316333 "INTTR" 1319609 NIL INTTR (NIL T T) -7 NIL NIL) (-558 1307938 1308680 1309544 "INTTOOLS" 1310779 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-557 1307524 1307615 1307732 "INTSLPE" 1307841 T INTSLPE (NIL) -7 NIL NIL) (-556 1305519 1307447 1307506 "INTRVL" 1307511 NIL INTRVL (NIL T) -8 NIL NIL) (-555 1303121 1303633 1304208 "INTRF" 1305004 NIL INTRF (NIL T) -7 NIL NIL) (-554 1302532 1302629 1302771 "INTRET" 1303019 NIL INTRET (NIL T) -7 NIL NIL) (-553 1300529 1300918 1301388 "INTRAT" 1302140 NIL INTRAT (NIL T T) -7 NIL NIL) (-552 1297757 1298340 1298966 "INTPM" 1300014 NIL INTPM (NIL T T) -7 NIL NIL) (-551 1294460 1295059 1295804 "INTPAF" 1297143 NIL INTPAF (NIL T T T) -7 NIL NIL) (-550 1289639 1290601 1291652 "INTPACK" 1293429 T INTPACK (NIL) -7 NIL NIL) (-549 1286551 1289368 1289495 "INT" 1289532 T INT (NIL) -8 NIL NIL) (-548 1285803 1285955 1286163 "INTHERTR" 1286393 NIL INTHERTR (NIL T T) -7 NIL NIL) (-547 1285242 1285322 1285510 "INTHERAL" 1285717 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-546 1283088 1283531 1283988 "INTHEORY" 1284805 T INTHEORY (NIL) -7 NIL NIL) (-545 1274396 1276017 1277796 "INTG0" 1281440 NIL INTG0 (NIL T T T) -7 NIL NIL) (-544 1254969 1259759 1264569 "INTFTBL" 1269606 T INTFTBL (NIL) -8 NIL NIL) (-543 1254218 1254356 1254529 "INTFACT" 1254828 NIL INTFACT (NIL T) -7 NIL NIL) (-542 1251603 1252049 1252613 "INTEF" 1253772 NIL INTEF (NIL T T) -7 NIL NIL) (-541 1250105 1250810 1250838 "INTDOM" 1251139 T INTDOM (NIL) -9 NIL 1251346) (-540 1249474 1249648 1249890 "INTDOM-" 1249895 NIL INTDOM- (NIL T) -8 NIL NIL) (-539 1246007 1247893 1247947 "INTCAT" 1248746 NIL INTCAT (NIL T) -9 NIL 1249066) (-538 1245480 1245582 1245710 "INTBIT" 1245899 T INTBIT (NIL) -7 NIL NIL) (-537 1244151 1244305 1244619 "INTALG" 1245325 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-536 1243608 1243698 1243868 "INTAF" 1244055 NIL INTAF (NIL T T) -7 NIL NIL) (-535 1237062 1243418 1243558 "INTABL" 1243563 NIL INTABL (NIL T T T) -8 NIL NIL) (-534 1232117 1234788 1234816 "INS" 1235750 T INS (NIL) -9 NIL 1236414) (-533 1229357 1230128 1231102 "INS-" 1231175 NIL INS- (NIL T) -8 NIL NIL) (-532 1228132 1228359 1228657 "INPSIGN" 1229110 NIL INPSIGN (NIL T T) -7 NIL NIL) (-531 1227250 1227367 1227564 "INPRODPF" 1228012 NIL INPRODPF (NIL T T) -7 NIL NIL) (-530 1226144 1226261 1226498 "INPRODFF" 1227130 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-529 1225144 1225296 1225556 "INNMFACT" 1225980 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-528 1224341 1224438 1224626 "INMODGCD" 1225043 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-527 1222850 1223094 1223418 "INFSP" 1224086 NIL INFSP (NIL T T T) -7 NIL NIL) (-526 1222034 1222151 1222334 "INFPROD0" 1222730 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-525 1218916 1220099 1220614 "INFORM" 1221527 T INFORM (NIL) -8 NIL NIL) (-524 1218526 1218586 1218684 "INFORM1" 1218851 NIL INFORM1 (NIL T) -7 NIL NIL) (-523 1218049 1218138 1218252 "INFINITY" 1218432 T INFINITY (NIL) -7 NIL NIL) (-522 1216666 1216915 1217236 "INEP" 1217797 NIL INEP (NIL T T T) -7 NIL NIL) (-521 1215942 1216563 1216628 "INDE" 1216633 NIL INDE (NIL T) -8 NIL NIL) (-520 1215506 1215574 1215691 "INCRMAPS" 1215869 NIL INCRMAPS (NIL T) -7 NIL NIL) (-519 1210817 1211742 1212686 "INBFF" 1214594 NIL INBFF (NIL T) -7 NIL NIL) (-518 1210486 1210562 1210590 "INBCON" 1210723 T INBCON (NIL) -9 NIL 1210801) (-517 1210326 1210361 1210437 "INBCON-" 1210442 NIL INBCON- (NIL T) -8 NIL NIL) (-516 1209828 1210047 1210139 "INAST" 1210254 T INAST (NIL) -8 NIL NIL) (-515 1209282 1209507 1209613 "IMPTAST" 1209742 T IMPTAST (NIL) -8 NIL NIL) (-514 1205776 1209126 1209230 "IMATRIX" 1209235 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-513 1204488 1204611 1204926 "IMATQF" 1205632 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-512 1202708 1202935 1203272 "IMATLIN" 1204244 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-511 1197334 1202632 1202690 "ILIST" 1202695 NIL ILIST (NIL T NIL) -8 NIL NIL) (-510 1195287 1197194 1197307 "IIARRAY2" 1197312 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-509 1190720 1195198 1195262 "IFF" 1195267 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-508 1190094 1190337 1190453 "IFAST" 1190624 T IFAST (NIL) -8 NIL NIL) (-507 1185137 1189386 1189574 "IFARRAY" 1189951 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-506 1184344 1185041 1185114 "IFAMON" 1185119 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-505 1183928 1183993 1184047 "IEVALAB" 1184254 NIL IEVALAB (NIL T T) -9 NIL NIL) (-504 1183603 1183671 1183831 "IEVALAB-" 1183836 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-503 1183261 1183517 1183580 "IDPO" 1183585 NIL IDPO (NIL T T) -8 NIL NIL) (-502 1182538 1183150 1183225 "IDPOAMS" 1183230 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-501 1181872 1182427 1182502 "IDPOAM" 1182507 NIL IDPOAM (NIL T T) -8 NIL NIL) (-500 1180957 1181207 1181260 "IDPC" 1181673 NIL IDPC (NIL T T) -9 NIL 1181822) (-499 1180453 1180849 1180922 "IDPAM" 1180927 NIL IDPAM (NIL T T) -8 NIL NIL) (-498 1179856 1180345 1180418 "IDPAG" 1180423 NIL IDPAG (NIL T T) -8 NIL NIL) (-497 1179586 1179771 1179821 "IDENT" 1179826 T IDENT (NIL) -8 NIL NIL) (-496 1175841 1176689 1177584 "IDECOMP" 1178743 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-495 1168714 1169764 1170811 "IDEAL" 1174877 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-494 1167878 1167990 1168189 "ICDEN" 1168598 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-493 1166977 1167358 1167505 "ICARD" 1167751 T ICARD (NIL) -8 NIL NIL) (-492 1165037 1165350 1165755 "IBPTOOLS" 1166654 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-491 1160671 1164657 1164770 "IBITS" 1164956 NIL IBITS (NIL NIL) -8 NIL NIL) (-490 1157394 1157970 1158665 "IBATOOL" 1160088 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-489 1155174 1155635 1156168 "IBACHIN" 1156929 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-488 1153051 1155020 1155123 "IARRAY2" 1155128 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-487 1149204 1152977 1153034 "IARRAY1" 1153039 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-486 1143199 1147618 1148098 "IAN" 1148744 T IAN (NIL) -8 NIL NIL) (-485 1142710 1142767 1142940 "IALGFACT" 1143136 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-484 1142238 1142351 1142379 "HYPCAT" 1142586 T HYPCAT (NIL) -9 NIL NIL) (-483 1141776 1141893 1142079 "HYPCAT-" 1142084 NIL HYPCAT- (NIL T) -8 NIL NIL) (-482 1141398 1141571 1141654 "HOSTNAME" 1141713 T HOSTNAME (NIL) -8 NIL NIL) (-481 1138077 1139408 1139449 "HOAGG" 1140430 NIL HOAGG (NIL T) -9 NIL 1141109) (-480 1136671 1137070 1137596 "HOAGG-" 1137601 NIL HOAGG- (NIL T T) -8 NIL NIL) (-479 1130559 1136112 1136278 "HEXADEC" 1136525 T HEXADEC (NIL) -8 NIL NIL) (-478 1129307 1129529 1129792 "HEUGCD" 1130336 NIL HEUGCD (NIL T) -7 NIL NIL) (-477 1128410 1129144 1129274 "HELLFDIV" 1129279 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-476 1126638 1128187 1128275 "HEAP" 1128354 NIL HEAP (NIL T) -8 NIL NIL) (-475 1125929 1126190 1126324 "HEADAST" 1126524 T HEADAST (NIL) -8 NIL NIL) (-474 1119849 1125844 1125906 "HDP" 1125911 NIL HDP (NIL NIL T) -8 NIL NIL) (-473 1113600 1119484 1119636 "HDMP" 1119750 NIL HDMP (NIL NIL T) -8 NIL NIL) (-472 1112925 1113064 1113228 "HB" 1113456 T HB (NIL) -7 NIL NIL) (-471 1106422 1112771 1112875 "HASHTBL" 1112880 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-470 1105925 1106143 1106235 "HASAST" 1106350 T HASAST (NIL) -8 NIL NIL) (-469 1103739 1105549 1105730 "HACKPI" 1105764 T HACKPI (NIL) -8 NIL NIL) (-468 1099434 1103592 1103705 "GTSET" 1103710 NIL GTSET (NIL T T T T) -8 NIL NIL) (-467 1092960 1099312 1099410 "GSTBL" 1099415 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-466 1085273 1091991 1092256 "GSERIES" 1092751 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-465 1084440 1084831 1084859 "GROUP" 1085062 T GROUP (NIL) -9 NIL 1085196) (-464 1083806 1083965 1084216 "GROUP-" 1084221 NIL GROUP- (NIL T) -8 NIL NIL) (-463 1082175 1082494 1082881 "GROEBSOL" 1083483 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-462 1081115 1081377 1081428 "GRMOD" 1081957 NIL GRMOD (NIL T T) -9 NIL 1082125) (-461 1080883 1080919 1081047 "GRMOD-" 1081052 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-460 1076208 1077237 1078237 "GRIMAGE" 1079903 T GRIMAGE (NIL) -8 NIL NIL) (-459 1074675 1074935 1075259 "GRDEF" 1075904 T GRDEF (NIL) -7 NIL NIL) (-458 1074119 1074235 1074376 "GRAY" 1074554 T GRAY (NIL) -7 NIL NIL) (-457 1073350 1073730 1073781 "GRALG" 1073934 NIL GRALG (NIL T T) -9 NIL 1074027) (-456 1073011 1073084 1073247 "GRALG-" 1073252 NIL GRALG- (NIL T T T) -8 NIL NIL) (-455 1069815 1072596 1072774 "GPOLSET" 1072918 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-454 1069169 1069226 1069484 "GOSPER" 1069752 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-453 1064928 1065607 1066133 "GMODPOL" 1068868 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-452 1063933 1064117 1064355 "GHENSEL" 1064740 NIL GHENSEL (NIL T T) -7 NIL NIL) (-451 1057984 1058827 1059854 "GENUPS" 1063017 NIL GENUPS (NIL T T) -7 NIL NIL) (-450 1057681 1057732 1057821 "GENUFACT" 1057927 NIL GENUFACT (NIL T) -7 NIL NIL) (-449 1057093 1057170 1057335 "GENPGCD" 1057599 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-448 1056567 1056602 1056815 "GENMFACT" 1057052 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-447 1055135 1055390 1055697 "GENEEZ" 1056310 NIL GENEEZ (NIL T T) -7 NIL NIL) (-446 1049048 1054746 1054908 "GDMP" 1055058 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-445 1038425 1042819 1043925 "GCNAALG" 1048031 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-444 1036887 1037715 1037743 "GCDDOM" 1037998 T GCDDOM (NIL) -9 NIL 1038155) (-443 1036357 1036484 1036699 "GCDDOM-" 1036704 NIL GCDDOM- (NIL T) -8 NIL NIL) (-442 1035029 1035214 1035518 "GB" 1036136 NIL GB (NIL T T T T) -7 NIL NIL) (-441 1023649 1025975 1028367 "GBINTERN" 1032720 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-440 1021486 1021778 1022199 "GBF" 1023324 NIL GBF (NIL T T T T) -7 NIL NIL) (-439 1020267 1020432 1020699 "GBEUCLID" 1021302 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-438 1019616 1019741 1019890 "GAUSSFAC" 1020138 T GAUSSFAC (NIL) -7 NIL NIL) (-437 1017983 1018285 1018599 "GALUTIL" 1019335 NIL GALUTIL (NIL T) -7 NIL NIL) (-436 1016291 1016565 1016889 "GALPOLYU" 1017710 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-435 1013656 1013946 1014353 "GALFACTU" 1015988 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-434 1005462 1006961 1008569 "GALFACT" 1012088 NIL GALFACT (NIL T) -7 NIL NIL) (-433 1002850 1003508 1003536 "FVFUN" 1004692 T FVFUN (NIL) -9 NIL 1005412) (-432 1002116 1002298 1002326 "FVC" 1002617 T FVC (NIL) -9 NIL 1002800) (-431 1001758 1001913 1001994 "FUNCTION" 1002068 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-430 999428 999979 1000468 "FT" 1001289 T FT (NIL) -8 NIL NIL) (-429 998246 998729 998932 "FTEM" 999245 T FTEM (NIL) -8 NIL NIL) (-428 996502 996791 997195 "FSUPFACT" 997937 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-427 994899 995188 995520 "FST" 996190 T FST (NIL) -8 NIL NIL) (-426 994070 994176 994371 "FSRED" 994781 NIL FSRED (NIL T T) -7 NIL NIL) (-425 992749 993004 993358 "FSPRMELT" 993785 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-424 989834 990272 990771 "FSPECF" 992312 NIL FSPECF (NIL T T) -7 NIL NIL) (-423 972276 980718 980758 "FS" 984606 NIL FS (NIL T) -9 NIL 986895) (-422 960926 963916 967972 "FS-" 968269 NIL FS- (NIL T T) -8 NIL NIL) (-421 960440 960494 960671 "FSINT" 960867 NIL FSINT (NIL T T) -7 NIL NIL) (-420 958767 959433 959736 "FSERIES" 960219 NIL FSERIES (NIL T T) -8 NIL NIL) (-419 957781 957897 958128 "FSCINT" 958647 NIL FSCINT (NIL T T) -7 NIL NIL) (-418 954015 956725 956766 "FSAGG" 957136 NIL FSAGG (NIL T) -9 NIL 957395) (-417 951777 952378 953174 "FSAGG-" 953269 NIL FSAGG- (NIL T T) -8 NIL NIL) (-416 950819 950962 951189 "FSAGG2" 951630 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-415 948474 948753 949307 "FS2UPS" 950537 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-414 948056 948099 948254 "FS2" 948425 NIL FS2 (NIL T T T T) -7 NIL NIL) (-413 946913 947084 947393 "FS2EXPXP" 947881 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-412 946339 946454 946606 "FRUTIL" 946793 NIL FRUTIL (NIL T) -7 NIL NIL) (-411 937800 941838 943194 "FR" 945015 NIL FR (NIL T) -8 NIL NIL) (-410 932875 935518 935558 "FRNAALG" 936954 NIL FRNAALG (NIL T) -9 NIL 937561) (-409 928553 929624 930899 "FRNAALG-" 931649 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-408 928191 928234 928361 "FRNAAF2" 928504 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-407 926598 927045 927340 "FRMOD" 928003 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-406 924377 924981 925298 "FRIDEAL" 926389 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-405 923572 923659 923948 "FRIDEAL2" 924284 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-404 922814 923228 923269 "FRETRCT" 923274 NIL FRETRCT (NIL T) -9 NIL 923450) (-403 921926 922157 922508 "FRETRCT-" 922513 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-402 919176 920352 920411 "FRAMALG" 921293 NIL FRAMALG (NIL T T) -9 NIL 921585) (-401 917310 917765 918395 "FRAMALG-" 918618 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-400 911270 916785 917061 "FRAC" 917066 NIL FRAC (NIL T) -8 NIL NIL) (-399 910906 910963 911070 "FRAC2" 911207 NIL FRAC2 (NIL T T) -7 NIL NIL) (-398 910542 910599 910706 "FR2" 910843 NIL FR2 (NIL T T) -7 NIL NIL) (-397 905272 908120 908148 "FPS" 909267 T FPS (NIL) -9 NIL 909824) (-396 904721 904830 904994 "FPS-" 905140 NIL FPS- (NIL T) -8 NIL NIL) (-395 902227 903862 903890 "FPC" 904115 T FPC (NIL) -9 NIL 904257) (-394 902020 902060 902157 "FPC-" 902162 NIL FPC- (NIL T) -8 NIL NIL) (-393 900898 901508 901549 "FPATMAB" 901554 NIL FPATMAB (NIL T) -9 NIL 901706) (-392 898598 899074 899500 "FPARFRAC" 900535 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-391 893991 894490 895172 "FORTRAN" 898030 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-390 891707 892207 892746 "FORT" 893472 T FORT (NIL) -7 NIL NIL) (-389 889383 889945 889973 "FORTFN" 891033 T FORTFN (NIL) -9 NIL 891657) (-388 889147 889197 889225 "FORTCAT" 889284 T FORTCAT (NIL) -9 NIL 889346) (-387 887207 887690 888089 "FORMULA" 888768 T FORMULA (NIL) -8 NIL NIL) (-386 886995 887025 887094 "FORMULA1" 887171 NIL FORMULA1 (NIL T) -7 NIL NIL) (-385 886518 886570 886743 "FORDER" 886937 NIL FORDER (NIL T T T T) -7 NIL NIL) (-384 885614 885778 885971 "FOP" 886345 T FOP (NIL) -7 NIL NIL) (-383 884222 884894 885068 "FNLA" 885496 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-382 882890 883279 883307 "FNCAT" 883879 T FNCAT (NIL) -9 NIL 884172) (-381 882456 882849 882877 "FNAME" 882882 T FNAME (NIL) -8 NIL NIL) (-380 881154 882083 882111 "FMTC" 882116 T FMTC (NIL) -9 NIL 882152) (-379 877516 878677 879306 "FMONOID" 880558 NIL FMONOID (NIL T) -8 NIL NIL) (-378 876735 877258 877407 "FM" 877412 NIL FM (NIL T T) -8 NIL NIL) (-377 874159 874805 874833 "FMFUN" 875977 T FMFUN (NIL) -9 NIL 876685) (-376 873428 873609 873637 "FMC" 873927 T FMC (NIL) -9 NIL 874109) (-375 870640 871474 871528 "FMCAT" 872723 NIL FMCAT (NIL T T) -9 NIL 873218) (-374 869533 870406 870506 "FM1" 870585 NIL FM1 (NIL T T) -8 NIL NIL) (-373 867307 867723 868217 "FLOATRP" 869084 NIL FLOATRP (NIL T) -7 NIL NIL) (-372 860858 864963 865593 "FLOAT" 866697 T FLOAT (NIL) -8 NIL NIL) (-371 858296 858796 859374 "FLOATCP" 860325 NIL FLOATCP (NIL T) -7 NIL NIL) (-370 857125 857929 857970 "FLINEXP" 857975 NIL FLINEXP (NIL T) -9 NIL 858068) (-369 856279 856514 856842 "FLINEXP-" 856847 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-368 855355 855499 855723 "FLASORT" 856131 NIL FLASORT (NIL T T) -7 NIL NIL) (-367 852572 853414 853466 "FLALG" 854693 NIL FLALG (NIL T T) -9 NIL 855160) (-366 846356 850058 850099 "FLAGG" 851361 NIL FLAGG (NIL T) -9 NIL 852013) (-365 845082 845421 845911 "FLAGG-" 845916 NIL FLAGG- (NIL T T) -8 NIL NIL) (-364 844124 844267 844494 "FLAGG2" 844935 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-363 841137 842111 842170 "FINRALG" 843298 NIL FINRALG (NIL T T) -9 NIL 843806) (-362 840297 840526 840865 "FINRALG-" 840870 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-361 839703 839916 839944 "FINITE" 840140 T FINITE (NIL) -9 NIL 840247) (-360 832161 834322 834362 "FINAALG" 838029 NIL FINAALG (NIL T) -9 NIL 839482) (-359 827502 828543 829687 "FINAALG-" 831066 NIL FINAALG- (NIL T T) -8 NIL NIL) (-358 826897 827257 827360 "FILE" 827432 NIL FILE (NIL T) -8 NIL NIL) (-357 825581 825893 825947 "FILECAT" 826631 NIL FILECAT (NIL T T) -9 NIL 826847) (-356 823501 824995 825023 "FIELD" 825063 T FIELD (NIL) -9 NIL 825143) (-355 822121 822506 823017 "FIELD-" 823022 NIL FIELD- (NIL T) -8 NIL NIL) (-354 819999 820756 821103 "FGROUP" 821807 NIL FGROUP (NIL T) -8 NIL NIL) (-353 819089 819253 819473 "FGLMICPK" 819831 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-352 814956 819014 819071 "FFX" 819076 NIL FFX (NIL T NIL) -8 NIL NIL) (-351 814557 814618 814753 "FFSLPE" 814889 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-350 810550 811329 812125 "FFPOLY" 813793 NIL FFPOLY (NIL T) -7 NIL NIL) (-349 810054 810090 810299 "FFPOLY2" 810508 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-348 805940 809973 810036 "FFP" 810041 NIL FFP (NIL T NIL) -8 NIL NIL) (-347 801373 805851 805915 "FF" 805920 NIL FF (NIL NIL NIL) -8 NIL NIL) (-346 796534 800716 800906 "FFNBX" 801227 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-345 791508 795669 795927 "FFNBP" 796388 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-344 786176 790792 791003 "FFNB" 791341 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-343 785008 785206 785521 "FFINTBAS" 785973 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-342 781292 783467 783495 "FFIELDC" 784115 T FFIELDC (NIL) -9 NIL 784491) (-341 779955 780325 780822 "FFIELDC-" 780827 NIL FFIELDC- (NIL T) -8 NIL NIL) (-340 779525 779570 779694 "FFHOM" 779897 NIL FFHOM (NIL T T T) -7 NIL NIL) (-339 777223 777707 778224 "FFF" 779040 NIL FFF (NIL T) -7 NIL NIL) (-338 772876 776965 777066 "FFCGX" 777166 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-337 768543 772608 772715 "FFCGP" 772819 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-336 763761 768270 768378 "FFCG" 768479 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-335 745819 754855 754941 "FFCAT" 760106 NIL FFCAT (NIL T T T) -9 NIL 761557) (-334 741017 742064 743378 "FFCAT-" 744608 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-333 740428 740471 740706 "FFCAT2" 740968 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-332 729640 733400 734620 "FEXPR" 739280 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-331 728640 729075 729116 "FEVALAB" 729200 NIL FEVALAB (NIL T) -9 NIL 729461) (-330 727799 728009 728347 "FEVALAB-" 728352 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-329 726392 727182 727385 "FDIV" 727698 NIL FDIV (NIL T T T T) -8 NIL NIL) (-328 723458 724173 724288 "FDIVCAT" 725856 NIL FDIVCAT (NIL T T T T) -9 NIL 726293) (-327 723220 723247 723417 "FDIVCAT-" 723422 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-326 722440 722527 722804 "FDIV2" 723127 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-325 721126 721385 721674 "FCPAK1" 722171 T FCPAK1 (NIL) -7 NIL NIL) (-324 720254 720626 720767 "FCOMP" 721017 NIL FCOMP (NIL T) -8 NIL NIL) (-323 703889 707303 710864 "FC" 716713 T FC (NIL) -8 NIL NIL) (-322 696542 700523 700563 "FAXF" 702365 NIL FAXF (NIL T) -9 NIL 703057) (-321 693821 694476 695301 "FAXF-" 695766 NIL FAXF- (NIL T T) -8 NIL NIL) (-320 688921 693197 693373 "FARRAY" 693678 NIL FARRAY (NIL T) -8 NIL NIL) (-319 684328 686360 686413 "FAMR" 687436 NIL FAMR (NIL T T) -9 NIL 687896) (-318 683218 683520 683955 "FAMR-" 683960 NIL FAMR- (NIL T T T) -8 NIL NIL) (-317 682414 683140 683193 "FAMONOID" 683198 NIL FAMONOID (NIL T) -8 NIL NIL) (-316 680244 680928 680981 "FAMONC" 681922 NIL FAMONC (NIL T T) -9 NIL 682308) (-315 678936 679998 680135 "FAGROUP" 680140 NIL FAGROUP (NIL T) -8 NIL NIL) (-314 676731 677050 677453 "FACUTIL" 678617 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-313 675830 676015 676237 "FACTFUNC" 676541 NIL FACTFUNC (NIL T) -7 NIL NIL) (-312 668235 675081 675293 "EXPUPXS" 675686 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-311 665718 666258 666844 "EXPRTUBE" 667669 T EXPRTUBE (NIL) -7 NIL NIL) (-310 661912 662504 663241 "EXPRODE" 665057 NIL EXPRODE (NIL T T) -7 NIL NIL) (-309 647286 660567 660995 "EXPR" 661516 NIL EXPR (NIL T) -8 NIL NIL) (-308 641693 642280 643093 "EXPR2UPS" 646584 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-307 641329 641386 641493 "EXPR2" 641630 NIL EXPR2 (NIL T T) -7 NIL NIL) (-306 632736 640461 640758 "EXPEXPAN" 641166 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-305 632563 632693 632722 "EXIT" 632727 T EXIT (NIL) -8 NIL NIL) (-304 632070 632287 632378 "EXITAST" 632492 T EXITAST (NIL) -8 NIL NIL) (-303 631697 631759 631872 "EVALCYC" 632002 NIL EVALCYC (NIL T) -7 NIL NIL) (-302 631238 631356 631397 "EVALAB" 631567 NIL EVALAB (NIL T) -9 NIL 631671) (-301 630719 630841 631062 "EVALAB-" 631067 NIL EVALAB- (NIL T T) -8 NIL NIL) (-300 628222 629490 629518 "EUCDOM" 630073 T EUCDOM (NIL) -9 NIL 630423) (-299 626627 627069 627659 "EUCDOM-" 627664 NIL EUCDOM- (NIL T) -8 NIL NIL) (-298 614167 616925 619675 "ESTOOLS" 623897 T ESTOOLS (NIL) -7 NIL NIL) (-297 613799 613856 613965 "ESTOOLS2" 614104 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-296 613550 613592 613672 "ESTOOLS1" 613751 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-295 607475 609203 609231 "ES" 611999 T ES (NIL) -9 NIL 613408) (-294 602422 603709 605526 "ES-" 605690 NIL ES- (NIL T) -8 NIL NIL) (-293 598797 599557 600337 "ESCONT" 601662 T ESCONT (NIL) -7 NIL NIL) (-292 598542 598574 598656 "ESCONT1" 598759 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-291 598217 598267 598367 "ES2" 598486 NIL ES2 (NIL T T) -7 NIL NIL) (-290 597847 597905 598014 "ES1" 598153 NIL ES1 (NIL T T) -7 NIL NIL) (-289 597063 597192 597368 "ERROR" 597691 T ERROR (NIL) -7 NIL NIL) (-288 590566 596922 597013 "EQTBL" 597018 NIL EQTBL (NIL T T) -8 NIL NIL) (-287 583123 585880 587329 "EQ" 589150 NIL -3907 (NIL T) -8 NIL NIL) (-286 582755 582812 582921 "EQ2" 583060 NIL EQ2 (NIL T T) -7 NIL NIL) (-285 578047 579093 580186 "EP" 581694 NIL EP (NIL T) -7 NIL NIL) (-284 576629 576930 577247 "ENV" 577750 T ENV (NIL) -8 NIL NIL) (-283 575828 576348 576376 "ENTIRER" 576381 T ENTIRER (NIL) -9 NIL 576427) (-282 572330 573783 574153 "EMR" 575627 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-281 571474 571659 571713 "ELTAGG" 572093 NIL ELTAGG (NIL T T) -9 NIL 572304) (-280 571193 571255 571396 "ELTAGG-" 571401 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-279 570982 571011 571065 "ELTAB" 571149 NIL ELTAB (NIL T T) -9 NIL NIL) (-278 570108 570254 570453 "ELFUTS" 570833 NIL ELFUTS (NIL T T) -7 NIL NIL) (-277 569850 569906 569934 "ELEMFUN" 570039 T ELEMFUN (NIL) -9 NIL NIL) (-276 569720 569741 569809 "ELEMFUN-" 569814 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-275 564611 567820 567861 "ELAGG" 568801 NIL ELAGG (NIL T) -9 NIL 569264) (-274 562896 563330 563993 "ELAGG-" 563998 NIL ELAGG- (NIL T T) -8 NIL NIL) (-273 561553 561833 562128 "ELABEXPR" 562621 T ELABEXPR (NIL) -8 NIL NIL) (-272 554419 556220 557047 "EFUPXS" 560829 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-271 547869 549670 550480 "EFULS" 553695 NIL EFULS (NIL T T T) -8 NIL NIL) (-270 545291 545649 546128 "EFSTRUC" 547501 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-269 534363 535928 537488 "EF" 543806 NIL EF (NIL T T) -7 NIL NIL) (-268 533464 533848 533997 "EAB" 534234 T EAB (NIL) -8 NIL NIL) (-267 532673 533423 533451 "E04UCFA" 533456 T E04UCFA (NIL) -8 NIL NIL) (-266 531882 532632 532660 "E04NAFA" 532665 T E04NAFA (NIL) -8 NIL NIL) (-265 531091 531841 531869 "E04MBFA" 531874 T E04MBFA (NIL) -8 NIL NIL) (-264 530300 531050 531078 "E04JAFA" 531083 T E04JAFA (NIL) -8 NIL NIL) (-263 529511 530259 530287 "E04GCFA" 530292 T E04GCFA (NIL) -8 NIL NIL) (-262 528722 529470 529498 "E04FDFA" 529503 T E04FDFA (NIL) -8 NIL NIL) (-261 527931 528681 528709 "E04DGFA" 528714 T E04DGFA (NIL) -8 NIL NIL) (-260 522109 523456 524820 "E04AGNT" 526587 T E04AGNT (NIL) -7 NIL NIL) (-259 520833 521313 521353 "DVARCAT" 521828 NIL DVARCAT (NIL T) -9 NIL 522027) (-258 520037 520249 520563 "DVARCAT-" 520568 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-257 512937 519836 519965 "DSMP" 519970 NIL DSMP (NIL T T T) -8 NIL NIL) (-256 507747 508882 509950 "DROPT" 511889 T DROPT (NIL) -8 NIL NIL) (-255 507412 507471 507569 "DROPT1" 507682 NIL DROPT1 (NIL T) -7 NIL NIL) (-254 502527 503653 504790 "DROPT0" 506295 T DROPT0 (NIL) -7 NIL NIL) (-253 500872 501197 501583 "DRAWPT" 502161 T DRAWPT (NIL) -7 NIL NIL) (-252 495459 496382 497461 "DRAW" 499846 NIL DRAW (NIL T) -7 NIL NIL) (-251 495092 495145 495263 "DRAWHACK" 495400 NIL DRAWHACK (NIL T) -7 NIL NIL) (-250 493823 494092 494383 "DRAWCX" 494821 T DRAWCX (NIL) -7 NIL NIL) (-249 493339 493407 493558 "DRAWCURV" 493749 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-248 483810 485769 487884 "DRAWCFUN" 491244 T DRAWCFUN (NIL) -7 NIL NIL) (-247 480623 482505 482546 "DQAGG" 483175 NIL DQAGG (NIL T) -9 NIL 483448) (-246 469142 475839 475922 "DPOLCAT" 477774 NIL DPOLCAT (NIL T T T T) -9 NIL 478319) (-245 463981 465327 467285 "DPOLCAT-" 467290 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-244 457136 463842 463940 "DPMO" 463945 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-243 450194 456916 457083 "DPMM" 457088 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-242 449614 449817 449931 "DOMAIN" 450100 T DOMAIN (NIL) -8 NIL NIL) (-241 443365 449249 449401 "DMP" 449515 NIL DMP (NIL NIL T) -8 NIL NIL) (-240 442965 443021 443165 "DLP" 443303 NIL DLP (NIL T) -7 NIL NIL) (-239 436609 442066 442293 "DLIST" 442770 NIL DLIST (NIL T) -8 NIL NIL) (-238 433455 435464 435505 "DLAGG" 436055 NIL DLAGG (NIL T) -9 NIL 436284) (-237 432305 432935 432963 "DIVRING" 433055 T DIVRING (NIL) -9 NIL 433138) (-236 431542 431732 432032 "DIVRING-" 432037 NIL DIVRING- (NIL T) -8 NIL NIL) (-235 429644 430001 430407 "DISPLAY" 431156 T DISPLAY (NIL) -7 NIL NIL) (-234 423586 429558 429621 "DIRPROD" 429626 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-233 422434 422637 422902 "DIRPROD2" 423379 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-232 411972 417924 417977 "DIRPCAT" 418387 NIL DIRPCAT (NIL NIL T) -9 NIL 419227) (-231 409298 409940 410821 "DIRPCAT-" 411158 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-230 408585 408745 408931 "DIOSP" 409132 T DIOSP (NIL) -7 NIL NIL) (-229 405287 407497 407538 "DIOPS" 407972 NIL DIOPS (NIL T) -9 NIL 408201) (-228 404836 404950 405141 "DIOPS-" 405146 NIL DIOPS- (NIL T T) -8 NIL NIL) (-227 403748 404342 404370 "DIFRING" 404557 T DIFRING (NIL) -9 NIL 404667) (-226 403394 403471 403623 "DIFRING-" 403628 NIL DIFRING- (NIL T) -8 NIL NIL) (-225 401219 402457 402498 "DIFEXT" 402861 NIL DIFEXT (NIL T) -9 NIL 403155) (-224 399504 399932 400598 "DIFEXT-" 400603 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-223 396826 399036 399077 "DIAGG" 399082 NIL DIAGG (NIL T) -9 NIL 399102) (-222 396210 396367 396619 "DIAGG-" 396624 NIL DIAGG- (NIL T T) -8 NIL NIL) (-221 391675 395169 395446 "DHMATRIX" 395979 NIL DHMATRIX (NIL T) -8 NIL NIL) (-220 387287 388196 389206 "DFSFUN" 390685 T DFSFUN (NIL) -7 NIL NIL) (-219 382255 386102 386444 "DFLOAT" 386965 T DFLOAT (NIL) -8 NIL NIL) (-218 380483 380764 381160 "DFINTTLS" 381963 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-217 377548 378504 378904 "DERHAM" 380149 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-216 375397 377323 377412 "DEQUEUE" 377492 NIL DEQUEUE (NIL T) -8 NIL NIL) (-215 374612 374745 374941 "DEGRED" 375259 NIL DEGRED (NIL T T) -7 NIL NIL) (-214 371007 371752 372605 "DEFINTRF" 373840 NIL DEFINTRF (NIL T) -7 NIL NIL) (-213 368534 369003 369602 "DEFINTEF" 370526 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-212 367911 368154 368269 "DEFAST" 368439 T DEFAST (NIL) -8 NIL NIL) (-211 361799 367352 367518 "DECIMAL" 367765 T DECIMAL (NIL) -8 NIL NIL) (-210 359311 359769 360275 "DDFACT" 361343 NIL DDFACT (NIL T T) -7 NIL NIL) (-209 358907 358950 359101 "DBLRESP" 359262 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-208 356617 356951 357320 "DBASE" 358665 NIL DBASE (NIL T) -8 NIL NIL) (-207 355886 356097 356243 "DATABUF" 356516 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-206 355019 355845 355873 "D03FAFA" 355878 T D03FAFA (NIL) -8 NIL NIL) (-205 354153 354978 355006 "D03EEFA" 355011 T D03EEFA (NIL) -8 NIL NIL) (-204 352103 352569 353058 "D03AGNT" 353684 T D03AGNT (NIL) -7 NIL NIL) (-203 351419 352062 352090 "D02EJFA" 352095 T D02EJFA (NIL) -8 NIL NIL) (-202 350735 351378 351406 "D02CJFA" 351411 T D02CJFA (NIL) -8 NIL NIL) (-201 350051 350694 350722 "D02BHFA" 350727 T D02BHFA (NIL) -8 NIL NIL) (-200 349367 350010 350038 "D02BBFA" 350043 T D02BBFA (NIL) -8 NIL NIL) (-199 342565 344153 345759 "D02AGNT" 347781 T D02AGNT (NIL) -7 NIL NIL) (-198 340334 340856 341402 "D01WGTS" 342039 T D01WGTS (NIL) -7 NIL NIL) (-197 339429 340293 340321 "D01TRNS" 340326 T D01TRNS (NIL) -8 NIL NIL) (-196 338524 339388 339416 "D01GBFA" 339421 T D01GBFA (NIL) -8 NIL NIL) (-195 337619 338483 338511 "D01FCFA" 338516 T D01FCFA (NIL) -8 NIL NIL) (-194 336714 337578 337606 "D01ASFA" 337611 T D01ASFA (NIL) -8 NIL NIL) (-193 335809 336673 336701 "D01AQFA" 336706 T D01AQFA (NIL) -8 NIL NIL) (-192 334904 335768 335796 "D01APFA" 335801 T D01APFA (NIL) -8 NIL NIL) (-191 333999 334863 334891 "D01ANFA" 334896 T D01ANFA (NIL) -8 NIL NIL) (-190 333094 333958 333986 "D01AMFA" 333991 T D01AMFA (NIL) -8 NIL NIL) (-189 332189 333053 333081 "D01ALFA" 333086 T D01ALFA (NIL) -8 NIL NIL) (-188 331284 332148 332176 "D01AKFA" 332181 T D01AKFA (NIL) -8 NIL NIL) (-187 330379 331243 331271 "D01AJFA" 331276 T D01AJFA (NIL) -8 NIL NIL) (-186 323676 325227 326788 "D01AGNT" 328838 T D01AGNT (NIL) -7 NIL NIL) (-185 323013 323141 323293 "CYCLOTOM" 323544 T CYCLOTOM (NIL) -7 NIL NIL) (-184 319748 320461 321188 "CYCLES" 322306 T CYCLES 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UTSODE (NIL T T) -7 NIL NIL) (-1217 3059951 3065270 3065313 "UTSCAT" 3066425 NIL UTSCAT (NIL T) -9 NIL 3067182) (-1216 3057305 3058021 3059010 "UTSCAT-" 3059015 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1215 3056932 3056975 3057108 "UTS2" 3057256 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1214 3048808 3054558 3055047 "UTS" 3056501 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1213 3043084 3045648 3045691 "URAGG" 3047761 NIL URAGG (NIL T) -9 NIL 3048483) (-1212 3040026 3040888 3042010 "URAGG-" 3042015 NIL URAGG- (NIL T T) -8 NIL NIL) (-1211 3035757 3038640 3039112 "UPXSSING" 3039690 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1210 3028872 3035661 3035733 "UPXSCONS" 3035738 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1209 3019232 3025975 3026037 "UPXSCCA" 3026693 NIL UPXSCCA (NIL T T) -9 NIL 3026935) (-1208 3018870 3018955 3019129 "UPXSCCA-" 3019134 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1207 3009156 3015672 3015715 "UPXSCAT" 3016363 NIL UPXSCAT (NIL T) -9 NIL 3016971) (-1206 3008586 3008665 3008844 "UPXS2" 3009071 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1205 3000560 3007701 3007983 "UPXS" 3008362 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1204 2999217 2999469 2999819 "UPSQFREE" 3000304 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1203 2993135 2996144 2996199 "UPSCAT" 2997360 NIL UPSCAT (NIL T T) -9 NIL 2998134) (-1202 2992339 2992546 2992873 "UPSCAT-" 2992878 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1201 2991966 2992009 2992142 "UPOLYC2" 2992290 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1200 2978090 2986053 2986096 "UPOLYC" 2988197 NIL UPOLYC (NIL T) -9 NIL 2989418) (-1199 2969455 2971868 2975003 "UPOLYC-" 2975008 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1198 2968794 2968901 2969065 "UPMP" 2969344 NIL UPMP (NIL T T) -7 NIL NIL) (-1197 2968347 2968428 2968567 "UPDIVP" 2968707 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1196 2966915 2967164 2967480 "UPDECOMP" 2968096 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1195 2966150 2966262 2966447 "UPCDEN" 2966799 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1194 2965669 2965738 2965887 "UP2" 2966075 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1193 2957166 2965235 2965373 "UP" 2965579 NIL UP (NIL NIL T) -8 NIL NIL) (-1192 2956381 2956508 2956713 "UNISEG2" 2957009 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1191 2954898 2955585 2955862 "UNISEG" 2956139 NIL UNISEG (NIL T) -8 NIL NIL) (-1190 2953958 2954138 2954364 "UNIFACT" 2954714 NIL UNIFACT (NIL T) -7 NIL NIL) (-1189 2942016 2953862 2953934 "ULSCONS" 2953939 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1188 2924836 2936755 2936817 "ULSCCAT" 2937537 NIL ULSCCAT (NIL T T) -9 NIL 2937834) (-1187 2923922 2924155 2924531 "ULSCCAT-" 2924536 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1186 2913985 2920415 2920458 "ULSCAT" 2921321 NIL ULSCAT (NIL T) -9 NIL 2922051) (-1185 2913415 2913494 2913673 "ULS2" 2913900 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1184 2897400 2912592 2912843 "ULS" 2913222 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1183 2895838 2896761 2896791 "UFD" 2897003 T UFD (NIL) -9 NIL 2897117) (-1182 2895632 2895678 2895773 "UFD-" 2895778 NIL UFD- (NIL T) -8 NIL NIL) (-1181 2894714 2894897 2895113 "UDVO" 2895438 T UDVO (NIL) -7 NIL NIL) (-1180 2892530 2892939 2893410 "UDPO" 2894278 NIL UDPO (NIL T) -7 NIL NIL) (-1179 2892317 2892485 2892516 "TYPEAST" 2892521 T TYPEAST (NIL) -8 NIL NIL) (-1178 2892250 2892255 2892285 "TYPE" 2892290 T TYPE (NIL) -9 NIL NIL) (-1177 2891221 2891423 2891663 "TWOFACT" 2892044 NIL TWOFACT (NIL T) -7 NIL NIL) (-1176 2890159 2890496 2890759 "TUPLE" 2890993 NIL TUPLE (NIL T) -8 NIL NIL) (-1175 2887850 2888369 2888908 "TUBETOOL" 2889642 T TUBETOOL (NIL) -7 NIL NIL) (-1174 2886699 2886904 2887145 "TUBE" 2887643 NIL TUBE (NIL T) -8 NIL NIL) (-1173 2875366 2879458 2879555 "TSETCAT" 2884824 NIL TSETCAT (NIL T T T T) -9 NIL 2886355) (-1172 2870100 2871698 2873589 "TSETCAT-" 2873594 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1171 2864864 2869072 2869355 "TS" 2869852 NIL TS (NIL T) -8 NIL NIL) (-1170 2859127 2859973 2860915 "TRMANIP" 2864000 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1169 2858568 2858631 2858794 "TRIMAT" 2859059 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1168 2856364 2856601 2856965 "TRIGMNIP" 2858317 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1167 2855884 2855997 2856027 "TRIGCAT" 2856240 T TRIGCAT (NIL) -9 NIL NIL) (-1166 2855553 2855632 2855773 "TRIGCAT-" 2855778 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1165 2852453 2854413 2854693 "TREE" 2855308 NIL TREE (NIL T) -8 NIL NIL) (-1164 2851727 2852255 2852285 "TRANFUN" 2852320 T TRANFUN (NIL) -9 NIL 2852386) (-1163 2851006 2851197 2851477 "TRANFUN-" 2851482 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1162 2850810 2850842 2850903 "TOPSP" 2850967 T TOPSP (NIL) -7 NIL NIL) (-1161 2850158 2850273 2850427 "TOOLSIGN" 2850691 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1160 2848819 2849335 2849574 "TEXTFILE" 2849941 T TEXTFILE (NIL) -8 NIL NIL) (-1159 2848600 2848631 2848703 "TEX1" 2848782 NIL TEX1 (NIL T) -7 NIL NIL) (-1158 2846465 2846979 2847417 "TEX" 2848184 T TEX (NIL) -8 NIL NIL) (-1157 2846113 2846176 2846266 "TEMUTL" 2846397 T TEMUTL (NIL) -7 NIL NIL) (-1156 2844267 2844547 2844872 "TBCMPPK" 2845836 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1155 2836157 2842427 2842483 "TBAGG" 2842883 NIL TBAGG (NIL T T) -9 NIL 2843094) (-1154 2831227 2832715 2834469 "TBAGG-" 2834474 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1153 2830611 2830718 2830863 "TANEXP" 2831116 NIL TANEXP (NIL T) -7 NIL NIL) (-1152 2830023 2830122 2830260 "TABLEAU" 2830508 NIL TABLEAU (NIL T) -8 NIL NIL) (-1151 2823526 2829880 2829973 "TABLE" 2829978 NIL TABLE (NIL T T) -8 NIL NIL) (-1150 2818134 2819354 2820602 "TABLBUMP" 2822312 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1149 2817562 2817662 2817790 "SYSTEM" 2818028 T SYSTEM (NIL) -7 NIL NIL) (-1148 2814025 2814720 2815503 "SYSSOLP" 2816813 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1147 2810317 2811024 2811758 "SYNTAX" 2813313 T SYNTAX (NIL) -8 NIL NIL) (-1146 2807475 2808077 2808709 "SYMTAB" 2809707 T SYMTAB (NIL) -8 NIL NIL) (-1145 2802748 2803644 2804621 "SYMS" 2806520 T SYMS (NIL) -8 NIL NIL) (-1144 2800030 2802209 2802439 "SYMPOLY" 2802556 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1143 2799547 2799622 2799745 "SYMFUNC" 2799942 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1142 2795524 2796784 2797606 "SYMBOL" 2798747 T SYMBOL (NIL) -8 NIL NIL) (-1141 2789063 2790752 2792472 "SWITCH" 2793826 T SWITCH (NIL) -8 NIL NIL) (-1140 2782333 2787884 2788187 "SUTS" 2788818 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1139 2774306 2781448 2781730 "SUPXS" 2782109 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1138 2773465 2773592 2773809 "SUPFRACF" 2774174 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1137 2773086 2773145 2773258 "SUP2" 2773400 NIL SUP2 (NIL T T) -7 NIL NIL) (-1136 2764655 2772704 2772830 "SUP" 2772995 NIL SUP (NIL T) -8 NIL NIL) (-1135 2763068 2763342 2763705 "SUMRF" 2764354 NIL SUMRF (NIL T) -7 NIL NIL) (-1134 2762382 2762448 2762647 "SUMFS" 2762989 NIL SUMFS (NIL T T) -7 NIL NIL) (-1133 2746407 2761559 2761810 "SULS" 2762189 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1132 2746036 2746229 2746299 "SUCHTAST" 2746359 T SUCHTAST (NIL) -8 NIL NIL) (-1131 2745358 2745561 2745701 "SUCH" 2745944 NIL SUCH (NIL T T) -8 NIL NIL) (-1130 2739252 2740264 2741223 "SUBSPACE" 2744446 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1129 2738682 2738772 2738936 "SUBRESP" 2739140 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1128 2732855 2733975 2735122 "STTFNC" 2737582 NIL STTFNC (NIL T) -7 NIL NIL) (-1127 2726224 2727520 2728831 "STTF" 2731591 NIL STTF (NIL T) -7 NIL NIL) (-1126 2717539 2719406 2721200 "STTAYLOR" 2724465 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1125 2710785 2717403 2717486 "STRTBL" 2717491 NIL STRTBL (NIL T) -8 NIL NIL) (-1124 2706176 2710740 2710771 "STRING" 2710776 T STRING (NIL) -8 NIL NIL) (-1123 2701064 2705549 2705579 "STRICAT" 2705638 T STRICAT (NIL) -9 NIL 2705700) (-1122 2700574 2700651 2700795 "STREAM3" 2700981 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1121 2699556 2699739 2699974 "STREAM2" 2700387 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1120 2699244 2699296 2699389 "STREAM1" 2699498 NIL STREAM1 (NIL T) -7 NIL NIL) (-1119 2691959 2696767 2697387 "STREAM" 2698659 NIL STREAM (NIL T) -8 NIL NIL) (-1118 2690975 2691156 2691387 "STINPROD" 2691775 NIL STINPROD (NIL T) -7 NIL NIL) (-1117 2690553 2690737 2690767 "STEP" 2690847 T STEP (NIL) -9 NIL 2690925) (-1116 2684098 2690452 2690529 "STBL" 2690534 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1115 2679275 2683320 2683363 "STAGG" 2683516 NIL STAGG (NIL T) -9 NIL 2683605) (-1114 2676983 2677583 2678453 "STAGG-" 2678458 NIL STAGG- (NIL T T) -8 NIL NIL) (-1113 2675178 2676753 2676845 "STACK" 2676926 NIL STACK (NIL T) -8 NIL NIL) (-1112 2667930 2673319 2673775 "SREGSET" 2674808 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1111 2660356 2661724 2663237 "SRDCMPK" 2666536 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1110 2653323 2657796 2657826 "SRAGG" 2659129 T SRAGG (NIL) -9 NIL 2659737) (-1109 2652340 2652595 2652974 "SRAGG-" 2652979 NIL SRAGG- (NIL T) -8 NIL NIL) (-1108 2646839 2651287 2651708 "SQMATRIX" 2651966 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1107 2640592 2643559 2644285 "SPLTREE" 2646185 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1106 2636582 2637248 2637894 "SPLNODE" 2640018 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1105 2635629 2635862 2635892 "SPFCAT" 2636336 T SPFCAT (NIL) -9 NIL NIL) (-1104 2634366 2634576 2634840 "SPECOUT" 2635387 T SPECOUT (NIL) -7 NIL NIL) (-1103 2626055 2627799 2627829 "SPADXPT" 2632221 T SPADXPT (NIL) -9 NIL 2634255) (-1102 2625816 2625856 2625925 "SPADPRSR" 2626008 T SPADPRSR (NIL) -7 NIL NIL) (-1101 2623999 2625771 2625802 "SPADAST" 2625807 T SPADAST (NIL) -8 NIL NIL) (-1100 2615970 2617717 2617760 "SPACEC" 2622133 NIL SPACEC (NIL T) -9 NIL 2623949) (-1099 2614141 2615902 2615951 "SPACE3" 2615956 NIL SPACE3 (NIL T) -8 NIL NIL) (-1098 2612893 2613064 2613355 "SORTPAK" 2613946 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1097 2610943 2611246 2611665 "SOLVETRA" 2612557 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1096 2609954 2610176 2610450 "SOLVESER" 2610716 NIL SOLVESER (NIL T) -7 NIL NIL) (-1095 2605174 2606055 2607057 "SOLVERAD" 2609006 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1094 2600989 2601598 2602327 "SOLVEFOR" 2604541 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1093 2595313 2600338 2600435 "SNTSCAT" 2600440 NIL SNTSCAT (NIL T T T T) -9 NIL 2600510) (-1092 2589456 2593636 2594027 "SMTS" 2595003 NIL SMTS (NIL T T T) -8 NIL NIL) (-1091 2583932 2589344 2589421 "SMP" 2589426 NIL SMP (NIL T T) -8 NIL NIL) (-1090 2582091 2582392 2582790 "SMITH" 2583629 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1089 2575072 2579223 2579326 "SMATCAT" 2580680 NIL SMATCAT (NIL NIL T T T) -9 NIL 2581230) (-1088 2572033 2572849 2574020 "SMATCAT-" 2574025 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1087 2569746 2571269 2571312 "SKAGG" 2571573 NIL SKAGG (NIL T) -9 NIL 2571708) (-1086 2565864 2568850 2569128 "SINT" 2569490 T SINT (NIL) -8 NIL NIL) (-1085 2565636 2565674 2565740 "SIMPAN" 2565820 T SIMPAN (NIL) -7 NIL NIL) (-1084 2564495 2564709 2564977 "SIGNRF" 2565402 NIL SIGNRF (NIL T) -7 NIL NIL) (-1083 2563321 2563465 2563749 "SIGNEF" 2564331 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1082 2562654 2562904 2563028 "SIGAST" 2563219 T SIGAST (NIL) -8 NIL NIL) (-1081 2561961 2562189 2562329 "SIG" 2562536 T SIG (NIL) -8 NIL NIL) (-1080 2559651 2560105 2560611 "SHP" 2561502 NIL SHP (NIL T NIL) -7 NIL NIL) (-1079 2553564 2559552 2559628 "SHDP" 2559633 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1078 2553163 2553329 2553359 "SGROUP" 2553452 T SGROUP (NIL) -9 NIL 2553514) (-1077 2553021 2553047 2553120 "SGROUP-" 2553125 NIL SGROUP- (NIL T) -8 NIL NIL) (-1076 2549857 2550554 2551277 "SGCF" 2552320 T SGCF (NIL) -7 NIL NIL) (-1075 2544279 2549304 2549401 "SFRTCAT" 2549406 NIL SFRTCAT (NIL T T T T) -9 NIL 2549445) (-1074 2537703 2538718 2539854 "SFRGCD" 2543262 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1073 2530831 2531902 2533088 "SFQCMPK" 2536636 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1072 2530453 2530542 2530652 "SFORT" 2530772 NIL SFORT (NIL T T) -8 NIL NIL) (-1071 2529598 2530293 2530414 "SEXOF" 2530419 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1070 2524374 2525063 2525158 "SEXCAT" 2528929 NIL SEXCAT (NIL T T T T T) -9 NIL 2529548) (-1069 2523508 2524255 2524323 "SEX" 2524328 T SEX (NIL) -8 NIL NIL) (-1068 2521765 2522225 2522528 "SETMN" 2523251 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1067 2521371 2521497 2521527 "SETCAT" 2521644 T SETCAT (NIL) -9 NIL 2521729) (-1066 2521151 2521203 2521302 "SETCAT-" 2521307 NIL SETCAT- (NIL T) -8 NIL NIL) (-1065 2517538 2519612 2519655 "SETAGG" 2520525 NIL SETAGG (NIL T) -9 NIL 2520865) (-1064 2516996 2517112 2517349 "SETAGG-" 2517354 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1063 2514176 2516930 2516978 "SET" 2516983 NIL SET (NIL T) -8 NIL NIL) (-1062 2513646 2513872 2513973 "SEQAST" 2514097 T SEQAST (NIL) -8 NIL NIL) (-1061 2512850 2513143 2513204 "SEGXCAT" 2513490 NIL SEGXCAT (NIL T T) -9 NIL 2513610) (-1060 2511757 2511970 2512013 "SEGCAT" 2512595 NIL SEGCAT (NIL T) -9 NIL 2512833) (-1059 2511378 2511437 2511550 "SEGBIND2" 2511692 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1058 2510427 2510757 2510957 "SEGBIND" 2511213 NIL SEGBIND (NIL T) -8 NIL NIL) (-1057 2510028 2510228 2510305 "SEGAST" 2510372 T SEGAST (NIL) -8 NIL NIL) (-1056 2509247 2509373 2509577 "SEG2" 2509872 NIL SEG2 (NIL T T) -7 NIL NIL) (-1055 2508303 2508913 2509095 "SEG" 2509100 NIL SEG (NIL T) -8 NIL NIL) (-1054 2507740 2508238 2508285 "SDVAR" 2508290 NIL SDVAR (NIL T) -8 NIL NIL) (-1053 2500071 2507510 2507640 "SDPOL" 2507645 NIL SDPOL (NIL T) -8 NIL NIL) (-1052 2498664 2498930 2499249 "SCPKG" 2499786 NIL SCPKG (NIL T) -7 NIL NIL) (-1051 2497800 2497980 2498180 "SCOPE" 2498486 T SCOPE (NIL) -8 NIL NIL) (-1050 2497021 2497154 2497333 "SCACHE" 2497655 NIL SCACHE (NIL T) -7 NIL NIL) (-1049 2496730 2496890 2496920 "SASTCAT" 2496925 T SASTCAT (NIL) -9 NIL 2496938) (-1048 2496169 2496490 2496575 "SAOS" 2496667 T SAOS (NIL) -8 NIL NIL) (-1047 2495734 2495769 2495942 "SAERFFC" 2496128 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1046 2495327 2495362 2495521 "SAEFACT" 2495693 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1045 2489310 2495224 2495304 "SAE" 2495309 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1044 2487631 2487945 2488346 "RURPK" 2488976 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1043 2486267 2486546 2486858 "RULESET" 2487465 NIL RULESET (NIL T T T) -8 NIL NIL) (-1042 2485906 2486061 2486144 "RULECOLD" 2486219 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1041 2483093 2483596 2484061 "RULE" 2485587 NIL RULE (NIL T T T) -8 NIL NIL) (-1040 2482591 2482810 2482904 "RSTRCAST" 2483021 T RSTRCAST (NIL) -8 NIL NIL) (-1039 2477440 2478234 2479154 "RSETGCD" 2481790 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1038 2466724 2471749 2471846 "RSETCAT" 2475965 NIL RSETCAT (NIL T T T T) -9 NIL 2477062) (-1037 2464651 2465190 2466014 "RSETCAT-" 2466019 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1036 2457038 2458413 2459933 "RSDCMPK" 2463250 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1035 2455043 2455484 2455558 "RRCC" 2456644 NIL RRCC (NIL T T) -9 NIL 2456988) (-1034 2454394 2454568 2454847 "RRCC-" 2454852 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1033 2453864 2454090 2454191 "RPTAST" 2454315 T RPTAST (NIL) -8 NIL NIL) (-1032 2428123 2437677 2437744 "RPOLCAT" 2448408 NIL RPOLCAT (NIL T T T) -9 NIL 2451567) (-1031 2419659 2421985 2425095 "RPOLCAT-" 2425100 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1030 2410708 2417870 2418352 "ROUTINE" 2419199 T ROUTINE (NIL) -8 NIL NIL) (-1029 2407468 2410259 2410408 "ROMAN" 2410581 T ROMAN (NIL) -8 NIL NIL) (-1028 2405745 2406328 2406588 "ROIRC" 2407273 NIL ROIRC (NIL T T) -8 NIL NIL) (-1027 2402200 2404435 2404465 "RNS" 2404769 T RNS (NIL) -9 NIL 2405041) (-1026 2400709 2401092 2401626 "RNS-" 2401701 NIL RNS- (NIL T) -8 NIL NIL) (-1025 2400158 2400540 2400570 "RNG" 2400575 T RNG (NIL) -9 NIL 2400596) (-1024 2399550 2399912 2399955 "RMODULE" 2400017 NIL RMODULE (NIL T) -9 NIL 2400059) (-1023 2398386 2398480 2398816 "RMCAT2" 2399451 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1022 2395091 2397560 2397885 "RMATRIX" 2398120 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1021 2388033 2390267 2390382 "RMATCAT" 2393741 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2394723) (-1020 2387408 2387555 2387862 "RMATCAT-" 2387867 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1019 2386975 2387050 2387178 "RINTERP" 2387327 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1018 2386063 2386583 2386613 "RING" 2386725 T RING (NIL) -9 NIL 2386820) (-1017 2385855 2385899 2385996 "RING-" 2386001 NIL RING- (NIL T) -8 NIL NIL) (-1016 2384696 2384933 2385191 "RIDIST" 2385619 T RIDIST (NIL) -7 NIL NIL) (-1015 2376039 2384164 2384370 "RGCHAIN" 2384544 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1014 2375685 2375748 2375851 "RFFACTOR" 2375970 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1013 2375410 2375445 2375542 "RFFACT" 2375644 NIL RFFACT (NIL T) -7 NIL NIL) (-1012 2373527 2373891 2374273 "RFDIST" 2375050 T RFDIST (NIL) -7 NIL NIL) (-1011 2370521 2371135 2371805 "RF" 2372891 NIL RF (NIL T) -7 NIL NIL) (-1010 2369974 2370066 2370229 "RETSOL" 2370423 NIL RETSOL (NIL T T) -7 NIL NIL) (-1009 2369562 2369642 2369685 "RETRACT" 2369878 NIL RETRACT (NIL T) -9 NIL NIL) (-1008 2369411 2369436 2369523 "RETRACT-" 2369528 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1007 2369040 2369233 2369303 "RETAST" 2369363 T RETAST (NIL) -8 NIL NIL) (-1006 2361896 2368693 2368820 "RESULT" 2368935 T RESULT (NIL) -8 NIL NIL) (-1005 2360522 2361165 2361364 "RESRING" 2361799 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1004 2360158 2360207 2360305 "RESLATC" 2360459 NIL RESLATC (NIL T) -7 NIL NIL) (-1003 2359864 2359898 2360005 "REPSQ" 2360117 NIL REPSQ (NIL T) -7 NIL NIL) (-1002 2359562 2359596 2359707 "REPDB" 2359823 NIL REPDB (NIL T) -7 NIL NIL) (-1001 2353472 2354851 2356074 "REP2" 2358374 NIL REP2 (NIL T) -7 NIL NIL) (-1000 2349849 2350530 2351338 "REP1" 2352699 NIL REP1 (NIL T) -7 NIL NIL) (-999 2347280 2347860 2348460 "REP" 2349269 T REP (NIL) -7 NIL NIL) (-998 2340045 2345433 2345887 "REGSET" 2346910 NIL REGSET (NIL T T T T) -8 NIL NIL) (-997 2338866 2339201 2339449 "REF" 2339830 NIL REF (NIL T) -8 NIL NIL) (-996 2338247 2338350 2338515 "REDORDER" 2338750 NIL REDORDER (NIL T T) -7 NIL NIL) (-995 2334298 2337475 2337698 "RECLOS" 2338076 NIL RECLOS (NIL T) -8 NIL NIL) (-994 2333355 2333536 2333749 "REALSOLV" 2334105 T REALSOLV (NIL) -7 NIL NIL) (-993 2329846 2330648 2331530 "REAL0Q" 2332520 NIL REAL0Q (NIL T) -7 NIL NIL) (-992 2325457 2326445 2327504 "REAL0" 2328827 NIL REAL0 (NIL T) -7 NIL NIL) (-991 2325305 2325346 2325374 "REAL" 2325379 T REAL (NIL) -9 NIL 2325414) (-990 2324807 2325026 2325118 "RDUCEAST" 2325233 T RDUCEAST (NIL) -8 NIL NIL) (-989 2324215 2324287 2324492 "RDIV" 2324729 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-988 2323288 2323462 2323673 "RDIST" 2324037 NIL RDIST (NIL T) -7 NIL NIL) (-987 2321889 2322176 2322546 "RDETRS" 2322996 NIL RDETRS (NIL T T) -7 NIL NIL) (-986 2319706 2320160 2320696 "RDETR" 2321431 NIL RDETR (NIL T T) -7 NIL NIL) (-985 2318320 2318598 2319000 "RDEEFS" 2319422 NIL RDEEFS (NIL T T) -7 NIL NIL) (-984 2316818 2317124 2317554 "RDEEF" 2318008 NIL RDEEF (NIL T T) -7 NIL NIL) (-983 2311164 2314026 2314054 "RCFIELD" 2315331 T RCFIELD (NIL) -9 NIL 2316061) (-982 2309233 2309737 2310430 "RCFIELD-" 2310503 NIL RCFIELD- (NIL T) -8 NIL NIL) (-981 2305564 2307349 2307390 "RCAGG" 2308461 NIL RCAGG (NIL T) -9 NIL 2308926) (-980 2305195 2305289 2305449 "RCAGG-" 2305454 NIL RCAGG- (NIL T T) -8 NIL NIL) (-979 2304535 2304647 2304810 "RATRET" 2305079 NIL RATRET (NIL T) -7 NIL NIL) (-978 2304092 2304159 2304278 "RATFACT" 2304463 NIL RATFACT (NIL T) -7 NIL NIL) (-977 2303407 2303527 2303677 "RANDSRC" 2303962 T RANDSRC (NIL) -7 NIL NIL) (-976 2303144 2303188 2303259 "RADUTIL" 2303356 T RADUTIL (NIL) -7 NIL NIL) (-975 2296230 2301887 2302204 "RADIX" 2302859 NIL RADIX (NIL NIL) -8 NIL NIL) (-974 2287897 2296074 2296202 "RADFF" 2296207 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-973 2287549 2287624 2287652 "RADCAT" 2287809 T RADCAT (NIL) -9 NIL NIL) (-972 2287334 2287382 2287479 "RADCAT-" 2287484 NIL RADCAT- (NIL T) -8 NIL NIL) (-971 2285485 2287109 2287198 "QUEUE" 2287278 NIL QUEUE (NIL T) -8 NIL NIL) (-970 2285123 2285166 2285293 "QUATCT2" 2285436 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-969 2278990 2282284 2282324 "QUATCAT" 2283104 NIL QUATCAT (NIL T) -9 NIL 2283870) (-968 2275155 2276185 2277565 "QUATCAT-" 2277659 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-967 2271738 2275092 2275137 "QUAT" 2275142 NIL QUAT (NIL T) -8 NIL NIL) (-966 2269258 2270822 2270863 "QUAGG" 2271238 NIL QUAGG (NIL T) -9 NIL 2271413) (-965 2268890 2269083 2269151 "QQUTAST" 2269210 T QQUTAST (NIL) -8 NIL NIL) (-964 2267815 2268288 2268460 "QFORM" 2268762 NIL QFORM (NIL NIL T) -8 NIL NIL) (-963 2267453 2267496 2267623 "QFCAT2" 2267766 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-962 2258802 2263989 2264029 "QFCAT" 2264687 NIL QFCAT (NIL T) -9 NIL 2265686) (-961 2254410 2255599 2257178 "QFCAT-" 2257272 NIL QFCAT- (NIL T T) -8 NIL NIL) (-960 2253870 2253980 2254110 "QEQUAT" 2254300 T QEQUAT (NIL) -8 NIL NIL) (-959 2247018 2248089 2249273 "QCMPACK" 2252803 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-958 2246263 2246437 2246669 "QALGSET2" 2246838 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-957 2243845 2244264 2244690 "QALGSET" 2245920 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-956 2242536 2242759 2243076 "PWFFINTB" 2243618 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-955 2240735 2240903 2241257 "PUSHVAR" 2242350 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-954 2236653 2237707 2237748 "PTRANFN" 2239632 NIL PTRANFN (NIL T) -9 NIL NIL) (-953 2235055 2235346 2235668 "PTPACK" 2236364 NIL PTPACK (NIL T) -7 NIL NIL) (-952 2234687 2234744 2234853 "PTFUNC2" 2234992 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-951 2229153 2233498 2233539 "PTCAT" 2233912 NIL PTCAT (NIL T) -9 NIL 2234074) (-950 2228811 2228846 2228970 "PSQFR" 2229112 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-949 2227406 2227704 2228038 "PSEUDLIN" 2228509 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-948 2214175 2216540 2218864 "PSETPK" 2225166 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-947 2207219 2209933 2210029 "PSETCAT" 2213050 NIL PSETCAT (NIL T T T T) -9 NIL 2213864) (-946 2205055 2205689 2206510 "PSETCAT-" 2206515 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-945 2204404 2204569 2204597 "PSCURVE" 2204865 T PSCURVE (NIL) -9 NIL 2205032) (-944 2200885 2202367 2202432 "PSCAT" 2203276 NIL PSCAT (NIL T T T) -9 NIL 2203516) (-943 2199948 2200164 2200564 "PSCAT-" 2200569 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-942 2198600 2199233 2199447 "PRTITION" 2199754 T PRTITION (NIL) -8 NIL NIL) (-941 2198102 2198321 2198413 "PRTDAST" 2198528 T PRTDAST (NIL) -8 NIL NIL) (-940 2187200 2189406 2191594 "PRS" 2195964 NIL PRS (NIL T T) -7 NIL NIL) (-939 2185058 2186550 2186590 "PRQAGG" 2186773 NIL PRQAGG (NIL T) -9 NIL 2186875) (-938 2184444 2184673 2184701 "PROPLOG" 2184886 T PROPLOG (NIL) -9 NIL 2185008) (-937 2181614 2182258 2182722 "PROPFRML" 2184012 NIL PROPFRML (NIL T) -8 NIL NIL) (-936 2181074 2181184 2181314 "PROPERTY" 2181504 T PROPERTY (NIL) -8 NIL NIL) (-935 2175159 2179240 2180060 "PRODUCT" 2180300 NIL PRODUCT (NIL T T) -8 NIL NIL) (-934 2174955 2174987 2175046 "PRINT" 2175120 T PRINT (NIL) -7 NIL NIL) (-933 2174295 2174412 2174564 "PRIMES" 2174835 NIL PRIMES (NIL T) -7 NIL NIL) (-932 2172360 2172761 2173227 "PRIMELT" 2173874 NIL PRIMELT (NIL T) -7 NIL NIL) (-931 2172089 2172138 2172166 "PRIMCAT" 2172290 T PRIMCAT (NIL) -9 NIL NIL) (-930 2171096 2171274 2171502 "PRIMARR2" 2171907 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-929 2167257 2171034 2171079 "PRIMARR" 2171084 NIL PRIMARR (NIL T) -8 NIL NIL) (-928 2166900 2166956 2167067 "PREASSOC" 2167195 NIL PREASSOC (NIL T T) -7 NIL NIL) (-927 2164220 2166358 2166592 "PR" 2166711 NIL PR (NIL T T) -8 NIL NIL) (-926 2163695 2163828 2163856 "PPCURVE" 2164061 T PPCURVE (NIL) -9 NIL 2164197) (-925 2163317 2163490 2163573 "PORTNUM" 2163632 T PORTNUM (NIL) -8 NIL NIL) (-924 2160676 2161075 2161667 "POLYROOT" 2162898 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-923 2160059 2160117 2160351 "POLYLIFT" 2160612 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-922 2156334 2156783 2157412 "POLYCATQ" 2159604 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-921 2143387 2148729 2148794 "POLYCAT" 2152308 NIL POLYCAT (NIL T T T) -9 NIL 2154236) (-920 2136894 2138736 2141101 "POLYCAT-" 2141106 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-919 2136481 2136549 2136669 "POLY2UP" 2136820 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-918 2136113 2136170 2136279 "POLY2" 2136418 NIL POLY2 (NIL T T) -7 NIL NIL) (-917 2130089 2135717 2135877 "POLY" 2135986 NIL POLY (NIL T) -8 NIL NIL) (-916 2128774 2129013 2129289 "POLUTIL" 2129863 NIL POLUTIL (NIL T T) -7 NIL NIL) (-915 2127129 2127406 2127737 "POLTOPOL" 2128496 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-914 2122647 2127065 2127111 "POINT" 2127116 NIL POINT (NIL T) -8 NIL NIL) (-913 2120834 2121191 2121566 "PNTHEORY" 2122292 T PNTHEORY (NIL) -7 NIL NIL) (-912 2119253 2119550 2119962 "PMTOOLS" 2120532 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-911 2118846 2118924 2119041 "PMSYM" 2119169 NIL PMSYM (NIL T) -7 NIL NIL) (-910 2118356 2118425 2118599 "PMQFCAT" 2118771 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-909 2117752 2117838 2117999 "PMPREDFS" 2118257 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-908 2117107 2117217 2117373 "PMPRED" 2117629 NIL PMPRED (NIL T) -7 NIL NIL) (-907 2115750 2115958 2116343 "PMPLCAT" 2116869 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-906 2115282 2115361 2115513 "PMLSAGG" 2115665 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-905 2114757 2114833 2115014 "PMKERNEL" 2115200 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-904 2114374 2114449 2114562 "PMINS" 2114676 NIL PMINS (NIL T) -7 NIL NIL) (-903 2113802 2113871 2114087 "PMFS" 2114299 NIL PMFS (NIL T T T) -7 NIL NIL) (-902 2113030 2113148 2113353 "PMDOWN" 2113679 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-901 2112304 2112415 2112578 "PMASSFS" 2112916 NIL PMASSFS (NIL T T) -7 NIL NIL) (-900 2111467 2111626 2111808 "PMASS" 2112142 T PMASS (NIL) -7 NIL NIL) (-899 2111122 2111190 2111284 "PLOTTOOL" 2111393 T PLOTTOOL (NIL) -7 NIL NIL) (-898 2106936 2107970 2108891 "PLOT3D" 2110221 T PLOT3D (NIL) -8 NIL NIL) (-897 2105848 2106025 2106260 "PLOT1" 2106740 NIL PLOT1 (NIL T) -7 NIL NIL) (-896 2100470 2101659 2102807 "PLOT" 2104720 T PLOT (NIL) -8 NIL NIL) (-895 2075864 2080536 2085387 "PLEQN" 2095736 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-894 2075557 2075604 2075707 "PINTERPA" 2075811 NIL PINTERPA (NIL T T) -7 NIL NIL) (-893 2074875 2074997 2075177 "PINTERP" 2075422 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-892 2073307 2074248 2074276 "PID" 2074458 T PID (NIL) -9 NIL 2074592) (-891 2073032 2073069 2073157 "PICOERCE" 2073264 NIL PICOERCE (NIL T) -7 NIL NIL) (-890 2072317 2072838 2072925 "PI" 2072965 T PI (NIL) -8 NIL NIL) (-889 2071637 2071776 2071952 "PGROEB" 2072173 NIL PGROEB (NIL T) -7 NIL NIL) (-888 2067224 2068038 2068943 "PGE" 2070752 T PGE (NIL) -7 NIL NIL) (-887 2065348 2065594 2065960 "PGCD" 2066941 NIL PGCD (NIL T T T T) -7 NIL NIL) (-886 2064686 2064789 2064950 "PFRPAC" 2065232 NIL PFRPAC (NIL T) -7 NIL NIL) (-885 2061368 2063234 2063587 "PFR" 2064365 NIL PFR (NIL T) -8 NIL NIL) (-884 2059757 2060001 2060326 "PFOTOOLS" 2061115 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-883 2058290 2058529 2058880 "PFOQ" 2059514 NIL PFOQ (NIL T T T) -7 NIL NIL) (-882 2056763 2056975 2057338 "PFO" 2058074 NIL PFO (NIL T T T T T) -7 NIL NIL) (-881 2054232 2055469 2055497 "PFECAT" 2056082 T PFECAT (NIL) -9 NIL 2056466) (-880 2053677 2053831 2054045 "PFECAT-" 2054050 NIL PFECAT- (NIL T) -8 NIL NIL) (-879 2052281 2052532 2052833 "PFBRU" 2053426 NIL PFBRU (NIL T T) -7 NIL NIL) (-878 2050148 2050499 2050931 "PFBR" 2051932 NIL PFBR (NIL T T T T) -7 NIL NIL) (-877 2046738 2050037 2050106 "PF" 2050111 NIL PF (NIL NIL) -8 NIL NIL) (-876 2042004 2042945 2043815 "PERMGRP" 2045901 NIL PERMGRP (NIL T) -8 NIL NIL) (-875 2040136 2041067 2041108 "PERMCAT" 2041554 NIL PERMCAT (NIL T) -9 NIL 2041859) (-874 2039789 2039830 2039954 "PERMAN" 2040089 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-873 2035705 2037165 2037841 "PERM" 2039146 NIL PERM (NIL T) -8 NIL NIL) (-872 2033147 2035274 2035405 "PENDTREE" 2035607 NIL PENDTREE (NIL T) -8 NIL NIL) (-871 2031260 2031994 2032035 "PDRING" 2032692 NIL PDRING (NIL T) -9 NIL 2032978) (-870 2030363 2030581 2030943 "PDRING-" 2030948 NIL PDRING- (NIL T T) -8 NIL NIL) (-869 2027504 2028255 2028946 "PDEPROB" 2029692 T PDEPROB (NIL) -8 NIL NIL) (-868 2025051 2025553 2026108 "PDEPACK" 2026969 T PDEPACK (NIL) -7 NIL NIL) (-867 2023963 2024153 2024404 "PDECOMP" 2024850 NIL PDECOMP (NIL T T) -7 NIL NIL) (-866 2021568 2022385 2022413 "PDECAT" 2023200 T PDECAT (NIL) -9 NIL 2023913) (-865 2021319 2021352 2021442 "PCOMP" 2021529 NIL PCOMP (NIL T T) -7 NIL NIL) (-864 2019524 2020120 2020417 "PBWLB" 2021048 NIL PBWLB (NIL T) -8 NIL NIL) (-863 2019156 2019213 2019322 "PATTERN2" 2019461 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-862 2016913 2017301 2017758 "PATTERN1" 2018745 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-861 2009419 2010986 2012324 "PATTERN" 2015596 NIL PATTERN (NIL T) -8 NIL NIL) (-860 2008983 2009050 2009182 "PATRES2" 2009346 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-859 2006378 2006932 2007413 "PATRES" 2008548 NIL PATRES (NIL T T) -8 NIL NIL) (-858 2004261 2004666 2005073 "PATMATCH" 2006045 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-857 2003797 2003980 2004021 "PATMAB" 2004128 NIL PATMAB (NIL T) -9 NIL 2004211) (-856 2002342 2002651 2002909 "PATLRES" 2003602 NIL PATLRES (NIL T T T) -8 NIL NIL) (-855 2001888 2002011 2002052 "PATAB" 2002057 NIL PATAB (NIL T) -9 NIL 2002229) (-854 1999369 1999901 2000474 "PARTPERM" 2001335 T PARTPERM (NIL) -7 NIL NIL) (-853 1998990 1999053 1999155 "PARSURF" 1999300 NIL PARSURF (NIL T) -8 NIL NIL) (-852 1998622 1998679 1998788 "PARSU2" 1998927 NIL PARSU2 (NIL T T) -7 NIL NIL) (-851 1998386 1998426 1998493 "PARSER" 1998575 T PARSER (NIL) -7 NIL NIL) (-850 1998007 1998070 1998172 "PARSCURV" 1998317 NIL PARSCURV (NIL T) -8 NIL NIL) (-849 1997639 1997696 1997805 "PARSC2" 1997944 NIL PARSC2 (NIL T T) -7 NIL NIL) (-848 1997278 1997336 1997433 "PARPCURV" 1997575 NIL PARPCURV (NIL T) -8 NIL NIL) (-847 1996910 1996967 1997076 "PARPC2" 1997215 NIL PARPC2 (NIL T T) -7 NIL NIL) (-846 1996430 1996516 1996635 "PAN2EXPR" 1996811 T PAN2EXPR (NIL) -7 NIL NIL) (-845 1995236 1995551 1995779 "PALETTE" 1996222 T PALETTE (NIL) -8 NIL NIL) (-844 1993704 1994241 1994601 "PAIR" 1994922 NIL PAIR (NIL T T) -8 NIL NIL) (-843 1987633 1992963 1993157 "PADICRC" 1993559 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-842 1980920 1986979 1987163 "PADICRAT" 1987481 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-841 1978167 1979695 1979735 "PADICCT" 1980316 NIL PADICCT (NIL NIL) -9 NIL 1980598) (-840 1976519 1978104 1978149 "PADIC" 1978154 NIL PADIC (NIL NIL) -8 NIL NIL) (-839 1975476 1975676 1975944 "PADEPAC" 1976306 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-838 1974688 1974821 1975027 "PADE" 1975338 NIL PADE (NIL T T T) -7 NIL NIL) (-837 1972738 1973524 1973841 "OWP" 1974455 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-836 1971847 1972343 1972515 "OVAR" 1972606 NIL OVAR (NIL NIL) -8 NIL NIL) (-835 1960901 1963072 1965242 "OUTFORM" 1969697 T OUTFORM (NIL) -8 NIL NIL) (-834 1960538 1960621 1960649 "OUTBCON" 1960800 T OUTBCON (NIL) -9 NIL 1960885) (-833 1960378 1960413 1960489 "OUTBCON-" 1960494 NIL OUTBCON- (NIL T) -8 NIL NIL) (-832 1959642 1959763 1959924 "OUT" 1960237 T OUT (NIL) -7 NIL NIL) (-831 1959050 1959371 1959460 "OSI" 1959573 T OSI (NIL) -8 NIL NIL) (-830 1958606 1958918 1958946 "OSGROUP" 1958951 T OSGROUP (NIL) -9 NIL 1958973) (-829 1957351 1957578 1957863 "ORTHPOL" 1958353 NIL ORTHPOL (NIL T) -7 NIL NIL) (-828 1954775 1957010 1957149 "OREUP" 1957294 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-827 1952227 1954466 1954593 "ORESUP" 1954717 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-826 1949755 1950255 1950816 "OREPCTO" 1951716 NIL OREPCTO (NIL T T) -7 NIL NIL) (-825 1943673 1945833 1945874 "OREPCAT" 1948222 NIL OREPCAT (NIL T) -9 NIL 1949326) (-824 1940841 1941616 1942667 "OREPCAT-" 1942672 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-823 1940018 1940290 1940318 "ORDSET" 1940627 T ORDSET (NIL) -9 NIL 1940791) (-822 1939537 1939659 1939852 "ORDSET-" 1939857 NIL ORDSET- (NIL T) -8 NIL NIL) (-821 1938191 1938948 1938976 "ORDRING" 1939178 T ORDRING (NIL) -9 NIL 1939303) (-820 1937836 1937930 1938074 "ORDRING-" 1938079 NIL ORDRING- (NIL T) -8 NIL NIL) (-819 1937242 1937679 1937707 "ORDMON" 1937712 T ORDMON (NIL) -9 NIL 1937733) (-818 1936404 1936551 1936746 "ORDFUNS" 1937091 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-817 1935915 1936274 1936302 "ORDFIN" 1936307 T ORDFIN (NIL) -9 NIL 1936328) (-816 1935181 1935308 1935494 "ORDCOMP2" 1935775 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-815 1931780 1933767 1934176 "ORDCOMP" 1934805 NIL ORDCOMP (NIL T) -8 NIL NIL) (-814 1928287 1929170 1930007 "OPTPROB" 1930963 T OPTPROB (NIL) -8 NIL NIL) (-813 1925089 1925728 1926432 "OPTPACK" 1927603 T OPTPACK (NIL) -7 NIL NIL) (-812 1922802 1923542 1923570 "OPTCAT" 1924389 T OPTCAT (NIL) -9 NIL 1925039) (-811 1922570 1922609 1922675 "OPQUERY" 1922756 T OPQUERY (NIL) -7 NIL NIL) (-810 1919738 1920881 1921385 "OP" 1922099 NIL OP (NIL T) -8 NIL NIL) (-809 1919043 1919158 1919332 "ONECOMP2" 1919610 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-808 1915895 1917840 1918209 "ONECOMP" 1918707 NIL ONECOMP (NIL T) -8 NIL NIL) (-807 1915314 1915420 1915550 "OMSERVER" 1915785 T OMSERVER (NIL) -7 NIL NIL) (-806 1912202 1914754 1914794 "OMSAGG" 1914855 NIL OMSAGG (NIL T) -9 NIL 1914919) (-805 1910825 1911088 1911370 "OMPKG" 1911940 T OMPKG (NIL) -7 NIL NIL) (-804 1909407 1910374 1910543 "OMLO" 1910706 NIL OMLO (NIL T T) -8 NIL NIL) (-803 1908332 1908479 1908706 "OMEXPR" 1909233 NIL OMEXPR (NIL T) -7 NIL NIL) (-802 1907510 1907753 1907913 "OMERRK" 1908192 T OMERRK (NIL) -8 NIL NIL) (-801 1906828 1907056 1907192 "OMERR" 1907394 T OMERR (NIL) -8 NIL NIL) (-800 1906306 1906505 1906613 "OMENC" 1906740 T OMENC (NIL) -8 NIL NIL) (-799 1900201 1901386 1902557 "OMDEV" 1905155 T OMDEV (NIL) -8 NIL NIL) (-798 1899270 1899441 1899635 "OMCONN" 1900027 T OMCONN (NIL) -8 NIL NIL) (-797 1898700 1898803 1898831 "OM" 1899130 T OM (NIL) -9 NIL NIL) (-796 1897356 1898298 1898326 "OINTDOM" 1898331 T OINTDOM (NIL) -9 NIL 1898352) (-795 1893162 1894346 1895062 "OFMONOID" 1896672 NIL OFMONOID (NIL T) -8 NIL NIL) (-794 1892600 1893099 1893144 "ODVAR" 1893149 NIL ODVAR (NIL T) -8 NIL NIL) (-793 1889812 1892097 1892282 "ODR" 1892475 NIL ODR (NIL T T NIL) -8 NIL NIL) (-792 1882197 1889588 1889714 "ODPOL" 1889719 NIL ODPOL (NIL T) -8 NIL NIL) (-791 1876080 1882069 1882174 "ODP" 1882179 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-790 1874846 1875061 1875336 "ODETOOLS" 1875854 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-789 1871815 1872471 1873187 "ODESYS" 1874179 NIL ODESYS (NIL T T) -7 NIL NIL) (-788 1866697 1867605 1868630 "ODERTRIC" 1870890 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-787 1866123 1866205 1866399 "ODERED" 1866609 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-786 1863019 1863565 1864240 "ODERAT" 1865548 NIL ODERAT (NIL T T) -7 NIL NIL) (-785 1859979 1860443 1861040 "ODEPRRIC" 1862548 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-784 1857848 1858417 1858926 "ODEPROB" 1859490 T ODEPROB (NIL) -8 NIL NIL) (-783 1854370 1854853 1855500 "ODEPRIM" 1857327 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-782 1853619 1853721 1853981 "ODEPAL" 1854262 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-781 1849781 1850572 1851436 "ODEPACK" 1852775 T ODEPACK (NIL) -7 NIL NIL) (-780 1848814 1848921 1849150 "ODEINT" 1849670 NIL ODEINT (NIL T T) -7 NIL NIL) (-779 1842915 1844340 1845787 "ODEIFTBL" 1847387 T ODEIFTBL (NIL) -8 NIL NIL) (-778 1838264 1839046 1840001 "ODEEF" 1842078 NIL ODEEF (NIL T T) -7 NIL NIL) (-777 1837599 1837688 1837918 "ODECONST" 1838169 NIL ODECONST (NIL T T T) -7 NIL NIL) (-776 1835750 1836385 1836413 "ODECAT" 1837018 T ODECAT (NIL) -9 NIL 1837549) (-775 1835388 1835431 1835558 "OCTCT2" 1835701 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-774 1832307 1835100 1835219 "OCT" 1835301 NIL OCT (NIL T) -8 NIL NIL) (-773 1831685 1832127 1832155 "OCAMON" 1832160 T OCAMON (NIL) -9 NIL 1832181) (-772 1826553 1828946 1828986 "OC" 1830083 NIL OC (NIL T) -9 NIL 1830941) (-771 1823801 1824542 1825525 "OC-" 1825619 NIL OC- (NIL T T) -8 NIL NIL) (-770 1823358 1823673 1823701 "OASGP" 1823706 T OASGP (NIL) -9 NIL 1823726) (-769 1822645 1823108 1823136 "OAMONS" 1823176 T OAMONS (NIL) -9 NIL 1823219) (-768 1822085 1822492 1822520 "OAMON" 1822525 T OAMON (NIL) -9 NIL 1822545) (-767 1821389 1821881 1821909 "OAGROUP" 1821914 T OAGROUP (NIL) -9 NIL 1821934) (-766 1821079 1821129 1821217 "NUMTUBE" 1821333 NIL NUMTUBE (NIL T) -7 NIL NIL) (-765 1814652 1816170 1817706 "NUMQUAD" 1819563 T NUMQUAD (NIL) -7 NIL NIL) (-764 1810408 1811396 1812421 "NUMODE" 1813647 T NUMODE (NIL) -7 NIL NIL) (-763 1807789 1808643 1808671 "NUMINT" 1809594 T NUMINT (NIL) -9 NIL 1810358) (-762 1806737 1806934 1807152 "NUMFMT" 1807591 T NUMFMT (NIL) -7 NIL NIL) (-761 1793096 1796041 1798573 "NUMERIC" 1804244 NIL NUMERIC (NIL T) -7 NIL NIL) (-760 1787520 1792545 1792640 "NTSCAT" 1792645 NIL NTSCAT (NIL T T T T) -9 NIL 1792684) (-759 1786714 1786879 1787072 "NTPOLFN" 1787359 NIL NTPOLFN (NIL T) -7 NIL NIL) (-758 1786346 1786403 1786512 "NSUP2" 1786651 NIL NSUP2 (NIL T T) -7 NIL NIL) (-757 1774231 1783171 1783983 "NSUP" 1785567 NIL NSUP (NIL T) -8 NIL NIL) (-756 1764276 1774005 1774138 "NSMP" 1774143 NIL NSMP (NIL T T) -8 NIL NIL) (-755 1762708 1763009 1763366 "NREP" 1763964 NIL NREP (NIL T) -7 NIL NIL) (-754 1761299 1761551 1761909 "NPCOEF" 1762451 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-753 1760365 1760480 1760696 "NORMRETR" 1761180 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-752 1758406 1758696 1759105 "NORMPK" 1760073 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-751 1758091 1758119 1758243 "NORMMA" 1758372 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-750 1757880 1757909 1757978 "NONE1" 1758055 NIL NONE1 (NIL T) -7 NIL NIL) (-749 1757707 1757837 1757866 "NONE" 1757871 T NONE (NIL) -8 NIL NIL) (-748 1757190 1757252 1757438 "NODE1" 1757639 NIL NODE1 (NIL T T) -7 NIL NIL) (-747 1755530 1756353 1756608 "NNI" 1756955 T NNI (NIL) -8 NIL NIL) (-746 1753950 1754263 1754627 "NLINSOL" 1755198 NIL NLINSOL (NIL T) -7 NIL NIL) (-745 1750117 1751085 1752007 "NIPROB" 1753048 T NIPROB (NIL) -8 NIL NIL) (-744 1748874 1749108 1749410 "NFINTBAS" 1749879 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-743 1747582 1747813 1748094 "NCODIV" 1748642 NIL NCODIV (NIL T T) -7 NIL NIL) (-742 1747344 1747381 1747456 "NCNTFRAC" 1747539 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-741 1745524 1745888 1746308 "NCEP" 1746969 NIL NCEP (NIL T) -7 NIL NIL) (-740 1744442 1745174 1745202 "NASRING" 1745312 T NASRING (NIL) -9 NIL 1745386) (-739 1744237 1744281 1744375 "NASRING-" 1744380 NIL NASRING- (NIL T) -8 NIL NIL) (-738 1743390 1743889 1743917 "NARNG" 1744034 T NARNG (NIL) -9 NIL 1744125) (-737 1743082 1743149 1743283 "NARNG-" 1743288 NIL NARNG- (NIL T) -8 NIL NIL) (-736 1741961 1742168 1742403 "NAGSP" 1742867 T NAGSP (NIL) -7 NIL NIL) (-735 1733233 1734917 1736590 "NAGS" 1740308 T NAGS (NIL) -7 NIL NIL) (-734 1731781 1732089 1732420 "NAGF07" 1732922 T NAGF07 (NIL) -7 NIL NIL) (-733 1726319 1727610 1728917 "NAGF04" 1730494 T NAGF04 (NIL) -7 NIL NIL) (-732 1719287 1720901 1722534 "NAGF02" 1724706 T NAGF02 (NIL) -7 NIL NIL) (-731 1714511 1715611 1716728 "NAGF01" 1718190 T NAGF01 (NIL) -7 NIL NIL) (-730 1708139 1709705 1711290 "NAGE04" 1712946 T NAGE04 (NIL) -7 NIL NIL) (-729 1699308 1701429 1703559 "NAGE02" 1706029 T NAGE02 (NIL) -7 NIL NIL) (-728 1695261 1696208 1697172 "NAGE01" 1698364 T NAGE01 (NIL) -7 NIL NIL) (-727 1693056 1693590 1694148 "NAGD03" 1694723 T NAGD03 (NIL) -7 NIL NIL) (-726 1684806 1686734 1688688 "NAGD02" 1691122 T NAGD02 (NIL) -7 NIL NIL) (-725 1678617 1680042 1681482 "NAGD01" 1683386 T NAGD01 (NIL) -7 NIL NIL) (-724 1674826 1675648 1676485 "NAGC06" 1677800 T NAGC06 (NIL) -7 NIL NIL) (-723 1673291 1673623 1673979 "NAGC05" 1674490 T NAGC05 (NIL) -7 NIL NIL) (-722 1672667 1672786 1672930 "NAGC02" 1673167 T NAGC02 (NIL) -7 NIL NIL) (-721 1671727 1672284 1672324 "NAALG" 1672403 NIL NAALG (NIL T) -9 NIL 1672464) (-720 1671562 1671591 1671681 "NAALG-" 1671686 NIL NAALG- (NIL T T) -8 NIL NIL) (-719 1665512 1666620 1667807 "MULTSQFR" 1670458 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-718 1664831 1664906 1665090 "MULTFACT" 1665424 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-717 1658054 1661919 1661972 "MTSCAT" 1663042 NIL MTSCAT (NIL T T) -9 NIL 1663556) (-716 1657766 1657820 1657912 "MTHING" 1657994 NIL MTHING (NIL T) -7 NIL NIL) (-715 1657558 1657591 1657651 "MSYSCMD" 1657726 T MSYSCMD (NIL) -7 NIL NIL) (-714 1654653 1657119 1657160 "MSETAGG" 1657165 NIL MSETAGG (NIL T) -9 NIL 1657199) (-713 1650765 1653408 1653728 "MSET" 1654366 NIL MSET (NIL T) -8 NIL NIL) (-712 1646650 1648144 1648889 "MRING" 1650065 NIL MRING (NIL T T) -8 NIL NIL) (-711 1646216 1646283 1646414 "MRF2" 1646577 NIL MRF2 (NIL T T T) -7 NIL NIL) (-710 1645834 1645869 1646013 "MRATFAC" 1646175 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-709 1643446 1643741 1644172 "MPRFF" 1645539 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-708 1637532 1643300 1643397 "MPOLY" 1643402 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-707 1637022 1637057 1637265 "MPCPF" 1637491 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-706 1636536 1636579 1636763 "MPC3" 1636973 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-705 1635731 1635812 1636033 "MPC2" 1636451 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-704 1634032 1634369 1634759 "MONOTOOL" 1635391 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-703 1633283 1633574 1633602 "MONOID" 1633821 T MONOID (NIL) -9 NIL 1633968) (-702 1632829 1632948 1633129 "MONOID-" 1633134 NIL MONOID- (NIL T) -8 NIL NIL) (-701 1623888 1629785 1629844 "MONOGEN" 1630518 NIL MONOGEN (NIL T T) -9 NIL 1630974) (-700 1621127 1621855 1622848 "MONOGEN-" 1622967 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-699 1619986 1620406 1620434 "MONADWU" 1620826 T MONADWU (NIL) -9 NIL 1621064) (-698 1619358 1619517 1619765 "MONADWU-" 1619770 NIL MONADWU- (NIL T) -8 NIL NIL) (-697 1618743 1618961 1618989 "MONAD" 1619196 T MONAD (NIL) -9 NIL 1619308) (-696 1618428 1618506 1618638 "MONAD-" 1618643 NIL MONAD- (NIL T) -8 NIL NIL) (-695 1616744 1617341 1617620 "MOEBIUS" 1618181 NIL MOEBIUS (NIL T) -8 NIL NIL) (-694 1616136 1616514 1616554 "MODULE" 1616559 NIL MODULE (NIL T) -9 NIL 1616585) (-693 1615704 1615800 1615990 "MODULE-" 1615995 NIL MODULE- (NIL T T) -8 NIL NIL) (-692 1613463 1614112 1614439 "MODRING" 1615528 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-691 1610451 1611568 1612089 "MODOP" 1612992 NIL MODOP (NIL T T) -8 NIL NIL) (-690 1608638 1609090 1609431 "MODMONOM" 1610250 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-689 1598386 1606830 1607253 "MODMON" 1608266 NIL MODMON (NIL T T) -8 NIL NIL) (-688 1595603 1597254 1597530 "MODFIELD" 1598261 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-687 1594607 1594884 1595074 "MMLFORM" 1595433 T MMLFORM (NIL) -8 NIL NIL) (-686 1594133 1594176 1594355 "MMAP" 1594558 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-685 1592402 1593135 1593176 "MLO" 1593599 NIL MLO (NIL T) -9 NIL 1593841) (-684 1589769 1590284 1590886 "MLIFT" 1591883 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-683 1589160 1589244 1589398 "MKUCFUNC" 1589680 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-682 1588759 1588829 1588952 "MKRECORD" 1589083 NIL MKRECORD (NIL T T) -7 NIL NIL) (-681 1587807 1587968 1588196 "MKFUNC" 1588570 NIL MKFUNC (NIL T) -7 NIL NIL) (-680 1587195 1587299 1587455 "MKFLCFN" 1587690 NIL MKFLCFN (NIL T) -7 NIL NIL) (-679 1586621 1586988 1587077 "MKCHSET" 1587139 NIL MKCHSET (NIL T) -8 NIL NIL) (-678 1585898 1586000 1586185 "MKBCFUNC" 1586514 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-677 1582642 1585452 1585588 "MINT" 1585782 T MINT (NIL) -8 NIL NIL) (-676 1581454 1581697 1581974 "MHROWRED" 1582397 NIL MHROWRED (NIL T) -7 NIL NIL) (-675 1576889 1579989 1580394 "MFLOAT" 1581069 T MFLOAT (NIL) -8 NIL NIL) (-674 1576246 1576322 1576493 "MFINFACT" 1576801 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-673 1572581 1573424 1574303 "MESH" 1575387 T MESH (NIL) -7 NIL NIL) (-672 1570971 1571283 1571636 "MDDFACT" 1572268 NIL MDDFACT (NIL T) -7 NIL NIL) (-671 1567813 1570130 1570171 "MDAGG" 1570426 NIL MDAGG (NIL T) -9 NIL 1570569) (-670 1557611 1567106 1567313 "MCMPLX" 1567626 T MCMPLX (NIL) -8 NIL NIL) (-669 1556752 1556898 1557098 "MCDEN" 1557460 NIL MCDEN (NIL T T) -7 NIL NIL) (-668 1554642 1554912 1555292 "MCALCFN" 1556482 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-667 1553553 1553726 1553967 "MAYBE" 1554440 NIL MAYBE (NIL T) -8 NIL NIL) (-666 1551165 1551688 1552250 "MATSTOR" 1553024 NIL MATSTOR (NIL T) -7 NIL NIL) (-665 1547170 1550537 1550785 "MATRIX" 1550950 NIL MATRIX (NIL T) -8 NIL NIL) (-664 1542939 1543643 1544379 "MATLIN" 1546527 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-663 1541533 1541686 1542019 "MATCAT2" 1542774 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-662 1531681 1534822 1534899 "MATCAT" 1539782 NIL MATCAT (NIL T T T) -9 NIL 1541199) (-661 1528045 1529058 1530414 "MATCAT-" 1530419 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-660 1526157 1526481 1526865 "MAPPKG3" 1527720 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-659 1525138 1525311 1525533 "MAPPKG2" 1525981 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-658 1523637 1523921 1524248 "MAPPKG1" 1524844 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-657 1522743 1523043 1523220 "MAPPAST" 1523480 T MAPPAST (NIL) -8 NIL NIL) (-656 1522354 1522412 1522535 "MAPHACK3" 1522679 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-655 1521946 1522007 1522121 "MAPHACK2" 1522286 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-654 1521384 1521487 1521629 "MAPHACK1" 1521837 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-653 1519490 1520084 1520388 "MAGMA" 1521112 NIL MAGMA (NIL T) -8 NIL NIL) (-652 1518996 1519214 1519305 "MACROAST" 1519419 T MACROAST (NIL) -8 NIL NIL) (-651 1515463 1517235 1517696 "M3D" 1518568 NIL M3D (NIL T) -8 NIL NIL) (-650 1509620 1513833 1513874 "LZSTAGG" 1514656 NIL LZSTAGG (NIL T) -9 NIL 1514951) (-649 1505593 1506751 1508208 "LZSTAGG-" 1508213 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-648 1502707 1503484 1503971 "LWORD" 1505138 NIL LWORD (NIL T) -8 NIL NIL) (-647 1502310 1502511 1502586 "LSTAST" 1502652 T LSTAST (NIL) -8 NIL NIL) (-646 1495542 1502081 1502215 "LSQM" 1502220 NIL LSQM (NIL NIL T) -8 NIL NIL) (-645 1494766 1494905 1495133 "LSPP" 1495397 NIL LSPP (NIL T T T T) -7 NIL NIL) (-644 1491608 1492265 1492978 "LSMP1" 1494085 NIL LSMP1 (NIL T) -7 NIL NIL) (-643 1489443 1489737 1490186 "LSMP" 1491304 NIL LSMP (NIL T T T T) -7 NIL NIL) (-642 1483371 1488611 1488652 "LSAGG" 1488714 NIL LSAGG (NIL T) -9 NIL 1488792) (-641 1480066 1480990 1482203 "LSAGG-" 1482208 NIL LSAGG- (NIL T T) -8 NIL NIL) (-640 1477692 1479210 1479459 "LPOLY" 1479861 NIL LPOLY (NIL T T) -8 NIL NIL) (-639 1477274 1477359 1477482 "LPEFRAC" 1477601 NIL LPEFRAC (NIL T) -7 NIL NIL) (-638 1476926 1477038 1477066 "LOGIC" 1477177 T LOGIC (NIL) -9 NIL 1477258) (-637 1476788 1476811 1476882 "LOGIC-" 1476887 NIL LOGIC- (NIL T) -8 NIL NIL) (-636 1475981 1476121 1476314 "LODOOPS" 1476644 NIL LODOOPS (NIL T T) -7 NIL NIL) (-635 1474519 1474754 1475107 "LODOF" 1475728 NIL LODOF (NIL T T) -7 NIL NIL) (-634 1470976 1473359 1473400 "LODOCAT" 1473838 NIL LODOCAT (NIL T) -9 NIL 1474049) (-633 1470709 1470767 1470894 "LODOCAT-" 1470899 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-632 1468078 1470550 1470668 "LODO2" 1470673 NIL LODO2 (NIL T T) -8 NIL NIL) (-631 1465562 1468015 1468060 "LODO1" 1468065 NIL LODO1 (NIL T) -8 NIL NIL) (-630 1463034 1465478 1465544 "LODO" 1465549 NIL LODO (NIL T NIL) -8 NIL NIL) (-629 1461894 1462059 1462371 "LODEEF" 1462857 NIL LODEEF (NIL T T T) -7 NIL NIL) (-628 1460241 1460988 1461241 "LO" 1461726 NIL LO (NIL T T T) -8 NIL NIL) (-627 1455527 1458371 1458412 "LNAGG" 1459359 NIL LNAGG (NIL T) -9 NIL 1459803) (-626 1454674 1454888 1455230 "LNAGG-" 1455235 NIL LNAGG- (NIL T T) -8 NIL NIL) (-625 1450837 1451599 1452238 "LMOPS" 1454089 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-624 1450232 1450594 1450635 "LMODULE" 1450696 NIL LMODULE (NIL T) -9 NIL 1450738) (-623 1447478 1449877 1450000 "LMDICT" 1450142 NIL LMDICT (NIL T) -8 NIL NIL) (-622 1447204 1447386 1447446 "LITERAL" 1447451 NIL LITERAL (NIL T) -8 NIL NIL) (-621 1446729 1446803 1446942 "LIST3" 1447124 NIL LIST3 (NIL T T T) -7 NIL NIL) (-620 1444863 1445175 1445574 "LIST2MAP" 1446376 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-619 1443870 1444048 1444276 "LIST2" 1444681 NIL LIST2 (NIL T T) -7 NIL NIL) (-618 1437099 1442816 1443114 "LIST" 1443605 NIL LIST (NIL T) -8 NIL NIL) (-617 1435849 1436485 1436526 "LINEXP" 1436781 NIL LINEXP (NIL T) -9 NIL 1436930) (-616 1434496 1434756 1435053 "LINDEP" 1435601 NIL LINDEP (NIL T T) -7 NIL NIL) (-615 1431334 1432034 1432792 "LIMITRF" 1433770 NIL LIMITRF (NIL T) -7 NIL NIL) (-614 1429633 1429921 1430330 "LIMITPS" 1431036 NIL LIMITPS (NIL T T) -7 NIL NIL) (-613 1428682 1429125 1429165 "LIECAT" 1429305 NIL LIECAT (NIL T) -9 NIL 1429456) (-612 1428523 1428550 1428638 "LIECAT-" 1428643 NIL LIECAT- (NIL T T) -8 NIL NIL) (-611 1423010 1428034 1428262 "LIE" 1428344 NIL LIE (NIL T T) -8 NIL NIL) (-610 1415624 1422459 1422624 "LIB" 1422865 T LIB (NIL) -8 NIL NIL) (-609 1411261 1412142 1413077 "LGROBP" 1414741 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-608 1410101 1410793 1410821 "LFCAT" 1411028 T LFCAT (NIL) -9 NIL 1411167) (-607 1407967 1408241 1408603 "LF" 1409822 NIL LF (NIL T T) -7 NIL NIL) (-606 1404871 1405499 1406187 "LEXTRIPK" 1407331 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-605 1401642 1402441 1402944 "LEXP" 1404451 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-604 1401145 1401363 1401455 "LETAST" 1401570 T LETAST (NIL) -8 NIL NIL) (-603 1399543 1399856 1400257 "LEADCDET" 1400827 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-602 1398733 1398807 1399036 "LAZM3PK" 1399464 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-601 1393703 1396810 1397348 "LAUPOL" 1398245 NIL LAUPOL (NIL T T) -8 NIL NIL) (-600 1393268 1393312 1393480 "LAPLACE" 1393653 NIL LAPLACE (NIL T T) -7 NIL NIL) (-599 1392369 1392919 1392960 "LALG" 1393022 NIL LALG (NIL T) -9 NIL 1393081) (-598 1392083 1392142 1392278 "LALG-" 1392283 NIL LALG- (NIL T T) -8 NIL NIL) (-597 1390057 1391184 1391435 "LA" 1391916 NIL LA (NIL T T T) -8 NIL NIL) (-596 1388857 1389274 1389503 "KTVLOGIC" 1389848 T KTVLOGIC (NIL) -8 NIL NIL) (-595 1387761 1387948 1388247 "KOVACIC" 1388657 NIL KOVACIC (NIL T T) -7 NIL NIL) (-594 1387596 1387620 1387661 "KONVERT" 1387723 NIL KONVERT (NIL T) -9 NIL NIL) (-593 1387431 1387455 1387496 "KOERCE" 1387558 NIL KOERCE (NIL T) -9 NIL NIL) (-592 1386933 1387014 1387144 "KERNEL2" 1387345 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-591 1384667 1385427 1385820 "KERNEL" 1386572 NIL KERNEL (NIL T) -8 NIL NIL) (-590 1378518 1383206 1383260 "KDAGG" 1383637 NIL KDAGG (NIL T T) -9 NIL 1383843) (-589 1378047 1378171 1378376 "KDAGG-" 1378381 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-588 1371224 1377708 1377863 "KAFILE" 1377925 NIL KAFILE (NIL T) -8 NIL NIL) (-587 1365711 1370735 1370963 "JORDAN" 1371045 NIL JORDAN (NIL T T) -8 NIL NIL) (-586 1365117 1365360 1365481 "JOINAST" 1365610 T JOINAST (NIL) -8 NIL NIL) (-585 1364846 1364905 1364992 "JAVACODE" 1365050 T JAVACODE (NIL) -8 NIL NIL) (-584 1361145 1363051 1363105 "IXAGG" 1364034 NIL IXAGG (NIL T T) -9 NIL 1364493) (-583 1360064 1360370 1360789 "IXAGG-" 1360794 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-582 1355644 1359986 1360045 "IVECTOR" 1360050 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-581 1354410 1354647 1354913 "ITUPLE" 1355411 NIL ITUPLE (NIL T) -8 NIL NIL) (-580 1352846 1353023 1353329 "ITRIGMNP" 1354232 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-579 1351591 1351795 1352078 "ITFUN3" 1352622 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-578 1351223 1351280 1351389 "ITFUN2" 1351528 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-577 1349060 1350085 1350384 "ITAYLOR" 1350957 NIL ITAYLOR (NIL T) -8 NIL NIL) (-576 1338054 1343206 1344366 "ISUPS" 1347933 NIL ISUPS (NIL T) -8 NIL NIL) (-575 1337158 1337298 1337534 "ISUMP" 1337901 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-574 1332422 1336959 1337038 "ISTRING" 1337111 NIL ISTRING (NIL NIL) -8 NIL NIL) (-573 1331925 1332143 1332235 "ISAST" 1332350 T ISAST (NIL) -8 NIL NIL) (-572 1331135 1331216 1331432 "IRURPK" 1331839 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-571 1330071 1330272 1330512 "IRSN" 1330915 T IRSN (NIL) -7 NIL NIL) (-570 1328100 1328455 1328891 "IRRF2F" 1329709 NIL IRRF2F (NIL T) -7 NIL NIL) (-569 1327847 1327885 1327961 "IRREDFFX" 1328056 NIL IRREDFFX (NIL T) -7 NIL NIL) (-568 1326462 1326721 1327020 "IROOT" 1327580 NIL IROOT (NIL T) -7 NIL NIL) (-567 1325534 1325647 1325868 "IR2F" 1326345 NIL IR2F (NIL T T) -7 NIL NIL) (-566 1323147 1323642 1324208 "IR2" 1325012 NIL IR2 (NIL T T) -7 NIL NIL) (-565 1319779 1320831 1321523 "IR" 1322487 NIL IR (NIL T) -8 NIL NIL) (-564 1319570 1319604 1319664 "IPRNTPK" 1319739 T IPRNTPK (NIL) -7 NIL NIL) (-563 1316191 1319459 1319528 "IPF" 1319533 NIL IPF (NIL NIL) -8 NIL NIL) (-562 1314556 1316116 1316173 "IPADIC" 1316178 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-561 1314320 1314460 1314488 "IOBCON" 1314493 T IOBCON (NIL) -9 NIL 1314514) (-560 1313817 1313875 1314065 "INVLAPLA" 1314256 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-559 1303514 1305855 1308229 "INTTR" 1311493 NIL INTTR (NIL T T) -7 NIL NIL) (-558 1299858 1300600 1301464 "INTTOOLS" 1302699 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-557 1299444 1299535 1299652 "INTSLPE" 1299761 T INTSLPE (NIL) -7 NIL NIL) (-556 1297439 1299367 1299426 "INTRVL" 1299431 NIL INTRVL (NIL T) -8 NIL NIL) (-555 1295041 1295553 1296128 "INTRF" 1296924 NIL INTRF (NIL T) -7 NIL NIL) (-554 1294452 1294549 1294691 "INTRET" 1294939 NIL INTRET (NIL T) -7 NIL NIL) (-553 1292449 1292838 1293308 "INTRAT" 1294060 NIL INTRAT (NIL T T) -7 NIL NIL) (-552 1289677 1290260 1290886 "INTPM" 1291934 NIL INTPM (NIL T T) -7 NIL NIL) (-551 1286403 1286995 1287733 "INTPAF" 1289070 NIL INTPAF (NIL T T T) -7 NIL NIL) (-550 1281582 1282544 1283595 "INTPACK" 1285372 T INTPACK (NIL) -7 NIL NIL) (-549 1280834 1280986 1281194 "INTHERTR" 1281424 NIL INTHERTR (NIL T T) -7 NIL NIL) (-548 1280273 1280353 1280541 "INTHERAL" 1280748 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-547 1278119 1278562 1279019 "INTHEORY" 1279836 T INTHEORY (NIL) -7 NIL NIL) (-546 1269485 1271088 1272849 "INTG0" 1276489 NIL INTG0 (NIL T T T) -7 NIL NIL) (-545 1255758 1259123 1262508 "INTFTBL" 1266120 T INTFTBL (NIL) -8 NIL NIL) (-544 1255007 1255145 1255318 "INTFACT" 1255617 NIL INTFACT (NIL T) -7 NIL NIL) (-543 1252398 1252842 1253404 "INTEF" 1254563 NIL INTEF (NIL T T) -7 NIL NIL) (-542 1250900 1251605 1251633 "INTDOM" 1251934 T INTDOM (NIL) -9 NIL 1252141) (-541 1250269 1250443 1250685 "INTDOM-" 1250690 NIL INTDOM- (NIL T) -8 NIL NIL) (-540 1246802 1248688 1248742 "INTCAT" 1249541 NIL INTCAT (NIL T) -9 NIL 1249861) (-539 1246275 1246377 1246505 "INTBIT" 1246694 T INTBIT (NIL) -7 NIL NIL) (-538 1244946 1245100 1245414 "INTALG" 1246120 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-537 1244403 1244493 1244663 "INTAF" 1244850 NIL INTAF (NIL T T) -7 NIL NIL) (-536 1237859 1244213 1244353 "INTABL" 1244358 NIL INTABL (NIL T T T) -8 NIL NIL) (-535 1234773 1237588 1237715 "INT" 1237752 T INT (NIL) -8 NIL NIL) (-534 1229830 1232499 1232527 "INS" 1233461 T INS (NIL) -9 NIL 1234125) (-533 1227070 1227841 1228815 "INS-" 1228888 NIL INS- (NIL T) -8 NIL NIL) (-532 1225918 1226123 1226399 "INPSIGN" 1226845 NIL INPSIGN (NIL T T) -7 NIL NIL) (-531 1225036 1225153 1225350 "INPRODPF" 1225798 NIL INPRODPF (NIL T T) -7 NIL NIL) (-530 1223930 1224047 1224284 "INPRODFF" 1224916 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-529 1222930 1223082 1223342 "INNMFACT" 1223766 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-528 1222127 1222224 1222412 "INMODGCD" 1222829 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-527 1220636 1220880 1221204 "INFSP" 1221872 NIL INFSP (NIL T T T) -7 NIL NIL) (-526 1219820 1219937 1220120 "INFPROD0" 1220516 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-525 1219430 1219490 1219588 "INFORM1" 1219755 NIL INFORM1 (NIL T) -7 NIL NIL) (-524 1216312 1217495 1218010 "INFORM" 1218923 T INFORM (NIL) -8 NIL NIL) (-523 1215835 1215924 1216038 "INFINITY" 1216218 T INFINITY (NIL) -7 NIL NIL) (-522 1214452 1214701 1215022 "INEP" 1215583 NIL INEP (NIL T T T) -7 NIL NIL) (-521 1213728 1214349 1214414 "INDE" 1214419 NIL INDE (NIL T) -8 NIL NIL) (-520 1213292 1213360 1213477 "INCRMAPS" 1213655 NIL INCRMAPS (NIL T) -7 NIL NIL) (-519 1208603 1209528 1210472 "INBFF" 1212380 NIL INBFF (NIL T) -7 NIL NIL) (-518 1208272 1208348 1208376 "INBCON" 1208509 T INBCON (NIL) -9 NIL 1208587) (-517 1208112 1208147 1208223 "INBCON-" 1208228 NIL INBCON- (NIL T) -8 NIL NIL) (-516 1207614 1207833 1207925 "INAST" 1208040 T INAST (NIL) -8 NIL NIL) (-515 1207068 1207293 1207399 "IMPTAST" 1207528 T IMPTAST (NIL) -8 NIL NIL) (-514 1203561 1206912 1207016 "IMATRIX" 1207021 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-513 1202273 1202396 1202711 "IMATQF" 1203417 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-512 1200493 1200720 1201057 "IMATLIN" 1202029 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-511 1195121 1200417 1200475 "ILIST" 1200480 NIL ILIST (NIL T NIL) -8 NIL NIL) (-510 1193074 1194981 1195094 "IIARRAY2" 1195099 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-509 1188509 1192985 1193049 "IFF" 1193054 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-508 1187883 1188126 1188242 "IFAST" 1188413 T IFAST (NIL) -8 NIL NIL) (-507 1182926 1187175 1187363 "IFARRAY" 1187740 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-506 1182133 1182830 1182903 "IFAMON" 1182908 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-505 1181717 1181782 1181836 "IEVALAB" 1182043 NIL IEVALAB (NIL T T) -9 NIL NIL) (-504 1181392 1181460 1181620 "IEVALAB-" 1181625 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-503 1180669 1181281 1181356 "IDPOAMS" 1181361 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-502 1180003 1180558 1180633 "IDPOAM" 1180638 NIL IDPOAM (NIL T T) -8 NIL NIL) (-501 1179661 1179917 1179980 "IDPO" 1179985 NIL IDPO (NIL T T) -8 NIL NIL) (-500 1178746 1178996 1179049 "IDPC" 1179462 NIL IDPC (NIL T T) -9 NIL 1179611) (-499 1178242 1178638 1178711 "IDPAM" 1178716 NIL IDPAM (NIL T T) -8 NIL NIL) (-498 1177645 1178134 1178207 "IDPAG" 1178212 NIL IDPAG (NIL T T) -8 NIL NIL) (-497 1177375 1177560 1177610 "IDENT" 1177615 T IDENT (NIL) -8 NIL NIL) (-496 1173630 1174478 1175373 "IDECOMP" 1176532 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-495 1166503 1167553 1168600 "IDEAL" 1172666 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-494 1165667 1165779 1165978 "ICDEN" 1166387 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-493 1164766 1165147 1165294 "ICARD" 1165540 T ICARD (NIL) -8 NIL NIL) (-492 1162826 1163139 1163544 "IBPTOOLS" 1164443 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-491 1158460 1162446 1162559 "IBITS" 1162745 NIL IBITS (NIL NIL) -8 NIL NIL) (-490 1155183 1155759 1156454 "IBATOOL" 1157877 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-489 1152963 1153424 1153957 "IBACHIN" 1154718 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-488 1150840 1152809 1152912 "IARRAY2" 1152917 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-487 1146993 1150766 1150823 "IARRAY1" 1150828 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-486 1140997 1145407 1145887 "IAN" 1146533 T IAN (NIL) -8 NIL NIL) (-485 1140508 1140565 1140738 "IALGFACT" 1140934 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-484 1140036 1140149 1140177 "HYPCAT" 1140384 T HYPCAT (NIL) -9 NIL NIL) (-483 1139574 1139691 1139877 "HYPCAT-" 1139882 NIL HYPCAT- (NIL T) -8 NIL NIL) (-482 1139196 1139369 1139452 "HOSTNAME" 1139511 T HOSTNAME (NIL) -8 NIL NIL) (-481 1135875 1137206 1137247 "HOAGG" 1138228 NIL HOAGG (NIL T) -9 NIL 1138907) (-480 1134469 1134868 1135394 "HOAGG-" 1135399 NIL HOAGG- (NIL T T) -8 NIL NIL) (-479 1128378 1133910 1134076 "HEXADEC" 1134323 T HEXADEC (NIL) -8 NIL NIL) (-478 1127126 1127348 1127611 "HEUGCD" 1128155 NIL HEUGCD (NIL T) -7 NIL NIL) (-477 1126229 1126963 1127093 "HELLFDIV" 1127098 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-476 1124457 1126006 1126094 "HEAP" 1126173 NIL HEAP (NIL T) -8 NIL NIL) (-475 1123748 1124009 1124143 "HEADAST" 1124343 T HEADAST (NIL) -8 NIL NIL) (-474 1117675 1123663 1123725 "HDP" 1123730 NIL HDP (NIL NIL T) -8 NIL NIL) (-473 1111457 1117310 1117462 "HDMP" 1117576 NIL HDMP (NIL NIL T) -8 NIL NIL) (-472 1110782 1110921 1111085 "HB" 1111313 T HB (NIL) -7 NIL NIL) (-471 1104281 1110628 1110732 "HASHTBL" 1110737 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-470 1103784 1104002 1104094 "HASAST" 1104209 T HASAST (NIL) -8 NIL NIL) (-469 1101602 1103408 1103589 "HACKPI" 1103623 T HACKPI (NIL) -8 NIL NIL) (-468 1097324 1101455 1101568 "GTSET" 1101573 NIL GTSET (NIL T T T T) -8 NIL NIL) (-467 1090852 1097202 1097300 "GSTBL" 1097305 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-466 1083167 1089883 1090148 "GSERIES" 1090643 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-465 1082334 1082725 1082753 "GROUP" 1082956 T GROUP (NIL) -9 NIL 1083090) (-464 1081700 1081859 1082110 "GROUP-" 1082115 NIL GROUP- (NIL T) -8 NIL NIL) (-463 1080069 1080388 1080775 "GROEBSOL" 1081377 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-462 1079009 1079271 1079322 "GRMOD" 1079851 NIL GRMOD (NIL T T) -9 NIL 1080019) (-461 1078777 1078813 1078941 "GRMOD-" 1078946 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-460 1074102 1075131 1076131 "GRIMAGE" 1077797 T GRIMAGE (NIL) -8 NIL NIL) (-459 1072569 1072829 1073153 "GRDEF" 1073798 T GRDEF (NIL) -7 NIL NIL) (-458 1072013 1072129 1072270 "GRAY" 1072448 T GRAY (NIL) -7 NIL NIL) (-457 1071244 1071624 1071675 "GRALG" 1071828 NIL GRALG (NIL T T) -9 NIL 1071921) (-456 1070905 1070978 1071141 "GRALG-" 1071146 NIL GRALG- (NIL T T T) -8 NIL NIL) (-455 1067709 1070490 1070668 "GPOLSET" 1070812 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-454 1067063 1067120 1067378 "GOSPER" 1067646 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-453 1062822 1063501 1064027 "GMODPOL" 1066762 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-452 1061827 1062011 1062249 "GHENSEL" 1062634 NIL GHENSEL (NIL T T) -7 NIL NIL) (-451 1055878 1056721 1057748 "GENUPS" 1060911 NIL GENUPS (NIL T T) -7 NIL NIL) (-450 1055575 1055626 1055715 "GENUFACT" 1055821 NIL GENUFACT (NIL T) -7 NIL NIL) (-449 1054987 1055064 1055229 "GENPGCD" 1055493 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-448 1054461 1054496 1054709 "GENMFACT" 1054946 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-447 1053029 1053284 1053591 "GENEEZ" 1054204 NIL GENEEZ (NIL T T) -7 NIL NIL) (-446 1046973 1052640 1052802 "GDMP" 1052952 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-445 1036372 1040744 1041850 "GCNAALG" 1045956 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-444 1034834 1035662 1035690 "GCDDOM" 1035945 T GCDDOM (NIL) -9 NIL 1036102) (-443 1034304 1034431 1034646 "GCDDOM-" 1034651 NIL GCDDOM- (NIL T) -8 NIL NIL) (-442 1022924 1025250 1027642 "GBINTERN" 1031995 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-441 1020761 1021053 1021474 "GBF" 1022599 NIL GBF (NIL T T T T) -7 NIL NIL) (-440 1019542 1019707 1019974 "GBEUCLID" 1020577 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-439 1018214 1018399 1018703 "GB" 1019321 NIL GB (NIL T T T T) -7 NIL NIL) (-438 1017563 1017688 1017837 "GAUSSFAC" 1018085 T GAUSSFAC (NIL) -7 NIL NIL) (-437 1015930 1016232 1016546 "GALUTIL" 1017282 NIL GALUTIL (NIL T) -7 NIL NIL) (-436 1014238 1014512 1014836 "GALPOLYU" 1015657 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-435 1011603 1011893 1012300 "GALFACTU" 1013935 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-434 1003409 1004908 1006516 "GALFACT" 1010035 NIL GALFACT (NIL T) -7 NIL NIL) (-433 1000797 1001455 1001483 "FVFUN" 1002639 T FVFUN (NIL) -9 NIL 1003359) (-432 1000063 1000245 1000273 "FVC" 1000564 T FVC (NIL) -9 NIL 1000747) (-431 999705 999860 999941 "FUNCTION" 1000015 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-430 998523 999006 999209 "FTEM" 999522 T FTEM (NIL) -8 NIL NIL) (-429 996205 996753 997239 "FT" 998057 T FT (NIL) -8 NIL NIL) (-428 994461 994750 995154 "FSUPFACT" 995896 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-427 992858 993147 993479 "FST" 994149 T FST (NIL) -8 NIL NIL) (-426 992029 992135 992330 "FSRED" 992740 NIL FSRED (NIL T T) -7 NIL NIL) (-425 990708 990963 991317 "FSPRMELT" 991744 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-424 987793 988231 988730 "FSPECF" 990271 NIL FSPECF (NIL T T) -7 NIL NIL) (-423 987307 987361 987538 "FSINT" 987734 NIL FSINT (NIL T T) -7 NIL NIL) (-422 985634 986300 986603 "FSERIES" 987086 NIL FSERIES (NIL T T) -8 NIL NIL) (-421 984648 984764 984995 "FSCINT" 985514 NIL FSCINT (NIL T T) -7 NIL NIL) (-420 983690 983833 984060 "FSAGG2" 984501 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-419 979924 982634 982675 "FSAGG" 983045 NIL FSAGG (NIL T) -9 NIL 983304) (-418 977686 978287 979083 "FSAGG-" 979178 NIL FSAGG- (NIL T T) -8 NIL NIL) (-417 975341 975620 976174 "FS2UPS" 977404 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-416 974198 974369 974678 "FS2EXPXP" 975166 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-415 973780 973823 973978 "FS2" 974149 NIL FS2 (NIL T T T T) -7 NIL NIL) (-414 956251 964664 964704 "FS" 968552 NIL FS (NIL T) -9 NIL 970841) (-413 944982 947945 951974 "FS-" 952271 NIL FS- (NIL T T) -8 NIL NIL) (-412 944408 944523 944675 "FRUTIL" 944862 NIL FRUTIL (NIL T) -7 NIL NIL) (-411 939515 942126 942166 "FRNAALG" 943562 NIL FRNAALG (NIL T) -9 NIL 944169) (-410 935244 936298 937556 "FRNAALG-" 938306 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-409 934882 934925 935052 "FRNAAF2" 935195 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-408 933289 933736 934031 "FRMOD" 934694 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-407 932484 932571 932860 "FRIDEAL2" 933196 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-406 930263 930867 931184 "FRIDEAL" 932275 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-405 929512 929919 929960 "FRETRCT" 929965 NIL FRETRCT (NIL T) -9 NIL 930141) (-404 928645 928869 929213 "FRETRCT-" 929218 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-403 925895 927071 927130 "FRAMALG" 928012 NIL FRAMALG (NIL T T) -9 NIL 928304) (-402 924029 924484 925114 "FRAMALG-" 925337 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-401 923665 923722 923829 "FRAC2" 923966 NIL FRAC2 (NIL T T) -7 NIL NIL) (-400 917646 923140 923416 "FRAC" 923421 NIL FRAC (NIL T) -8 NIL NIL) (-399 917282 917339 917446 "FR2" 917583 NIL FR2 (NIL T T) -7 NIL NIL) (-398 908858 912862 914191 "FR" 915985 NIL FR (NIL T) -8 NIL NIL) (-397 903592 906436 906464 "FPS" 907583 T FPS (NIL) -9 NIL 908140) (-396 903041 903150 903314 "FPS-" 903460 NIL FPS- (NIL T) -8 NIL NIL) (-395 900549 902182 902210 "FPC" 902435 T FPC (NIL) -9 NIL 902577) (-394 900342 900382 900479 "FPC-" 900484 NIL FPC- (NIL T) -8 NIL NIL) (-393 899220 899830 899871 "FPATMAB" 899876 NIL FPATMAB (NIL T) -9 NIL 900028) (-392 896920 897396 897822 "FPARFRAC" 898857 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-391 892352 892851 893533 "FORTRAN" 896352 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-390 890028 890590 890618 "FORTFN" 891678 T FORTFN (NIL) -9 NIL 892302) (-389 889792 889842 889870 "FORTCAT" 889929 T FORTCAT (NIL) -9 NIL 889991) (-388 887508 888008 888547 "FORT" 889273 T FORT (NIL) -7 NIL NIL) (-387 887296 887326 887395 "FORMULA1" 887472 NIL FORMULA1 (NIL T) -7 NIL NIL) (-386 885356 885839 886238 "FORMULA" 886917 T FORMULA (NIL) -8 NIL NIL) (-385 884879 884931 885104 "FORDER" 885298 NIL FORDER (NIL T T T T) -7 NIL NIL) (-384 883975 884139 884332 "FOP" 884706 T FOP (NIL) -7 NIL NIL) (-383 882583 883255 883429 "FNLA" 883857 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-382 881251 881640 881668 "FNCAT" 882240 T FNCAT (NIL) -9 NIL 882533) (-381 880817 881210 881238 "FNAME" 881243 T FNAME (NIL) -8 NIL NIL) (-380 879515 880444 880472 "FMTC" 880477 T FMTC (NIL) -9 NIL 880513) (-379 875877 877038 877667 "FMONOID" 878919 NIL FMONOID (NIL T) -8 NIL NIL) (-378 873301 873947 873975 "FMFUN" 875119 T FMFUN (NIL) -9 NIL 875827) (-377 870513 871347 871401 "FMCAT" 872596 NIL FMCAT (NIL T T) -9 NIL 873091) (-376 869782 869963 869991 "FMC" 870281 T FMC (NIL) -9 NIL 870463) (-375 868675 869548 869648 "FM1" 869727 NIL FM1 (NIL T T) -8 NIL NIL) (-374 867894 868417 868566 "FM" 868571 NIL FM (NIL T T) -8 NIL NIL) (-373 865668 866084 866578 "FLOATRP" 867445 NIL FLOATRP (NIL T) -7 NIL NIL) (-372 863106 863606 864184 "FLOATCP" 865135 NIL FLOATCP (NIL T) -7 NIL NIL) (-371 856661 860762 861392 "FLOAT" 862496 T FLOAT (NIL) -8 NIL NIL) (-370 855490 856294 856335 "FLINEXP" 856340 NIL FLINEXP (NIL T) -9 NIL 856433) (-369 854644 854879 855207 "FLINEXP-" 855212 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-368 853720 853864 854088 "FLASORT" 854496 NIL FLASORT (NIL T T) -7 NIL NIL) (-367 850937 851779 851831 "FLALG" 853058 NIL FLALG (NIL T T) -9 NIL 853525) (-366 849979 850122 850349 "FLAGG2" 850790 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-365 843763 847465 847506 "FLAGG" 848768 NIL FLAGG (NIL T) -9 NIL 849420) (-364 842489 842828 843318 "FLAGG-" 843323 NIL FLAGG- (NIL T T) -8 NIL NIL) (-363 839502 840476 840535 "FINRALG" 841663 NIL FINRALG (NIL T T) -9 NIL 842171) (-362 838662 838891 839230 "FINRALG-" 839235 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-361 838068 838281 838309 "FINITE" 838505 T FINITE (NIL) -9 NIL 838612) (-360 830526 832687 832727 "FINAALG" 836394 NIL FINAALG (NIL T) -9 NIL 837847) (-359 825867 826908 828052 "FINAALG-" 829431 NIL FINAALG- (NIL T T) -8 NIL NIL) (-358 824551 824863 824917 "FILECAT" 825601 NIL FILECAT (NIL T T) -9 NIL 825817) (-357 823946 824306 824409 "FILE" 824481 NIL FILE (NIL T) -8 NIL NIL) (-356 821868 823360 823388 "FIELD" 823428 T FIELD (NIL) -9 NIL 823508) (-355 820488 820873 821384 "FIELD-" 821389 NIL FIELD- (NIL T) -8 NIL NIL) (-354 818366 819123 819470 "FGROUP" 820174 NIL FGROUP (NIL T) -8 NIL NIL) (-353 817456 817620 817840 "FGLMICPK" 818198 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-352 813325 817381 817438 "FFX" 817443 NIL FFX (NIL T NIL) -8 NIL NIL) (-351 812926 812987 813122 "FFSLPE" 813258 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-350 812430 812466 812675 "FFPOLY2" 812884 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-349 808423 809202 809998 "FFPOLY" 811666 NIL FFPOLY (NIL T) -7 NIL NIL) (-348 804311 808342 808405 "FFP" 808410 NIL FFP (NIL T NIL) -8 NIL NIL) (-347 799474 803654 803844 "FFNBX" 804165 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-346 794450 798609 798867 "FFNBP" 799328 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-345 789120 793734 793945 "FFNB" 794283 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-344 787952 788150 788465 "FFINTBAS" 788917 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-343 784238 786411 786439 "FFIELDC" 787059 T FFIELDC (NIL) -9 NIL 787435) (-342 782901 783271 783768 "FFIELDC-" 783773 NIL FFIELDC- (NIL T) -8 NIL NIL) (-341 782471 782516 782640 "FFHOM" 782843 NIL FFHOM (NIL T T T) -7 NIL NIL) (-340 780169 780653 781170 "FFF" 781986 NIL FFF (NIL T) -7 NIL NIL) (-339 775824 779911 780012 "FFCGX" 780112 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-338 771493 775556 775663 "FFCGP" 775767 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-337 766713 771220 771328 "FFCG" 771429 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-336 766124 766167 766402 "FFCAT2" 766664 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-335 748191 757218 757304 "FFCAT" 762469 NIL FFCAT (NIL T T T) -9 NIL 763920) (-334 743389 744436 745750 "FFCAT-" 746980 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-333 738824 743300 743364 "FF" 743369 NIL FF (NIL NIL NIL) -8 NIL NIL) (-332 728038 731796 733016 "FEXPR" 737676 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-331 727038 727473 727514 "FEVALAB" 727598 NIL FEVALAB (NIL T) -9 NIL 727859) (-330 726197 726407 726745 "FEVALAB-" 726750 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-329 723263 723978 724093 "FDIVCAT" 725661 NIL FDIVCAT (NIL T T T T) -9 NIL 726098) (-328 723025 723052 723222 "FDIVCAT-" 723227 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-327 722245 722332 722609 "FDIV2" 722932 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-326 720838 721628 721831 "FDIV" 722144 NIL FDIV (NIL T T T T) -8 NIL NIL) (-325 719524 719783 720072 "FCPAK1" 720569 T FCPAK1 (NIL) -7 NIL NIL) (-324 718652 719024 719165 "FCOMP" 719415 NIL FCOMP (NIL T) -8 NIL NIL) (-323 702287 705701 709262 "FC" 715111 T FC (NIL) -8 NIL NIL) (-322 694942 698921 698961 "FAXF" 700763 NIL FAXF (NIL T) -9 NIL 701455) (-321 692221 692876 693701 "FAXF-" 694166 NIL FAXF- (NIL T T) -8 NIL NIL) (-320 687321 691597 691773 "FARRAY" 692078 NIL FARRAY (NIL T) -8 NIL NIL) (-319 682735 684760 684813 "FAMR" 685836 NIL FAMR (NIL T T) -9 NIL 686296) (-318 681625 681927 682362 "FAMR-" 682367 NIL FAMR- (NIL T T T) -8 NIL NIL) (-317 680821 681547 681600 "FAMONOID" 681605 NIL FAMONOID (NIL T) -8 NIL NIL) (-316 678651 679335 679388 "FAMONC" 680329 NIL FAMONC (NIL T T) -9 NIL 680715) (-315 677343 678405 678542 "FAGROUP" 678547 NIL FAGROUP (NIL T) -8 NIL NIL) (-314 675138 675457 675860 "FACUTIL" 677024 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-313 674237 674422 674644 "FACTFUNC" 674948 NIL FACTFUNC (NIL T) -7 NIL NIL) (-312 666644 673488 673700 "EXPUPXS" 674093 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-311 664127 664667 665253 "EXPRTUBE" 666078 T EXPRTUBE (NIL) -7 NIL NIL) (-310 660321 660913 661650 "EXPRODE" 663466 NIL EXPRODE (NIL T T) -7 NIL NIL) (-309 654728 655315 656128 "EXPR2UPS" 659619 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-308 654364 654421 654528 "EXPR2" 654665 NIL EXPR2 (NIL T T) -7 NIL NIL) (-307 639799 653019 653447 "EXPR" 653968 NIL EXPR (NIL T) -8 NIL NIL) (-306 631232 638931 639228 "EXPEXPAN" 639636 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-305 630739 630956 631047 "EXITAST" 631161 T EXITAST (NIL) -8 NIL NIL) (-304 630566 630696 630725 "EXIT" 630730 T EXIT (NIL) -8 NIL NIL) (-303 630193 630255 630368 "EVALCYC" 630498 NIL EVALCYC (NIL T) -7 NIL NIL) (-302 629734 629852 629893 "EVALAB" 630063 NIL EVALAB (NIL T) -9 NIL 630167) (-301 629215 629337 629558 "EVALAB-" 629563 NIL EVALAB- (NIL T T) -8 NIL NIL) (-300 626718 627986 628014 "EUCDOM" 628569 T EUCDOM (NIL) -9 NIL 628919) (-299 625123 625565 626155 "EUCDOM-" 626160 NIL EUCDOM- (NIL T) -8 NIL NIL) (-298 624755 624812 624921 "ESTOOLS2" 625060 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-297 624506 624548 624628 "ESTOOLS1" 624707 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-296 612046 614804 617554 "ESTOOLS" 621776 T ESTOOLS (NIL) -7 NIL NIL) (-295 611791 611823 611905 "ESCONT1" 612008 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-294 608166 608926 609706 "ESCONT" 611031 T ESCONT (NIL) -7 NIL NIL) (-293 607841 607891 607991 "ES2" 608110 NIL ES2 (NIL T T) -7 NIL NIL) (-292 607471 607529 607638 "ES1" 607777 NIL ES1 (NIL T T) -7 NIL NIL) (-291 601396 603124 603152 "ES" 605920 T ES (NIL) -9 NIL 607329) (-290 596343 597630 599447 "ES-" 599611 NIL ES- (NIL T) -8 NIL NIL) (-289 595559 595688 595864 "ERROR" 596187 T ERROR (NIL) -7 NIL NIL) (-288 589064 595418 595509 "EQTBL" 595514 NIL EQTBL (NIL T T) -8 NIL NIL) (-287 588696 588753 588862 "EQ2" 589001 NIL EQ2 (NIL T T) -7 NIL NIL) (-286 581253 584010 585459 "EQ" 587280 NIL -3873 (NIL T) -8 NIL NIL) (-285 576545 577591 578684 "EP" 580192 NIL EP (NIL T) -7 NIL NIL) (-284 575127 575428 575745 "ENV" 576248 T ENV (NIL) -8 NIL NIL) (-283 574326 574846 574874 "ENTIRER" 574879 T ENTIRER (NIL) -9 NIL 574925) (-282 570884 572335 572705 "EMR" 574125 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-281 570028 570213 570267 "ELTAGG" 570647 NIL ELTAGG (NIL T T) -9 NIL 570858) (-280 569747 569809 569950 "ELTAGG-" 569955 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-279 569536 569565 569619 "ELTAB" 569703 NIL ELTAB (NIL T T) -9 NIL NIL) (-278 568662 568808 569007 "ELFUTS" 569387 NIL ELFUTS (NIL T T) -7 NIL NIL) (-277 568404 568460 568488 "ELEMFUN" 568593 T ELEMFUN (NIL) -9 NIL NIL) (-276 568274 568295 568363 "ELEMFUN-" 568368 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-275 563165 566374 566415 "ELAGG" 567355 NIL ELAGG (NIL T) -9 NIL 567818) (-274 561450 561884 562547 "ELAGG-" 562552 NIL ELAGG- (NIL T T) -8 NIL NIL) (-273 560107 560387 560682 "ELABEXPR" 561175 T ELABEXPR (NIL) -8 NIL NIL) (-272 553100 554774 555601 "EFUPXS" 559383 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-271 546677 548351 549161 "EFULS" 552376 NIL EFULS (NIL T T T) -8 NIL NIL) (-270 544099 544457 544936 "EFSTRUC" 546309 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-269 533171 534736 536296 "EF" 542614 NIL EF (NIL T T) -7 NIL NIL) (-268 532272 532656 532805 "EAB" 533042 T EAB (NIL) -8 NIL NIL) (-267 531481 532231 532259 "E04UCFA" 532264 T E04UCFA (NIL) -8 NIL NIL) (-266 530690 531440 531468 "E04NAFA" 531473 T E04NAFA (NIL) -8 NIL NIL) (-265 529899 530649 530677 "E04MBFA" 530682 T E04MBFA (NIL) -8 NIL NIL) (-264 529108 529858 529886 "E04JAFA" 529891 T E04JAFA (NIL) -8 NIL NIL) (-263 528319 529067 529095 "E04GCFA" 529100 T E04GCFA (NIL) -8 NIL NIL) (-262 527530 528278 528306 "E04FDFA" 528311 T E04FDFA (NIL) -8 NIL NIL) (-261 526739 527489 527517 "E04DGFA" 527522 T E04DGFA (NIL) -8 NIL NIL) (-260 520917 522264 523628 "E04AGNT" 525395 T E04AGNT (NIL) -7 NIL NIL) (-259 519641 520121 520161 "DVARCAT" 520636 NIL DVARCAT (NIL T) -9 NIL 520835) (-258 518845 519057 519371 "DVARCAT-" 519376 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-257 511786 518644 518773 "DSMP" 518778 NIL DSMP (NIL T T T) -8 NIL NIL) (-256 511451 511510 511608 "DROPT1" 511721 NIL DROPT1 (NIL T) -7 NIL NIL) (-255 506566 507692 508829 "DROPT0" 510334 T DROPT0 (NIL) -7 NIL NIL) (-254 501376 502511 503579 "DROPT" 505518 T DROPT (NIL) -8 NIL NIL) (-253 499721 500046 500432 "DRAWPT" 501010 T DRAWPT (NIL) -7 NIL NIL) (-252 499354 499407 499525 "DRAWHACK" 499662 NIL DRAWHACK (NIL T) -7 NIL NIL) (-251 498085 498354 498645 "DRAWCX" 499083 T DRAWCX (NIL) -7 NIL NIL) (-250 497601 497669 497820 "DRAWCURV" 498011 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-249 488072 490031 492146 "DRAWCFUN" 495506 T DRAWCFUN (NIL) -7 NIL NIL) (-248 482659 483582 484661 "DRAW" 487046 NIL DRAW (NIL T) -7 NIL NIL) (-247 479472 481354 481395 "DQAGG" 482024 NIL DQAGG (NIL T) -9 NIL 482297) (-246 468027 474688 474771 "DPOLCAT" 476623 NIL DPOLCAT (NIL T T T T) -9 NIL 477168) (-245 462917 464246 466187 "DPOLCAT-" 466192 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-244 456079 462778 462876 "DPMO" 462881 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-243 449144 455859 456026 "DPMM" 456031 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-242 448564 448767 448881 "DOMAIN" 449050 T DOMAIN (NIL) -8 NIL NIL) (-241 442346 448199 448351 "DMP" 448465 NIL DMP (NIL NIL T) -8 NIL NIL) (-240 441946 442002 442146 "DLP" 442284 NIL DLP (NIL T) -7 NIL NIL) (-239 435592 441047 441274 "DLIST" 441751 NIL DLIST (NIL T) -8 NIL NIL) (-238 432439 434447 434488 "DLAGG" 435038 NIL DLAGG (NIL T) -9 NIL 435267) (-237 431289 431919 431947 "DIVRING" 432039 T DIVRING (NIL) -9 NIL 432122) (-236 430526 430716 431016 "DIVRING-" 431021 NIL DIVRING- (NIL T) -8 NIL NIL) (-235 428628 428985 429391 "DISPLAY" 430140 T DISPLAY (NIL) -7 NIL NIL) (-234 427476 427679 427944 "DIRPROD2" 428421 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-233 421425 427390 427453 "DIRPROD" 427458 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-232 410970 416915 416968 "DIRPCAT" 417378 NIL DIRPCAT (NIL NIL T) -9 NIL 418218) (-231 408296 408938 409819 "DIRPCAT-" 410156 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-230 407583 407743 407929 "DIOSP" 408130 T DIOSP (NIL) -7 NIL NIL) (-229 404285 406495 406536 "DIOPS" 406970 NIL DIOPS (NIL T) -9 NIL 407199) (-228 403834 403948 404139 "DIOPS-" 404144 NIL DIOPS- (NIL T T) -8 NIL NIL) (-227 402746 403340 403368 "DIFRING" 403555 T DIFRING (NIL) -9 NIL 403665) (-226 402392 402469 402621 "DIFRING-" 402626 NIL DIFRING- (NIL T) -8 NIL NIL) (-225 400217 401455 401496 "DIFEXT" 401859 NIL DIFEXT (NIL T) -9 NIL 402153) (-224 398502 398930 399596 "DIFEXT-" 399601 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-223 395824 398034 398075 "DIAGG" 398080 NIL DIAGG (NIL T) -9 NIL 398100) (-222 395208 395365 395617 "DIAGG-" 395622 NIL DIAGG- (NIL T T) -8 NIL NIL) (-221 390672 394167 394444 "DHMATRIX" 394977 NIL DHMATRIX (NIL T) -8 NIL NIL) (-220 386284 387193 388203 "DFSFUN" 389682 T DFSFUN (NIL) -7 NIL NIL) (-219 381256 385099 385441 "DFLOAT" 385962 T DFLOAT (NIL) -8 NIL NIL) (-218 379484 379765 380161 "DFINTTLS" 380964 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-217 376549 377505 377905 "DERHAM" 379150 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-216 374398 376324 376413 "DEQUEUE" 376493 NIL DEQUEUE (NIL T) -8 NIL NIL) (-215 373613 373746 373942 "DEGRED" 374260 NIL DEGRED (NIL T T) -7 NIL NIL) (-214 370188 370888 371696 "DEFINTRF" 372886 NIL DEFINTRF (NIL T) -7 NIL NIL) (-213 367827 368268 368839 "DEFINTEF" 369735 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-212 367204 367447 367562 "DEFAST" 367732 T DEFAST (NIL) -8 NIL NIL) (-211 361113 366645 366811 "DECIMAL" 367058 T DECIMAL (NIL) -8 NIL NIL) (-210 358625 359083 359589 "DDFACT" 360657 NIL DDFACT (NIL T T) -7 NIL NIL) (-209 358221 358264 358415 "DBLRESP" 358576 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-208 355931 356265 356634 "DBASE" 357979 NIL DBASE (NIL T) -8 NIL NIL) (-207 355200 355411 355557 "DATABUF" 355830 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-206 354333 355159 355187 "D03FAFA" 355192 T D03FAFA (NIL) -8 NIL NIL) (-205 353467 354292 354320 "D03EEFA" 354325 T D03EEFA (NIL) -8 NIL NIL) (-204 351417 351883 352372 "D03AGNT" 352998 T D03AGNT (NIL) -7 NIL NIL) (-203 350733 351376 351404 "D02EJFA" 351409 T D02EJFA (NIL) -8 NIL NIL) (-202 350049 350692 350720 "D02CJFA" 350725 T D02CJFA (NIL) -8 NIL NIL) (-201 349365 350008 350036 "D02BHFA" 350041 T D02BHFA (NIL) -8 NIL NIL) (-200 348681 349324 349352 "D02BBFA" 349357 T D02BBFA (NIL) -8 NIL NIL) (-199 341879 343467 345073 "D02AGNT" 347095 T D02AGNT (NIL) -7 NIL NIL) (-198 339648 340170 340716 "D01WGTS" 341353 T D01WGTS (NIL) -7 NIL NIL) (-197 338743 339607 339635 "D01TRNS" 339640 T D01TRNS (NIL) -8 NIL NIL) (-196 337838 338702 338730 "D01GBFA" 338735 T D01GBFA (NIL) -8 NIL NIL) (-195 336933 337797 337825 "D01FCFA" 337830 T D01FCFA (NIL) -8 NIL NIL) (-194 336028 336892 336920 "D01ASFA" 336925 T D01ASFA (NIL) -8 NIL NIL) (-193 335123 335987 336015 "D01AQFA" 336020 T D01AQFA (NIL) -8 NIL NIL) (-192 334218 335082 335110 "D01APFA" 335115 T D01APFA (NIL) -8 NIL NIL) (-191 333313 334177 334205 "D01ANFA" 334210 T D01ANFA (NIL) -8 NIL NIL) (-190 332408 333272 333300 "D01AMFA" 333305 T D01AMFA (NIL) -8 NIL NIL) (-189 331503 332367 332395 "D01ALFA" 332400 T D01ALFA (NIL) -8 NIL NIL) (-188 330598 331462 331490 "D01AKFA" 331495 T D01AKFA (NIL) -8 NIL NIL) (-187 329693 330557 330585 "D01AJFA" 330590 T D01AJFA (NIL) -8 NIL NIL) (-186 322990 324541 326102 "D01AGNT" 328152 T D01AGNT (NIL) -7 NIL NIL) (-185 322327 322455 322607 "CYCLOTOM" 322858 T CYCLOTOM (NIL) -7 NIL NIL) (-184 319062 319775 320502 "CYCLES" 321620 T CYCLES (NIL) -7 NIL NIL) (-183 318374 318508 318679 "CVMP" 318923 NIL CVMP (NIL T) -7 NIL NIL) (-182 316145 316403 316779 "CTRIGMNP" 318102 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-181 315656 315845 315944 "CTORCALL" 316066 T CTORCALL (NIL) -8 NIL NIL) (-180 315030 315129 315282 "CSTTOOLS" 315553 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-179 310829 311486 312244 "CRFP" 314342 NIL CRFP (NIL T T) -7 NIL NIL) (-178 310331 310550 310642 "CRCEAST" 310757 T CRCEAST (NIL) -8 NIL NIL) (-177 309378 309563 309791 "CRAPACK" 310135 NIL CRAPACK (NIL T) -7 NIL NIL) (-176 308762 308863 309067 "CPMATCH" 309254 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-175 308487 308515 308621 "CPIMA" 308728 NIL CPIMA (NIL T T T) -7 NIL NIL) (-174 304851 305523 306241 "COORDSYS" 307822 NIL COORDSYS (NIL T) -7 NIL NIL) (-173 304235 304364 304514 "CONTOUR" 304721 T CONTOUR (NIL) -8 NIL NIL) (-172 300163 302238 302730 "CONTFRAC" 303775 NIL CONTFRAC (NIL T) -8 NIL NIL) (-171 300043 300064 300092 "CONDUIT" 300129 T CONDUIT (NIL) -9 NIL NIL) (-170 299236 299756 299784 "COMRING" 299789 T COMRING (NIL) -9 NIL 299841) (-169 298317 298594 298778 "COMPPROP" 299072 T COMPPROP (NIL) -8 NIL NIL) (-168 297978 298013 298141 "COMPLPAT" 298276 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-167 297614 297671 297778 "COMPLEX2" 297915 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-166 287691 297423 297532 "COMPLEX" 297537 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 287409 287444 287542 "COMPFACT" 287650 NIL COMPFACT (NIL T T) -7 NIL NIL) (-164 271816 282023 282063 "COMPCAT" 283067 NIL COMPCAT (NIL T) -9 NIL 284462) (-163 261352 264269 267889 "COMPCAT-" 268245 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-162 261081 261109 261212 "COMMUPC" 261318 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-161 260876 260909 260968 "COMMONOP" 261042 T COMMONOP (NIL) -7 NIL NIL) (-160 260480 260680 260755 "COMMAAST" 260821 T COMMAAST (NIL) -8 NIL NIL) (-159 260063 260231 260318 "COMM" 260413 T COMM (NIL) -8 NIL NIL) (-158 259312 259506 259534 "COMBOPC" 259872 T COMBOPC (NIL) -9 NIL 260047) (-157 258208 258418 258660 "COMBINAT" 259102 NIL COMBINAT (NIL T) -7 NIL NIL) (-156 254406 254979 255619 "COMBF" 257630 NIL COMBF (NIL T T) -7 NIL NIL) (-155 253192 253522 253757 "COLOR" 254191 T COLOR (NIL) -8 NIL NIL) (-154 252695 252913 253005 "COLONAST" 253120 T COLONAST (NIL) -8 NIL NIL) (-153 252335 252382 252507 "CMPLXRT" 252642 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-152 251810 252035 252134 "CLLCTAST" 252256 T CLLCTAST (NIL) -8 NIL NIL) (-151 247312 248340 249420 "CLIP" 250750 T CLIP (NIL) -7 NIL NIL) (-150 245694 246418 246657 "CLIF" 247139 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-149 241916 243840 243881 "CLAGG" 244810 NIL CLAGG (NIL T) -9 NIL 245346) (-148 240338 240795 241378 "CLAGG-" 241383 NIL CLAGG- (NIL T T) -8 NIL NIL) (-147 239882 239967 240107 "CINTSLPE" 240247 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-146 237383 237854 238402 "CHVAR" 239410 NIL CHVAR (NIL T T T) -7 NIL NIL) (-145 236646 237166 237194 "CHARZ" 237199 T CHARZ (NIL) -9 NIL 237214) (-144 236400 236440 236518 "CHARPOL" 236600 NIL CHARPOL (NIL T) -7 NIL NIL) (-143 235547 236100 236128 "CHARNZ" 236175 T CHARNZ (NIL) -9 NIL 236231) (-142 233572 234237 234572 "CHAR" 235232 T CHAR (NIL) -8 NIL NIL) (-141 233298 233359 233387 "CFCAT" 233498 T CFCAT (NIL) -9 NIL NIL) (-140 232543 232654 232836 "CDEN" 233182 NIL CDEN (NIL T T T) -7 NIL NIL) (-139 228535 231696 231976 "CCLASS" 232283 T CCLASS (NIL) -8 NIL NIL) (-138 228454 228480 228515 "CATEGORY" 228520 T -10 (NIL) -8 NIL NIL) (-137 227928 228154 228253 "CATAST" 228375 T CATAST (NIL) -8 NIL NIL) (-136 227431 227649 227741 "CASEAST" 227856 T CASEAST (NIL) -8 NIL NIL) (-135 226539 226687 226908 "CARTEN2" 227278 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-134 221591 222568 223321 "CARTEN" 225842 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-133 219933 220741 220998 "CARD" 221354 T CARD (NIL) -8 NIL NIL) (-132 219536 219737 219812 "CAPSLAST" 219878 T CAPSLAST (NIL) -8 NIL NIL) (-131 218908 219236 219264 "CACHSET" 219396 T CACHSET (NIL) -9 NIL 219473) (-130 218404 218700 218728 "CABMON" 218778 T CABMON (NIL) -9 NIL 218834) (-129 214352 218351 218385 "BYTEARY" 218390 T BYTEARY (NIL) -8 NIL NIL) (-128 213521 213899 214042 "BYTE" 214229 T BYTE (NIL) -8 NIL NIL) (-127 211080 213213 213320 "BTREE" 213447 NIL BTREE (NIL T) -8 NIL NIL) (-126 208580 210728 210850 "BTOURN" 210990 NIL BTOURN (NIL T) -8 NIL NIL) (-125 206000 208051 208092 "BTCAT" 208160 NIL BTCAT (NIL T) -9 NIL 208237) (-124 205667 205747 205896 "BTCAT-" 205901 NIL BTCAT- (NIL T T) -8 NIL NIL) (-123 200959 204810 204838 "BTAGG" 205060 T BTAGG (NIL) -9 NIL 205221) (-122 200449 200574 200780 "BTAGG-" 200785 NIL BTAGG- (NIL T) -8 NIL NIL) (-121 197495 199727 199942 "BSTREE" 200266 NIL BSTREE (NIL T) -8 NIL NIL) (-120 196633 196759 196943 "BRILL" 197351 NIL BRILL (NIL T) -7 NIL NIL) (-119 193335 195361 195402 "BRAGG" 196051 NIL BRAGG (NIL T) -9 NIL 196308) (-118 191867 192272 192826 "BRAGG-" 192831 NIL BRAGG- (NIL T T) -8 NIL NIL) (-117 185154 191213 191397 "BPADICRT" 191715 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-116 183506 185091 185136 "BPADIC" 185141 NIL BPADIC (NIL NIL) -8 NIL NIL) (-115 183204 183234 183348 "BOUNDZRO" 183470 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-114 180825 181269 181789 "BOP1" 182717 NIL BOP1 (NIL T) -7 NIL NIL) (-113 176340 177431 178298 "BOP" 179978 T BOP (NIL) -8 NIL NIL) (-112 175078 175764 175957 "BOOLEAN" 176167 T BOOLEAN (NIL) -8 NIL NIL) (-111 174440 174818 174872 "BMODULE" 174877 NIL BMODULE (NIL T T) -9 NIL 174942) (-110 170270 174238 174311 "BITS" 174387 T BITS (NIL) -8 NIL NIL) (-109 169367 169802 169954 "BINFILE" 170138 T BINFILE (NIL) -8 NIL NIL) (-108 168779 168901 169043 "BINDING" 169245 T BINDING (NIL) -8 NIL NIL) (-107 162692 168223 168388 "BINARY" 168634 T BINARY (NIL) -8 NIL NIL) (-106 160519 161947 161988 "BGAGG" 162248 NIL BGAGG (NIL T) -9 NIL 162385) (-105 160350 160382 160473 "BGAGG-" 160478 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 159448 159734 159939 "BFUNCT" 160165 T BFUNCT (NIL) -8 NIL NIL) (-103 158132 158313 158601 "BEZOUT" 159272 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 154651 156984 157314 "BBTREE" 157835 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154385 154438 154466 "BASTYPE" 154585 T BASTYPE (NIL) -9 NIL NIL) (-100 154237 154266 154339 "BASTYPE-" 154344 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 153675 153751 153901 "BALFACT" 154148 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 152558 153090 153276 "AUTOMOR" 153520 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152284 152289 152315 "ATTREG" 152320 T ATTREG (NIL) -9 NIL NIL) (-96 150563 150981 151333 "ATTRBUT" 151950 T ATTRBUT (NIL) -8 NIL NIL) (-95 150198 150391 150457 "ATTRAST" 150515 T ATTRAST (NIL) -8 NIL NIL) (-94 149734 149847 149873 "ATRIG" 150074 T ATRIG (NIL) -9 NIL NIL) (-93 149543 149584 149671 "ATRIG-" 149676 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149165 149325 149351 "ASTCAT" 149409 T ASTCAT (NIL) -9 NIL 149472) (-91 148892 148951 149070 "ASTCAT-" 149075 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147089 148668 148756 "ASTACK" 148835 NIL ASTACK (NIL T) -8 NIL NIL) (-89 145594 145891 146256 "ASSOCEQ" 146771 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 144648 145253 145377 "ASP9" 145501 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 143539 144253 144395 "ASP80" 144537 NIL ASP80 (NIL NIL) -8 NIL NIL) (-86 143303 143487 143526 "ASP8" 143531 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 142279 142980 143098 "ASP78" 143216 NIL ASP78 (NIL NIL) -8 NIL NIL) (-84 141270 141959 142076 "ASP77" 142193 NIL ASP77 (NIL NIL) -8 NIL NIL) (-83 140204 140908 141039 "ASP74" 141170 NIL ASP74 (NIL NIL) -8 NIL NIL) (-82 139126 139839 139971 "ASP73" 140103 NIL ASP73 (NIL NIL) -8 NIL NIL) (-81 138047 138761 138893 "ASP7" 139025 NIL ASP7 (NIL NIL) -8 NIL NIL) (-80 137024 137724 137842 "ASP6" 137960 NIL ASP6 (NIL NIL) -8 NIL NIL) (-79 135994 136701 136819 "ASP55" 136937 NIL ASP55 (NIL NIL) -8 NIL NIL) (-78 134966 135668 135787 "ASP50" 135906 NIL ASP50 (NIL NIL) -8 NIL NIL) (-77 134076 134667 134777 "ASP49" 134887 NIL ASP49 (NIL NIL) -8 NIL NIL) (-76 132883 133615 133783 "ASP42" 133965 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-75 131682 132416 132586 "ASP41" 132770 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-74 130792 131383 131493 "ASP4" 131603 NIL ASP4 (NIL NIL) -8 NIL NIL) (-73 129764 130469 130587 "ASP35" 130705 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 129529 129712 129751 "ASP34" 129756 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129266 129333 129409 "ASP33" 129484 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128183 128901 129033 "ASP31" 129165 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 127948 128131 128170 "ASP30" 128175 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 127683 127752 127828 "ASP29" 127903 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127448 127631 127670 "ASP28" 127675 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127213 127396 127435 "ASP27" 127440 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126319 126911 127022 "ASP24" 127133 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125257 125960 126090 "ASP20" 126220 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 124223 124931 125050 "ASP19" 125169 NIL ASP19 (NIL NIL) -8 NIL NIL) (-62 123960 124027 124103 "ASP12" 124178 NIL ASP12 (NIL NIL) -8 NIL NIL) (-61 122834 123559 123703 "ASP10" 123847 NIL ASP10 (NIL NIL) -8 NIL NIL) (-60 121944 122535 122645 "ASP1" 122755 NIL ASP1 (NIL NIL) -8 NIL NIL) (-59 119843 121788 121879 "ARRAY2" 121884 NIL ARRAY2 (NIL T) -8 NIL NIL) (-58 118875 119048 119269 "ARRAY12" 119666 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-57 114691 118523 118637 "ARRAY1" 118792 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 109050 110921 110996 "ARR2CAT" 113626 NIL ARR2CAT (NIL T T T) -9 NIL 114384) (-55 106484 107228 108182 "ARR2CAT-" 108187 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-54 105232 105384 105690 "APPRULE" 106320 NIL APPRULE (NIL T T T) -7 NIL NIL) (-53 104883 104931 105050 "APPLYORE" 105178 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-52 104161 104284 104441 "ANY1" 104757 NIL ANY1 (NIL T) -7 NIL NIL) (-51 103135 103426 103621 "ANY" 103984 T ANY (NIL) -8 NIL NIL) (-50 100700 101572 101899 "ANTISYM" 102859 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-49 100215 100404 100501 "ANON" 100621 T ANON (NIL) -8 NIL NIL) (-48 94358 98756 99209 "AN" 99780 T AN (NIL) -8 NIL NIL) (-47 90739 92093 92144 "AMR" 92892 NIL AMR (NIL T T) -9 NIL 93492) (-46 89851 90072 90435 "AMR-" 90440 NIL AMR- (NIL T T T) -8 NIL NIL) (-45 74407 89768 89829 "ALIST" 89834 NIL ALIST (NIL T T) -8 NIL NIL) (-44 71276 74001 74170 "ALGSC" 74325 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-43 67832 68386 68993 "ALGPKG" 70716 NIL ALGPKG (NIL T T) -7 NIL NIL) (-42 67109 67210 67394 "ALGMFACT" 67718 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 62848 63533 64188 "ALGMANIP" 66632 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54265 62474 62624 "ALGFF" 62781 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-39 53461 53592 53771 "ALGFACT" 54123 NIL ALGFACT (NIL T) -7 NIL NIL) (-38 52491 53057 53095 "ALGEBRA" 53155 NIL ALGEBRA (NIL T) -9 NIL 53214) (-37 52209 52268 52400 "ALGEBRA-" 52405 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-36 34475 50212 50264 "ALAGG" 50400 NIL ALAGG (NIL T T) -9 NIL 50561) (-35 34011 34124 34150 "AHYP" 34351 T AHYP (NIL) -9 NIL NIL) (-34 32942 33190 33216 "AGG" 33715 T AGG (NIL) -9 NIL 33994) (-33 32376 32538 32752 "AGG-" 32757 NIL AGG- (NIL T) -8 NIL NIL) (-32 30053 30475 30893 "AF" 32018 NIL AF (NIL T T) -7 NIL NIL) (-31 29560 29778 29868 "ADDAST" 29981 T ADDAST (NIL) -8 NIL NIL) (-30 28829 29087 29243 "ACPLOT" 29422 T ACPLOT (NIL) -8 NIL NIL) (-29 18356 26221 26272 "ACFS" 26983 NIL ACFS (NIL T) -9 NIL 27222) (-28 16370 16860 17635 "ACFS-" 17640 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14589 14615 "ACF" 15494 T ACF (NIL) -9 NIL 15906) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
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are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1122 (-219))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2062 + (-3 (|:| |str| (-1119 (-219))) + (|:| |notEvaluated| "Internal singularities not yet evaluated"))) + (|:| -1556 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") + (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *1 (-544))))) -(((*1 *2 *3) (-12 (-5 *3 (-1142)) (-5 *2 (-1230)) (-5 *1 (-1145)))) - ((*1 *2) (-12 (-5 *2 (-1230)) (-5 *1 (-1145))))) -(((*1 *2 *1) - (|partial| -12 (-4 *1 (-920 *3 *4 *2)) (-4 *3 (-1018)) (-4 *4 (-769)) - (-4 *2 (-823)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-769)) (-4 *5 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|bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1119 (-219))) + (|:| |notEvaluated| "Internal singularities not yet evaluated"))) + (|:| -1556 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *1 (-545))))) +(((*1 *1 *2) (-12 (-5 *2 - (-621 + (-618 (-2 - (|:| -3337 - (-2 (|:| |var| (-1142)) (|:| |fn| (-309 (-219))) - (|:| -2062 (-1060 (-816 (-219)))) (|:| |abserr| (-219)) + (|:| -4203 + (-2 (|:| |var| (-1142)) (|:| |fn| (-307 (-219))) + (|:| -1556 (-1055 (-815 (-219)))) (|:| |abserr| (-219)) (|:| |relerr| (-219)))) - (|:| -1792 + (|:| -2184 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") @@ 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\ No newline at end of file |