diff options
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 3 | ||||
| -rw-r--r-- | src/algebra/indexedp.spad.pamphlet | 121 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1274 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1578 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1326 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8888 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25661 |
7 files changed, 19417 insertions, 19434 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 76b0f796..104c4f10 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -296,7 +296,8 @@ OrderedType(): Category == BasicType with )abbrev domain ORDSTRCT OrderedStructure OrderedStructure(T: Type,f: (T,T) -> Boolean): Public == Private where Public == Join(OrderedType,HomotopicTo T) - Private == T add + Private == add + Rep == T coerce(x: %): T == rep x coerce(y: T): % == per y x < y == f(rep x,rep y) diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet index 59b76a81..43d67cf4 100644 --- a/src/algebra/indexedp.spad.pamphlet +++ b/src/algebra/indexedp.spad.pamphlet @@ -65,10 +65,7 @@ IndexedDirectProductCategory(A:SetCategory,S:OrderedSet): Category == IndexedDirectProductObject(A,S): Public == Private where A: SetCategory S: OrderedSet - Public == IndexedDirectProductCategory(A,S) with - indexedDirectProductObject: List Pair(S,A) -> % - ++ \spad{indexedDirectProductObject l} constructs an indexed - ++ direct product object with support-value pairs given in \spad{l}. + Public == IndexedDirectProductCategory(A,S) Private == add Term == Pair(S,A) Rep == List Term @@ -108,8 +105,6 @@ IndexedDirectProductObject(A,S): Public == Private where termIndex first rep x terms x == rep x - indexedDirectProductObject l == - per sort((x,y) +-> termIndex x > termIndex y, l) @ \section{domain IDPAM IndexedDirectProductAbelianMonoid} @@ -119,10 +114,7 @@ IndexedDirectProductObject(A,S): Public == Private where ++ generators indexed by the ordered set S. All items have finite support. ++ Only non-zero terms are stored. IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedSet): - Join(AbelianMonoid,IndexedDirectProductCategory(A,S)) with - construct: List Pair(A,S) -> % - ++ \spad{l} returns an IndexedDirectProductAbelianMonoid object - ++ with support and value as specified in the list of pairs \spad{l}. + Join(AbelianMonoid,IndexedDirectProductCategory(A,S)) == IndexedDirectProductObject(A,S) add --representations Term == Pair(S,A) @@ -203,10 +195,6 @@ IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedSet): pair2Term(t: Pair(A,S)): Term == [second t, first t] - construct l == - per indexedDirectProductObject - [pair2Term t for t in l | not zero? first t] - @ \section{domain IDPOAM IndexedDirectProductOrderedAbelianMonoid} <<domain IDPOAM IndexedDirectProductOrderedAbelianMonoid>>= @@ -279,66 +267,61 @@ IndexedDirectProductOrderedAbelianMonoidSup(A:OrderedAbelianMonoidSup,S:OrderedS ++ generators indexed by the ordered set S. ++ All items have finite support: only non-zero terms are stored. IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedSet): - Join(AbelianGroup,IndexedDirectProductCategory(A,S)) + Join(AbelianGroup,IndexedDirectProductCategory(A,S)) with + construct: List Pair(A,S) -> % + ++ \spad{construct l} returns an object that is a linear + ++ combination with support in \spad{A} and coefficients + ++ in \spad{A}. == IndexedDirectProductAbelianMonoid(A,S) add --representations - Term:= Record(k:S,c:A) - Rep:= List Term - x,y: % - r: A - n: Integer - f: A -> A - s: S - -x == [[u.k,-u.c] for u in x] - n * x == - n = 0 => 0 - n = 1 => x - [[u.k,a] for u in x | (a:=n*u.c) ~= 0$A] + Term == Pair(S,A) + termIndex(t: Term): S == first t + termValue(t: Term): A == second t - qsetrest!: (Rep, Rep) -> Rep - qsetrest!(l: Rep, e: Rep): Rep == RPLACD(l, e)$Lisp + -x == [[termIndex u,-termValue u] for u in terms x] pretend % + n:Integer * x:% == + n = 0 => 0 + n = 1 => x + [[termIndex u,a] for u in terms x + | not zero?(a := n * termValue u)] pretend % - x - y == - null x => -y - null y => x - endcell: Rep := empty() - res: Rep := empty() - while not empty? x and not empty? y repeat - newcell := empty() - if x.first.k = y.first.k then - r:= x.first.c - y.first.c - if not zero? r then - newcell := cons([x.first.k, r], empty()) - x := rest x - y := rest y - else if x.first.k > y.first.k then - newcell := cons(x.first, empty()) - x := rest x - else - newcell := cons([y.first.k,-y.first.c], empty()) - y := rest y - if not empty? newcell then - if not empty? endcell then - qsetrest!(endcell, newcell) - endcell := newcell - else - res := newcell; - endcell := res - end := - empty? x => - y - x - if empty? res then res := end - else qsetrest!(endcell, end) - res + qsetrest!: (List Term, List Term) -> List Term + qsetrest!(l, e) == RPLACD(l, e)$Lisp --- x - y == --- empty? x => - y --- empty? y => x --- y.first.k > x.first.k => cons([y.first.k,-y.first.c],(x - y.rest)) --- x.first.k > y.first.k => cons(x.first,(x.rest - y)) --- r:= x.first.c - y.first.c --- r = 0 => x.rest - y.rest --- cons([x.first.k,r],(x.rest - y.rest)) + x - y == + x' := terms x + y' := terms y + null x' => -y + null y' => x + endcell: List Term := nil + res: List Term := nil + while not empty? x' and not empty? y' repeat + newcell: List Term := nil + if termIndex x'.first = termIndex y'.first then + r := termValue x'.first - termValue y'.first + if not zero? r then + newcell := cons([termIndex x'.first, r], empty()) + x' := rest x' + y' := rest y' + else if termIndex x'.first > termIndex y'.first then + newcell := cons(x'.first, empty()) + x' := rest x' + else + newcell := cons([termIndex y'.first,-termValue y'.first], empty()) + y' := rest y' + if not empty? newcell then + if not empty? endcell then + qsetrest!(endcell, newcell) + endcell := newcell + else + res := newcell; + endcell := res + end := + empty? x' => terms(-(y' pretend %)) + x' + if empty? res then res := end + else qsetrest!(endcell, end) + res pretend % @ \section{License} diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 8e8a7036..661fe5d0 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2294130 . 3486833881) +(2293931 . 3486841615) (-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."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(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| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(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| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(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| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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}."))) @@ -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(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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(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| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4462 . T) (-4460 . T) (-4459 . T) ((-4467 "*") . T) (-4458 . T) (-4463 . T) (-4457 . T)) +((-4461 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4457 . T) (-4462 . T) (-4456 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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."))) @@ -56,14 +56,14 @@ 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 -1962) +(-32 R -1963) ((|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 -1059) (QUOTE (-576))))) (-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 -4465))) +((|HasAttribute| |#1| (QUOTE -4464))) (-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."))) NIL @@ -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}."))) -((-4465 . T) (-4466 . T)) +((-4464 . T) (-4465 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-39 UP) ((|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 -1962 UP UPUP -1633) +(-40 -1963 UP UPUP -3125) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4458 |has| (-419 |#2|) (-374)) (-4463 |has| (-419 |#2|) (-374)) (-4457 |has| (-419 |#2|) (-374)) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2760 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2760 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2760 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2760 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2760 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2760 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-41 R -1962) +((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2759 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2759 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2759 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2759 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2759 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2759 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +(-41 R -1963) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-317)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4462 |has| |#1| (-568)) (-4460 . T) (-4459 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-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."))) -((-4465 . T) (-4466 . T)) -((-2760 (-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|))))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-861))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|))))))) +((-4464 . T) (-4465 . T)) +((-2759 (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|))))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-861))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4462 . T)) +((-4461 . 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}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1962) +(-54 |Base| R -1963) ((|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 @@ -158,7 +158,7 @@ NIL NIL (-57 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"))) -((-4465 . T) (-4466 . T)) +((-4464 . T) (-4465 . T)) NIL (-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),...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -2629) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2628) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2629) +(-62 -2628) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2629) +(-63 -2628) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2629) +(-64 -2628) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2629) +(-65 -2628) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -2629) +(-66 -2628) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -2629) +(-67 -2628) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2629) +(-68 -2628) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -2629) +(-69 -2628) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -2629) +(-70 -2628) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -2629) +(-71 -2628) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -2629) +(-72 -2628) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -2629) +(-73 -2628) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -2629) +(-74 -2628) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2629) +(-77 -2628) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2629) +(-78 -2628) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2629) +(-79 -2628) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2629) +(-80 -2628) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2629) +(-81 -2628) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -2629) +(-82 -2628) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2629) +(-83 -2628) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2629) +(-84 -2628) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2629) +(-85 -2628) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2629) +(-86 -2628) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2629) +(-87 -2628) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2629) +(-88 -2628) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2629) +(-89 -2628) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-374)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4465 . T)) +((-4464 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4465 . T) ((-4467 "*") . T) (-4466 . T) (-4462 . T) (-4460 . T) (-4459 . T) (-4458 . T) (-4463 . T) (-4457 . T) (-4456 . T) (-4455 . T) (-4454 . T) (-4453 . T) (-4461 . T) (-4464 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4452 . T)) +((-4464 . T) ((-4466 "*") . T) (-4465 . T) (-4461 . T) (-4459 . T) (-4458 . T) (-4457 . T) (-4462 . T) (-4456 . T) (-4455 . T) (-4454 . T) (-4453 . T) (-4452 . T) (-4460 . T) (-4463 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4451 . T)) NIL (-99 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4462 . T)) +((-4461 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4467 "*")))) +((|HasAttribute| |#1| (QUOTE (-4466 "*")))) (-105) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4465 . T)) +((-4464 . T)) NIL (-106 A 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| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\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."))) @@ -358,23 +358,23 @@ NIL NIL (-107 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."))) -((-4466 . T)) +((-4465 . T)) NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2760 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2759 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-861))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-112) (QUOTE (-102)))) (-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}"))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -392,22 +392,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1962 UP) +(-116 -1963 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 (-117 |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 -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-118 |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}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-928))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1043))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-861))) (-2760 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-861)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1173))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-928)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-117 |#1|) (QUOTE (-928))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1043))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-861))) (-2759 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-861)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1173))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-928)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4466))) +((|HasAttribute| |#1| (QUOTE -4465))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -418,15 +418,15 @@ NIL NIL (-122 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"))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -434,20 +434,20 @@ NIL NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4465 . T) (-4466 . T)) +((-4464 . T) (-4465 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-128 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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2760 (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-130) (QUOTE (-861))) (-2760 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2759 (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-130) (QUOTE (-861))) (-2759 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -470,13 +470,13 @@ NIL NIL (-135) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4467 "*") . T)) +(((-4466 "*") . T)) NIL -(-136 |minix| -2706 S T$) +(-136 |minix| -2705 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2706 R) +(-137 |minix| -2705 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -498,8 +498,8 @@ NIL NIL (-142) ((|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}."))) -((-4465 . T) (-4455 . T) (-4466 . T)) -((-2760 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4464 . T) (-4454 . T) (-4465 . T)) +((-2759 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-143 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{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{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 @@ -514,7 +514,7 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4462 . T)) +((-4461 . T)) NIL (-147 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -522,9 +522,9 @@ NIL NIL (-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4462 . T)) +((-4461 . T)) NIL -(-149 -1962 UP UPUP) +(-149 -1963 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 @@ -535,14 +535,14 @@ NIL (-151 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 -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasAttribute| |#1| (QUOTE -4465))) +((|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasAttribute| |#1| (QUOTE -4464))) (-152 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."))) NIL NIL (-153 |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."))) -((-4460 . T) (-4459 . T) (-4462 . T)) +((-4459 . T) (-4458 . T) (-4461 . T)) NIL (-154) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -564,7 +564,7 @@ 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 -(-159 R -1962) +(-159 R -1963) ((|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 @@ -595,10 +595,10 @@ NIL (-166 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 (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4461)) (|HasAttribute| |#2| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasAttribute| |#2| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4458 -2760 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-928)))) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4461 |has| |#1| (-6 -4461)) (-4464 |has| |#1| (-6 -4464)) (-4178 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 -2759 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-928)))) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4463 |has| |#1| (-6 -4463)) (-4177 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-168 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4458 -2760 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-928)))) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4461 |has| |#1| (-6 -4461)) (-4464 |has| |#1| (-6 -4464)) (-4178 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2760 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-928))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-928)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-928))))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-2760 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasAttribute| |#1| (QUOTE -4464)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-360))))) +((-4457 -2759 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-928)))) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4463 |has| |#1| (-6 -4463)) (-4177 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2759 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-928))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-928)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-928))))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-2759 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4463)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-360))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -626,7 +626,7 @@ NIL NIL (-174) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-175) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -634,7 +634,7 @@ NIL NIL (-176 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4467 "*") . T) (-4458 . T) (-4463 . T) (-4457 . T) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") . T) (-4457 . T) (-4462 . T) (-4456 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-177) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1962) +(-190 R -1963) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1962 UP UPUP R) +(-217 -1963 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 -(-218 -1962 FP) +(-218 -1963 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 (-219) ((|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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2760 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2759 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-220) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1962) +(-221 R -1963) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -826,19 +826,19 @@ NIL NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-225 |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}."))) -((-4462 . T)) +((-4461 . T)) NIL -(-226 R -1962) +(-226 R -1963) ((|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 (-227) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4166 . T) (-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4165 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -846,19 +846,19 @@ NIL NIL (-229 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}"))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4467 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-230 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 (-231 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."))) -((-4466 . T)) +((-4465 . T)) NIL (-232 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-4462 . T)) +((-4461 . T)) NIL (-233 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -870,7 +870,7 @@ NIL NIL (-235 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-236 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -882,36 +882,36 @@ NIL NIL (-238) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4462 . T)) +((-4461 . T)) NIL (-239 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\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}."))) NIL -((|HasAttribute| |#1| (QUOTE -4465))) +((|HasAttribute| |#1| (QUOTE -4464))) (-240 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}."))) -((-4466 . T)) +((-4465 . T)) NIL (-241) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-242 S -2706 R) +(-242 S -2705 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4462)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (QUOTE (-1121)))) -(-243 -2706 R) +((|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4461)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (QUOTE (-1121)))) +(-243 -2705 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4459 |has| |#2| (-1070)) (-4460 |has| |#2| (-1070)) (-4462 |has| |#2| (-6 -4462)) (-4465 . T)) +((-4458 |has| |#2| (-1070)) (-4459 |has| |#2| (-1070)) (-4461 |has| |#2| (-6 -4461)) (-4464 . T)) NIL -(-244 -2706 A B) +(-244 -2705 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-245 -2706 R) +(-245 -2705 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."))) -((-4459 |has| |#2| (-1070)) (-4460 |has| |#2| (-1070)) (-4462 |has| |#2| (-6 -4462)) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST 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(-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasAttribute| |#2| (QUOTE -4461)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1070)))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197))))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))))) (-246) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -922,7 +922,7 @@ NIL NIL (-248) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4458 . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-249 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\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."))) @@ -930,20 +930,20 @@ NIL NIL (-250 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}"))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-251 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-252 R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-253 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4467 "*") |has| |#2| (-174)) (-4458 |has| |#2| (-568)) (-4463 |has| |#2| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#2| (QUOTE (-928))) (-2760 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2760 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (-2759 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2759 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) (-254) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) NIL @@ -958,23 +958,23 @@ NIL NIL (-257 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4462 -2760 (-2675 (|has| |#4| (-1070)) (|has| |#4| (-238))) (|has| |#4| (-6 -4462)) (-2675 (|has| |#4| (-1070)) (|has| |#4| (-917 (-1197))))) (-4459 |has| |#4| (-1070)) (-4460 |has| |#4| (-1070)) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-238))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-738))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-805))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-861))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1070))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST 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(QUOTE (-576)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1121)))) (-2759 (|HasAttribute| |#3| (QUOTE -4461)) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (LIST (QUOTE -917) (QUOTE (-1197)))))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (LIST (QUOTE -919) (QUOTE (-1197))))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (-259 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-238)))) (-260 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."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-261 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}."))) -((-4465 . T) (-4466 . T)) +((-4464 . T) (-4465 . T)) NIL (-262) ((|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."))) @@ -1022,8 +1022,8 @@ NIL NIL (-273 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"))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-928))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#3| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#3| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#3| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#3| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#3| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#3| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-274 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}.")) (|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 @@ -1068,11 +1068,11 @@ 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 -(-285 R -1962) +(-285 R -1963) ((|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{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 -(-286 R -1962) +(-286 R -1963) ((|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{ki} was rewritten as \\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 @@ -1098,7 +1098,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121)))) (-292 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}."))) -((-4466 . T)) +((-4465 . T)) NIL (-293 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}."))) @@ -1119,18 +1119,18 @@ NIL (-297 S |Dom| |Im|) ((|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!| ((|#3| $ |#2| |#3|) "\\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| ((|#3| $ |#2| |#3|) "\\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| ((|#3| $ |#2|) "\\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| ((|#3| $ |#2| |#3|) "\\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 -((|HasAttribute| |#1| (QUOTE -4466))) +((|HasAttribute| |#1| (QUOTE -4465))) (-298 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-299 S R |Mod| -1765 -3391 |exactQuo|) +(-299 S R |Mod| -1892 -2185 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-300) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4458 . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-301) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1146,21 +1146,21 @@ NIL NIL (-304 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."))) -((-4462 -2760 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4459 |has| |#1| (-1070)) (-4460 |has| |#1| (-1070))) -((|HasCategory| |#1| (QUOTE (-374))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2760 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738)))) (|HasCategory| |#1| (QUOTE (-485))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-312))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485)))) (-2760 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738)))) (-2760 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-738)))) +((-4461 -2759 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4458 |has| |#1| (-1070)) (-4459 |has| |#1| (-1070))) +((|HasCategory| |#1| (QUOTE (-374))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2759 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738)))) (|HasCategory| |#1| (QUOTE (-485))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-312))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-485)))) (-2759 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738)))) (-2759 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-738)))) (-305 |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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|)))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102)))) (-306) ((|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 -(-307 -1962 S) +(-307 -1963 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 -(-308 E -1962) +(-308 E -1963) ((|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 @@ -1198,7 +1198,7 @@ NIL NIL (-317) ((|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 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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-318 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1208,7 +1208,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-320 -1962) +(-320 -1963) ((|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 @@ -1222,8 +1222,8 @@ NIL NIL (-323 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))}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-1043))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-861))) (-2760 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-861)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-1173))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (-12 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| $ (QUOTE (-146)))) (-2760 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| $ (QUOTE (-146)))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-1043))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-861))) (-2759 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-861)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-1173))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (-12 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| $ (QUOTE (-146)))) (-2759 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| $ (QUOTE (-146)))))) (-324 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 @@ -1234,9 +1234,9 @@ NIL NIL (-326 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."))) -((-4462 -2760 (-12 (|has| |#1| (-568)) (-2760 (|has| |#1| (-1070)) (|has| |#1| (-485)))) (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4460 |has| |#1| (-174)) (-4459 |has| |#1| (-174)) ((-4467 "*") |has| |#1| (-568)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-568)) (-4457 |has| |#1| (-568))) -((-2760 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-568))) (-2760 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-21))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-1070))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2760 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-2760 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2760 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2760 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568)))) (-2760 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-2760 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2760 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2760 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2760 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2760 (-12 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) -(-327 R -1962) +((-4461 -2759 (-12 (|has| |#1| (-568)) (-2759 (|has| |#1| (-1070)) (|has| |#1| (-485)))) (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) ((-4466 "*") |has| |#1| (-568)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-568)) (-4456 |has| |#1| (-568))) +((-2759 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-568))) (-2759 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-21))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-1070))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2759 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-2759 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2759 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2759 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568)))) (-2759 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-2759 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2759 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2759 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2759 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2759 (-12 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) +(-327 R -1963) ((|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{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + 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 @@ -1246,8 +1246,8 @@ NIL NIL (-329 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3570) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2760 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1491) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2759 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4160) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-330 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 @@ -1258,7 +1258,7 @@ NIL NIL (-332 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-576) (QUOTE (-804)))) (-333 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * 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| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1274,19 +1274,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) (-336 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-337 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."))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-338 S -1962) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-338 S -1963) ((|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 (-379)))) -(-339 -1962) +(-339 -1963) ((|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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-340) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1308,15 +1308,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-345 S -1962 UP UPUP R) +(-345 S -1963 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 -(-346 -1962 UP UPUP R) +(-346 -1963 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 -(-347 -1962 UP UPUP R) +(-347 -1963 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 @@ -1330,32 +1330,32 @@ NIL NIL (-350 |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{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.}"))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-351 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 -(-352 S -1962 UP UPUP) +(-352 S -1963 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(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 (-379))) (|HasCategory| |#2| (QUOTE (-374)))) -(-353 -1962 UP UPUP) +(-353 -1963 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(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."))) -((-4458 |has| (-419 |#2|) (-374)) (-4463 |has| (-419 |#2|) (-374)) (-4457 |has| (-419 |#2|) (-374)) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-354 |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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-355 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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-356 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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-357 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 @@ -1370,33 +1370,33 @@ NIL NIL (-360) ((|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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-361 R UP -1962) +(-361 R UP -1963) ((|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{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{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{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{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{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{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-362 |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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-363 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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-364 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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 |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}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-366 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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) -(-367 -1962 GF) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +(-367 -1963 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 @@ -1404,21 +1404,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-369 -1962 FP FPP) +(-369 -1963 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 fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-370 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}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-371 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 NIL (-372 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\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| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4462 . T)) +((-4461 . T)) NIL (-373 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1426,7 +1426,7 @@ NIL NIL (-374) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-375 |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."))) @@ -1442,7 +1442,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-568)))) (-378 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{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{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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4462 |has| |#1| (-568)) (-4460 . T) (-4459 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) NIL (-379) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1454,7 +1454,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-374)))) (-381 R UP) ((|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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-382 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1463,14 +1463,14 @@ NIL (-383 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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4466)) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121)))) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121)))) (-384 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4465 . T)) +((-4464 . T)) NIL (-385 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4460 . T) (-4459 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) NIL (-386 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1490,7 +1490,7 @@ NIL NIL (-390) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4448 . T) (-4456 . T) (-4166 . T) (-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4447 . T) (-4455 . T) (-4165 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-391 |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}."))) @@ -1498,11 +1498,11 @@ NIL NIL (-392 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}"))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-393 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}."))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-394) ((|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}."))) @@ -1514,7 +1514,7 @@ NIL NIL (-396 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-397 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1526,7 +1526,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-861)))) (-399) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-400) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1538,13 +1538,13 @@ NIL NIL (-402 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-403) ((|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 -(-404 -1962 UP UPUP R) +(-404 -1963 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 @@ -1568,11 +1568,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-410 -2629 |returnType| -1927 |symbols|) +(-410 -2628 |returnType| -1930 |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 -(-411 -1962 UP) +(-411 -1963 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 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.}")) (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1586,15 +1586,15 @@ NIL NIL (-414) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-415 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#1| (QUOTE -4456))) +((|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#1| (QUOTE -4455))) (-416) ((|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\"."))) -((-4166 . T) (-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4165 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-417 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."))) @@ -1606,15 +1606,15 @@ NIL NIL (-419 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."))) -((-4452 -12 (|has| |#1| (-6 -4463)) (|has| |#1| (-464)) (|has| |#1| (-6 -4452))) (-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-861)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4463)) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4451 -12 (|has| |#1| (-6 -4462)) (|has| |#1| (-464)) (|has| |#1| (-6 -4451))) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-861)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4451)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-420 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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 (-421 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-422 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1628,11 +1628,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-425 R -1962 UP A) +(-425 R -1963 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4462 . T)) +((-4461 . T)) NIL -(-426 R -1962 UP A |ibasis|) +(-426 R -1963 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1059) (|devaluate| |#2|)))) @@ -1646,12 +1646,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-429 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is 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{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."))) -((-4462 |has| |#1| (-568)) (-4460 . T) (-4459 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) NIL (-430 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."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1242))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1242)))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1242))) (-2759 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1242)))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) (-431 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 @@ -1678,17 +1678,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-379)))) (-437 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4465 . T) (-4455 . T) (-4466 . T)) +((-4464 . T) (-4454 . T) (-4465 . T)) NIL -(-438 R -1962) +(-438 R -1963) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-439 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4452 -12 (|has| |#1| (-6 -4452)) (|has| |#2| (-6 -4452))) (-4459 . T) (-4460 . T) (-4462 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4452)) (|HasAttribute| |#2| (QUOTE -4452)))) -(-440 R -1962) +((-4451 -12 (|has| |#1| (-6 -4451)) (|has| |#2| (-6 -4451))) (-4458 . T) (-4459 . T) (-4461 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4451)) (|HasAttribute| |#2| (QUOTE -4451)))) +(-440 R -1963) ((|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 @@ -1698,17 +1698,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-442 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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}."))) -((-4462 -2760 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4460 |has| |#1| (-174)) (-4459 |has| |#1| (-174)) ((-4467 "*") |has| |#1| (-568)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-568)) (-4457 |has| |#1| (-568))) +((-4461 -2759 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) ((-4466 "*") |has| |#1| (-568)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-568)) (-4456 |has| |#1| (-568))) NIL -(-443 R -1962) +(-443 R -1963) ((|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 -(-444 R -1962) +(-444 R -1963) ((|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{ai = 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{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-445 R -1962) +(-445 R -1963) ((|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 @@ -1716,7 +1716,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-447 R -1962 UP) +(-447 R -1963 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 -1059) (QUOTE (-48))))) @@ -1748,7 +1748,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-455 R UP -1962) +(-455 R UP -1963) ((|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 @@ -1786,16 +1786,16 @@ NIL NIL (-464) ((|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}."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-465 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"))) -((-4462 |has| (-419 (-971 |#1|)) (-568)) (-4460 . T) (-4459 . T)) +((-4461 |has| (-419 (-971 |#1|)) (-568)) (-4459 . T) (-4458 . T)) ((|HasCategory| (-419 (-971 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-971 |#1|)) (QUOTE (-568)))) (-466 |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"))) -(((-4467 "*") |has| |#2| (-174)) (-4458 |has| |#2| (-568)) (-4463 |has| |#2| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#2| (QUOTE (-928))) (-2760 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2760 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (-2759 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2759 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) (-467 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 @@ -1822,7 +1822,7 @@ NIL NIL (-473 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-474 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1830,7 +1830,7 @@ NIL NIL (-475 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-476 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}."))) @@ -1860,7 +1860,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -1962 R) +(-483 |lv| -1963 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1870,23 +1870,23 @@ NIL NIL (-485) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4462 . T)) +((-4461 . T)) NIL (-486 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3570) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2760 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1491) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2759 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4160) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-487 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4466 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121)))) +((-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|)))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121)))) (-488 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)}"))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-489) ((|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{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-490) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1894,29 +1894,29 @@ NIL NIL (-491 |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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|)))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102)))) (-492) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-493 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2759 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-500 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4465)) (|HasAttribute| |#1| (QUOTE -4466)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) +((|HasAttribute| |#1| (QUOTE -4464)) (|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-501 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,33 +1952,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -1962 UP |AlExt| |AlPol|) +(-506 -1963 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-507) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-508 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-509 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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-510 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 -(-511 R UP -1962) +(-511 R UP -1963) ((|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{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\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{mi} is given by \\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{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{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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-512 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-861))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-112) (QUOTE (-102)))) (-513 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)}."))) @@ -1992,7 +1992,7 @@ 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{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{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 -(-516 -1962 |Expon| |VarSet| |DPoly|) +(-516 -1963 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1197))))) @@ -2005,11 +2005,11 @@ NIL NIL NIL (-519 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored.")) (|construct| (($ (|List| (|Pair| |#1| |#2|))) "\\spad{construct l} returns an object that is a linear combination with support in \\spad{A} and coefficients in \\spad{A}."))) NIL NIL (-520 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored.")) (|construct| (($ (|List| (|Pair| |#1| |#2|))) "\\spad{l} returns an IndexedDirectProductAbelianMonoid object with support and value as specified in the list of pairs \\spad{l}."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) NIL NIL (-521 A S) @@ -2025,7 +2025,7 @@ NIL NIL NIL (-524 A S) -((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|indexedDirectProductObject| (($ (|List| (|Pair| |#2| |#1|))) "\\spad{indexedDirectProductObject l} constructs an indexed direct product object with support-value pairs given in \\spad{l}."))) +((|constructor| (NIL "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 (-525 S A B) @@ -2042,36 +2042,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-804)))) (-528 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}"))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-529) ((|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 NIL (-530 |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}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((-2760 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2759 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) (-531 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}."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-532 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."))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-533 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 -((|HasAttribute| |#3| (QUOTE -4466))) +((|HasAttribute| |#3| (QUOTE -4465))) (-534 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "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. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4466))) +((|HasAttribute| |#7| (QUOTE -4465))) (-535 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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4467 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-536) ((|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 @@ -2104,7 +2104,7 @@ 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 -(-544 K -1962 |Par|) +(-544 K -1963 |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 @@ -2128,7 +2128,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-550 K -1962 |Par|) +(-550 K -1963 |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 @@ -2158,7 +2158,7 @@ NIL NIL (-557) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) -((-4463 . T) (-4464 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-558) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2178,13 +2178,13 @@ NIL NIL (-562 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#2|)))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2760 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (QUOTE (-102)))) -(-563 R -1962) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|)))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102)))) +(-563 R -1963) ((|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 -(-564 R0 -1962 UP UPUP R) +(-564 R0 -1963 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 @@ -2194,7 +2194,7 @@ NIL NIL (-566 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."))) -((-4166 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4165 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-567 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."))) @@ -2202,9 +2202,9 @@ NIL NIL (-568) ((|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."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-569 R -1962) +(-569 R -1963) ((|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,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2216,7 +2216,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-572 R -1962 L) +(-572 R -1963 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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) @@ -2224,31 +2224,31 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-574 -1962 UP UPUP R) +(-574 -1963 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 -(-575 -1962 UP) +(-575 -1963 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 (-576) ((|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."))) -((-4447 . T) (-4453 . T) (-4457 . T) (-4452 . T) (-4463 . T) (-4464 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4446 . T) (-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-577) ((|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 -(-578 R -1962 L) +(-578 R -1963 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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(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 -668) (|devaluate| |#2|)))) -(-579 R -1962) +(-579 R -1963) ((|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 -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1160)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) -(-580 -1962 UP) +(-580 -1963 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,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(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 @@ -2256,27 +2256,27 @@ 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 -(-582 -1962) +(-582 -1963) ((|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, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(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 (-583 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."))) -((-4166 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4165 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-584) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-585 R -1962) +(-585 R -1963) ((|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 -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) -(-586 -1962 UP) +(-586 -1963 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' + +/[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(+,[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(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-587 R -1962) +(-587 R -1963) ((|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 @@ -2298,21 +2298,21 @@ NIL NIL (-592 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-593 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) (-594) ((|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 -(-595 R -1962) +(-595 R -1963) ((|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 -(-596 E -1962) +(-596 E -1963) ((|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 @@ -2320,9 +2320,9 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-598 -1962) +(-598 -1963) ((|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}."))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-1197))))) (-599 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"))) @@ -2350,19 +2350,19 @@ NIL NIL (-605 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2760 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-145) (QUOTE (-861))) (-2760 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2759 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-145) (QUOTE (-861))) (-2759 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-606 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 (-607 |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}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3570) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) (-608 |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}.")) (|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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4467 "*") |has| |#1| (-568)) (-4458 |has| |#1| (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-568)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-568)))) (-609) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2376,7 +2376,7 @@ 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 -(-612 R -1962 FG) +(-612 R -1963 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{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{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 @@ -2386,12 +2386,12 @@ NIL NIL (-614 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-615 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 -4466)) (|HasCategory| |#2| (QUOTE (-861))) (|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#3| (QUOTE (-1121)))) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-861))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#3| (QUOTE (-1121)))) (-616 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2406,19 +2406,19 @@ NIL NIL (-619 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4462 -2760 (-2675 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4460 . T) (-4459 . T)) -((-2760 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4461 -2759 (-2674 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4459 . T) (-4458 . T)) +((-2759 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-620 |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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4440) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-1179) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|)) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-1179) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|)) (QUOTE (-102)))) (-621 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 (-622 |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}."))) -((-4466 . T)) +((-4465 . T)) NIL (-623 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"))) @@ -2436,7 +2436,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-627 -1962 UP) +(-627 -1963 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2458,19 +2458,19 @@ NIL NIL (-632 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."))) -((-4462 . T)) +((-4461 . T)) NIL (-633 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}."))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-860)))) -(-634 R -1962) +(-634 R -1963) ((|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 (-635 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"))) -((-4460 . T) (-4459 . T) ((-4467 "*") . T) (-4458 . T) (-4462 . T)) +((-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4457 . T) (-4461 . T)) ((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-636 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."))) @@ -2486,7 +2486,7 @@ NIL NIL (-639 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4462 . T)) +((-4461 . T)) NIL (-640 R |ls|) ((|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}}."))) @@ -2496,30 +2496,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-642 R -1962) +(-642 R -1963) ((|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{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\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 -(-643 |lv| -1962) +(-643 |lv| -1963) ((|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 (-644) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4466 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1179) (QUOTE (-861))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (QUOTE (-1121)))) +((-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4439) (QUOTE (-52))))))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1179) (QUOTE (-861))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (QUOTE (-1121)))) (-645 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-646 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4460 . T) (-4459 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) NIL (-647 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4462 -2760 (-2675 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4460 . T) (-4459 . T)) -((-2760 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4461 -2759 (-2674 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4459 . T) (-4458 . T)) +((-2759 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-648 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2554,8 +2554,8 @@ NIL NIL (-656 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} is the empty list."))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-657 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2566,8 +2566,8 @@ NIL NIL (-659 S) ((|substitute| (($ |#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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-660 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2579,22 +2579,22 @@ NIL (-662 A 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| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\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}..) )}.") (($ |#2| $ (|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,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\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|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4466))) +((|HasAttribute| |#1| (QUOTE -4465))) (-663 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,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-664 R -1962 L) +(-664 R -1963 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 (-665 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}}"))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-666 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-667 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2602,15 +2602,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-668 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}."))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-669 -1962 UP) +(-669 -1963 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)))) -(-670 A -3850) +(-670 A -4337) ((|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}}"))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-671 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."))) @@ -2626,7 +2626,7 @@ NIL NIL (-674 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}."))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-803)))) (-675 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 fi = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2634,7 +2634,7 @@ NIL NIL (-676 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4460 . T) (-4459 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-174)))) (-677 A 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| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) @@ -2642,13 +2642,13 @@ NIL NIL (-678 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}."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL -(-679 -1962) +(-679 -1963) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-680 -1962 |Row| |Col| M) +(-680 -1963 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2658,8 +2658,8 @@ NIL NIL (-682 |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."))) -((-4462 . T) (-4465 . T) (-4459 . T) (-4460 . T)) -((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4467 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2760 (|HasAttribute| |#2| (QUOTE (-4467 "*"))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4461 . T) (-4464 . T) (-4458 . T) (-4459 . T)) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2759 (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-683) ((|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 @@ -2679,7 +2679,7 @@ NIL (-687 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 -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-688) ((|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 @@ -2723,10 +2723,10 @@ NIL (-698 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|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 (-4467 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) +((|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) (-699 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|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"))) -((-4465 . T) (-4466 . T)) +((-4464 . T) (-4465 . T)) NIL (-700 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."))) @@ -2734,8 +2734,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568)))) (-701 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."))) -((-4465 . T) (-4466 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4467 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4464 . T) (-4465 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-702 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 @@ -2744,7 +2744,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-704 S -1962 FLAF FLAS) +(-704 S -1963 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 @@ -2754,11 +2754,11 @@ NIL NIL (-706) ((|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"))) -((-4458 . T) (-4463 |has| (-711) (-374)) (-4457 |has| (-711) (-374)) (-4178 . T) (-4464 |has| (-711) (-6 -4464)) (-4461 |has| (-711) (-6 -4461)) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-2760 (|HasCategory| (-711) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-2760 (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197))))) (-2760 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (-2760 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1043))) (|HasCategory| (-711) (QUOTE (-1223))) (-12 (|HasCategory| (-711) (QUOTE (-1023))) (|HasCategory| (-711) (QUOTE (-1223)))) (-2760 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-928))))) (-2760 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-928)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-928))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1081))) (|HasCategory| (-711) (QUOTE (-1223)))) (|HasCategory| (-711) (QUOTE (-1081))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928))) (-2760 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-374)))) (-2760 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-2760 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4464)) (|HasAttribute| (-711) (QUOTE -4461)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-146)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-360))))) +((-4457 . T) (-4462 |has| (-711) (-374)) (-4456 |has| (-711) (-374)) (-4177 . T) (-4463 |has| (-711) (-6 -4463)) (-4460 |has| (-711) (-6 -4460)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-2759 (|HasCategory| (-711) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-2759 (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197))))) (-2759 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (-2759 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1043))) (|HasCategory| (-711) (QUOTE (-1223))) (-12 (|HasCategory| (-711) (QUOTE (-1023))) (|HasCategory| (-711) (QUOTE (-1223)))) (-2759 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-928))))) (-2759 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-928)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-928))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1081))) (|HasCategory| (-711) (QUOTE (-1223)))) (|HasCategory| (-711) (QUOTE (-1081))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928))) (-2759 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-374)))) (-2759 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-2759 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4463)) (|HasAttribute| (-711) (QUOTE -4460)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-146)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-360))))) (-707 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}."))) -((-4466 . T)) +((-4465 . T)) NIL (-708 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}."))) @@ -2768,13 +2768,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-710 OV E -1962 PG) +(-710 OV E -1963 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 (-711) ((|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}"))) -((-4166 . T) (-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4165 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-712 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."))) @@ -2782,7 +2782,7 @@ NIL NIL (-713) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4464 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4463 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-714 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2810,7 +2810,7 @@ NIL NIL (-720 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#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)}.}"))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-721 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2820,25 +2820,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-723 R |Mod| -1765 -3391 |exactQuo|) +(-723 R |Mod| -1892 -2185 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-724 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-725 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-726 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4460 |has| |#1| (-174)) (-4459 |has| |#1| (-174)) (-4462 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-727 R |Mod| -1765 -3391 |exactQuo|) +(-727 R |Mod| -1892 -2185 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4462 . T)) +((-4461 . T)) NIL (-728 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2846,11 +2846,11 @@ NIL NIL (-729 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL -(-730 -1962) +(-730 -1963) ((|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]]}."))) -((-4462 . T)) +((-4461 . T)) NIL (-731 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2874,7 +2874,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-360))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-379)))) (-736 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."))) -((-4458 |has| |#1| (-374)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 |has| |#1| (-374)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-737 S) ((|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."))) @@ -2884,7 +2884,7 @@ 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 -(-739 -1962 UP) +(-739 -1963 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 @@ -2902,8 +2902,8 @@ NIL NIL (-743 |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."))) -(((-4467 "*") |has| |#2| (-174)) (-4458 |has| |#2| (-568)) (-4463 |has| |#2| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#2| (QUOTE (-928))) (-2760 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2760 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (-2759 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2759 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) (-744 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2918,15 +2918,15 @@ NIL NIL (-747 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4460 |has| |#1| (-174)) (-4459 |has| |#1| (-174)) (-4462 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-861)))) (-748 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4455 . T) (-4466 . T)) +((-4454 . T) (-4465 . T)) NIL (-749 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}."))) -((-4465 . T) (-4455 . T) (-4466 . T)) +((-4464 . T) (-4454 . T) (-4465 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-750) ((|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."))) @@ -2938,7 +2938,7 @@ NIL NIL (-752 |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}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4460 . T) (-4459 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-753 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"))) @@ -2954,7 +2954,7 @@ NIL NIL (-756 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-757) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -3036,11 +3036,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-777 -1962) +(-777 -1963) ((|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 -(-778 P -1962) +(-778 P -1963) ((|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 @@ -3048,7 +3048,7 @@ NIL NIL NIL NIL -(-780 UP -1962) +(-780 UP -1963) ((|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{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{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{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{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{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{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 @@ -3062,9 +3062,9 @@ NIL NIL (-783) ((|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."))) -(((-4467 "*") . T)) +(((-4466 "*") . T)) NIL -(-784 R -1962) +(-784 R -1963) ((|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 @@ -3084,7 +3084,7 @@ 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 -(-789 -1962 |ExtF| |SUEx| |ExtP| |n|) +(-789 -1963 |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 @@ -3098,23 +3098,23 @@ NIL NIL (-792 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."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . 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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 (-794 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)}"))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-795 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 -419) (QUOTE (-576)))))) (-796 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.}"))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-797 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}."))) @@ -3166,25 +3166,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-379)))) (-809 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,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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-810 -2760 R OS S) +(-810 -2759 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-811 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2760 (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2760 (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2759 (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2759 (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-812) ((|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 -(-813 R -1962 L) +(-813 R -1963 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{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-814 R -1962) +(-814 R -1963) ((|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."))) NIL NIL @@ -3192,7 +3192,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-816 R -1962) +(-816 R -1963) ((|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 @@ -3200,11 +3200,11 @@ 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 -(-818 -1962 UP UPUP R) +(-818 -1963 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 -(-819 -1962 UP L LQ) +(-819 -1963 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 @@ -3212,41 +3212,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-821 -1962 UP L LQ) +(-821 -1963 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^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{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{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 ai}} is \\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 -(-822 -1962 UP) +(-822 -1963 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-823 -1962 L UP A LO) +(-823 -1963 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 -(-824 -1962 UP) +(-824 -1963 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{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 ai}} is \\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)))) -(-825 -1962 LO) +(-825 -1963 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 -(-826 -1962 LODO) +(-826 -1963 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(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL -(-827 -2706 S |f|) +(-827 -2705 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}."))) -((-4459 |has| |#2| (-1070)) (-4460 |has| |#2| (-1070)) (-4462 |has| |#2| (-6 -4462)) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST 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T) (-4460 . T) (-4459 . T)) +(((-4466 "*") |has| |#2| (-374)) (-4457 |has| |#2| (-374)) (-4462 |has| |#2| (-374)) (-4456 |has| |#2| (-374)) (-4461 . T) (-4459 . T) (-4458 . T)) ((|HasCategory| |#2| (QUOTE (-374)))) (-830 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -3258,7 +3258,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-861)))) (-832) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-833) ((|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}"))) @@ -3286,7 +3286,7 @@ NIL NIL (-839 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}."))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-238)))) (-840) ((|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."))) @@ -3298,7 +3298,7 @@ NIL NIL (-842 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4465 . T) (-4455 . T) (-4466 . T)) +((-4464 . T) (-4454 . T) (-4465 . T)) NIL (-843) ((|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."))) @@ -3310,8 +3310,8 @@ NIL NIL (-845 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."))) -((-4462 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2760 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2760 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4461 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2759 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2759 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-846 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3322,7 +3322,7 @@ NIL NIL (-848 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4460 |has| |#1| (-174)) (-4459 |has| |#1| (-174)) (-4462 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) (-849) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3350,13 +3350,13 @@ NIL NIL (-855 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4462 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2760 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2760 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4461 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2759 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2759 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-856) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-857 -2706 S) +(-857 -2705 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3370,7 +3370,7 @@ NIL NIL (-860) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4462 . T)) +((-4461 . T)) NIL (-861) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) @@ -3394,19 +3394,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) (-866 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-867 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 (-374))) (|HasCategory| |#1| (QUOTE (-568)))) -(-868 R |sigma| -3643) +(-868 R |sigma| -3642) ((|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."))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) -(-869 |x| R |sigma| -3643) +(-869 |x| R |sigma| -3642) ((|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}."))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) (-870 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..)}."))) @@ -3450,7 +3450,7 @@ NIL NIL (-880 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4460 |has| |#1| (-174)) (-4459 |has| |#1| (-174)) (-4462 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (-881 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3462,24 +3462,24 @@ NIL NIL (-883 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-884 |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)."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-885 |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)."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-884 |#1|) (QUOTE (-928))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-148))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-884 |#1|) (QUOTE (-1043))) (|HasCategory| (-884 |#1|) (QUOTE (-832))) (|HasCategory| (-884 |#1|) (QUOTE (-861))) (-2760 (|HasCategory| (-884 |#1|) (QUOTE (-832))) (|HasCategory| (-884 |#1|) (QUOTE (-861)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (QUOTE (-1173))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (QUOTE (-237))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (QUOTE (-238))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -884) (|devaluate| |#1|)) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (QUOTE (-317))) (|HasCategory| (-884 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-928)))) (|HasCategory| (-884 |#1|) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-884 |#1|) (QUOTE (-928))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-148))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-884 |#1|) (QUOTE (-1043))) (|HasCategory| (-884 |#1|) (QUOTE (-832))) (|HasCategory| (-884 |#1|) (QUOTE (-861))) (-2759 (|HasCategory| (-884 |#1|) (QUOTE (-832))) (|HasCategory| (-884 |#1|) (QUOTE (-861)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (QUOTE (-1173))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (QUOTE (-237))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (QUOTE (-238))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -884) (|devaluate| |#1|)) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (QUOTE (-317))) (|HasCategory| (-884 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-928)))) (|HasCategory| (-884 |#1|) (QUOTE (-146))))) (-886 |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)}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861))) (-2760 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861))) (-2759 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) (-887 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 (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))))) (-888) ((|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 @@ -3580,7 +3580,7 @@ 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 -(-913 UP -1962) +(-913 UP -1963) ((|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 @@ -3594,11 +3594,11 @@ NIL NIL (-916 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-917 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4462 . T)) +((-4461 . T)) NIL (-918 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) @@ -3611,14 +3611,14 @@ NIL (-920 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-921 |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 (-922 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}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|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."))) -((-4462 . T)) +((-4461 . T)) NIL (-923 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}.")) (|support| (((|Set| |#1|) $) "\\spad{support(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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3626,8 +3626,8 @@ NIL NIL (-924 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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.")) (|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."))) -((-4462 . T)) -((-2760 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-861)))) +((-4461 . T)) +((-2759 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-861)))) (-925 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 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 @@ -3642,13 +3642,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-146)))) (-928) ((|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 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}."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-929 |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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) -(-930 R0 -1962 UP UPUP R) +(-930 R0 -1963 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 @@ -3662,7 +3662,7 @@ NIL NIL (-933 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-934 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) @@ -3676,7 +3676,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em 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(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em 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 ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,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(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,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 -(-937 -1962) +(-937 -1963) ((|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 @@ -3686,17 +3686,17 @@ NIL NIL (-939) ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-940) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4467 "*") . T)) +(((-4466 "*") . T)) NIL -(-941 -1962 P) +(-941 -1963 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-942 |xx| -1962) +(-942 |xx| -1963) ((|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 @@ -3720,7 +3720,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-948 R -1962) +(-948 R -1963) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3732,7 +3732,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-951 S R -1962) +(-951 S R -1963) ((|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 @@ -3752,7 +3752,7 @@ 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 -901) (|devaluate| |#1|)))) -(-956 R -1962 -2020) +(-956 R -1963 -2020) ((|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 @@ -3778,8 +3778,8 @@ NIL NIL (-962 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-963 |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 @@ -3799,12 +3799,12 @@ NIL (-967 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 (-928))) (|HasAttribute| |#2| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) +((|HasCategory| |#2| (QUOTE (-928))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-968 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}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-969 E V R P -1962) +(-969 E V R P -1963) ((|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 @@ -3814,9 +3814,9 @@ NIL NIL (-971 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}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-928))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-972 E V R P -1962) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-972 E V R P -1963) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-464)))) @@ -3838,13 +3838,13 @@ NIL NIL (-977 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"))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-978) ((|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 -(-979 -1962) +(-979 -1963) ((|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{ai = 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{ai = 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 @@ -3858,12 +3858,12 @@ NIL NIL (-982 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}"))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4463))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4462))) (-983 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"))) -((-4462 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) 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(|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) +((-4461 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-984) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3886,7 +3886,7 @@ NIL NIL (-989 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4465 . T) (-4466 . T)) +((-4464 . T) (-4465 . T)) NIL (-990 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}}"))) @@ -3906,7 +3906,7 @@ NIL NIL (-994 |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}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-995) ((|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}."))) @@ -3918,7 +3918,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-568)))) (-997 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."))) -((-4465 . T)) +((-4464 . T)) NIL (-998 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."))) @@ -3934,7 +3934,7 @@ NIL NIL (-1001 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")) (|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}."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-1002 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3952,7 +3952,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1006 K R UP -1962) +(-1006 K R UP -1963) ((|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{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{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\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{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{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -3982,7 +3982,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1173)))) (-1013 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}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1014 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|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}."))) @@ -3994,7 +3994,7 @@ NIL NIL (-1016 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."))) -((-4465 . T) (-4466 . T)) +((-4464 . T) (-4465 . T)) NIL (-1017 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}."))) @@ -4002,7 +4002,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-300)))) (-1018 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}."))) -((-4458 |has| |#1| (-300)) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 |has| |#1| (-300)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1019 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}."))) @@ -4010,12 +4010,12 @@ NIL NIL (-1020 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.}"))) -((-4458 |has| |#1| (-300)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2760 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4457 |has| |#1| (-300)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2759 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557)))) (-1021 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}."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1022 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4024,14 +4024,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1024 -1962 UP UPUP |radicnd| |n|) +(-1024 -1963 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4458 |has| (-419 |#2|) (-374)) (-4463 |has| (-419 |#2|) (-374)) (-4457 |has| (-419 |#2|) (-374)) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2760 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2760 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2760 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2760 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2760 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2760 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2759 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2759 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2759 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2759 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2759 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2759 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (-1025 |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."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2760 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2759 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-1026) ((|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 @@ -4051,7 +4051,7 @@ NIL (-1030 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 -4466)) (|HasCategory| |#2| (QUOTE (-1121)))) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-1121)))) (-1031 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}."))) NIL @@ -4062,21 +4062,21 @@ NIL NIL (-1033) ((|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}}"))) -((-4458 . T) (-4463 . T) (-4457 . T) (-4460 . T) (-4459 . T) ((-4467 "*") . T) (-4462 . T)) +((-4457 . T) (-4462 . T) (-4456 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4461 . T)) NIL -(-1034 R -1962) +(-1034 R -1963) ((|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 -(-1035 R -1962) +(-1035 R -1963) ((|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 -(-1036 -1962 UP) +(-1036 -1963 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 -(-1037 -1962 UP) +(-1037 -1963 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 @@ -4110,9 +4110,9 @@ NIL NIL (-1045 |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"))) -((-4458 . T) (-4463 . T) (-4457 . T) (-4460 . T) (-4459 . T) ((-4467 "*") . T) (-4462 . T)) -((-2760 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (QUOTE (-576))))) -(-1046 -1962 L) +((-4457 . T) (-4462 . T) (-4456 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4461 . T)) +((-2759 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (QUOTE (-576))))) +(-1046 -1963 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{fi} must satisfy \\spad{op 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 @@ -4122,12 +4122,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1121)))) (-1048 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."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1049 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(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em 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 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 ai} and {\\em 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 (-4467 "*")))) +((|HasAttribute| |#1| (QUOTE (-4466 "*")))) (-1050 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 @@ -4148,14 +4148,14 @@ 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 -(-1055 -1962 |Expon| |VarSet| |FPol| |LFPol|) +(-1055 -1963 |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"))) -(((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1056) ((|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.}"))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1197))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1121))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1197))) (LIST (QUOTE |:|) (QUOTE -4439) (QUOTE (-52))))))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1121))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-102)))) (-1057) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4198,7 +4198,7 @@ NIL NIL (-1067 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}."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) ((-12 (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-1121))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -792) (|devaluate| |#1|) (LIST (QUOTE -878) (|devaluate| |#2|)))))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-878 |#2|) (QUOTE (-379))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-102)))) (-1068) ((|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"))) @@ -4210,9 +4210,9 @@ NIL NIL (-1070) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4462 . T)) +((-4461 . T)) NIL -(-1071 |xx| -1962) +(-1071 |xx| -1963) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4226,12 +4226,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (QUOTE (-568))) (|HasCategory| |#4| (QUOTE (-174)))) (-1074 |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"))) -((-4465 . T) (-4460 . T) (-4459 . T)) +((-4464 . T) (-4459 . T) (-4458 . T)) NIL (-1075 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4465 . T) (-4460 . T) (-4459 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2760 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-876))))) +((-4464 . T) (-4459 . T) (-4458 . T)) +((|HasCategory| |#3| (QUOTE (-174))) (-2759 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-876))))) (-1076 |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 @@ -4254,7 +4254,7 @@ NIL NIL (-1081) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1082 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4262,19 +4262,19 @@ NIL NIL (-1083) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4453 . T) (-4457 . T) (-4452 . T) (-4463 . T) (-4464 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1084) ((|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}"))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1197))) (LIST (QUOTE |:|) (QUOTE -4440) (QUOTE (-52))))))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1121))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2760 (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1197))) (LIST (QUOTE |:|) (QUOTE -4439) (QUOTE (-52))))))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1121))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2759 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (QUOTE (-102)))) (-1085 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1013) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1197))))) (-1086 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-1087) ((|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'."))) @@ -4298,7 +4298,7 @@ NIL NIL (-1092 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,...,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,...,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(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}."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-1093 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."))) @@ -4316,11 +4316,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1097 |Base| R -1962) +(-1097 |Base| R -1963) ((|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 -(-1098 |Base| R -1962) +(-1098 |Base| R -1963) ((|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 @@ -4334,8 +4334,8 @@ NIL NIL (-1101 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."))) -((-4458 |has| |#1| (-374)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) +((-4457 |has| |#1| (-374)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (-1102 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 @@ -4362,8 +4362,8 @@ NIL NIL (-1108 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"))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-928))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . 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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 @@ -4406,7 +4406,7 @@ NIL NIL (-1119 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}."))) -((-4455 . T)) +((-4454 . T)) NIL (-1120 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}."))) @@ -4422,8 +4422,8 @@ NIL NIL (-1123 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)}}"))) -((-4465 . T) (-4455 . T) (-4466 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4464 . T) (-4454 . T) (-4465 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-1124 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL @@ -4450,7 +4450,7 @@ NIL NIL (-1130 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.}"))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-1131) ((|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| (|PositiveInteger|)) (|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| (|PositiveInteger|)) (|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| (|PositiveInteger|))) "\\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 pi} in the corresponding double coset. Note: the resulting permutation {\\em 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,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 pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4466,8 +4466,8 @@ NIL NIL (-1134 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4459 |has| |#3| (-1070)) (-4460 |has| |#3| (-1070)) (-4462 |has| |#3| (-6 -4462)) (-4465 . 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(LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576)))))) (|HasCategory| (-576) (QUOTE (-861))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (LIST (QUOTE -919) (QUOTE (-1197))))) (-2759 (|HasCategory| |#3| (QUOTE (-1070))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576)))))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#3| (QUOTE (-1121)))) (|HasAttribute| |#3| (QUOTE -4461)) (-12 (|HasCategory| |#3| (QUOTE (-238))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (LIST (QUOTE -917) (QUOTE (-1197))))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (-1135 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 @@ -4476,7 +4476,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1137 R -1962) +(-1137 R -1963) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4494,19 +4494,19 @@ NIL NIL (-1141) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4453 . T) (-4457 . T) (-4452 . T) (-4463 . T) (-4464 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1142 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4465 . T) (-4466 . T)) +((-4464 . T) (-4465 . T)) NIL (-1143 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) NIL -((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4467 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4466 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) (-1144 |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."))) -((-4465 . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4464 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1145 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}."))) @@ -4514,17 +4514,17 @@ NIL NIL (-1146 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."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-928))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1147 |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}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1148 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}"))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1149 UP -1962) +(-1149 UP -1963) ((|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 @@ -4578,19 +4578,19 @@ NIL NIL (-1162 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."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121))) (-2760 (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121)))) (-2760 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121))))) (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121))) (-2759 (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121)))) (-2759 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121))))) (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102)))) (-1163 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) -((-4462 . T) (-4454 |has| |#2| (-6 (-4467 "*"))) (-4465 . T) (-4459 . T) (-4460 . T)) -((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4467 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-374))) (-2760 (|HasAttribute| |#2| (QUOTE (-4467 "*"))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4461 . T) (-4453 |has| |#2| (-6 (-4466 "*"))) (-4464 . T) (-4458 . T) (-4459 . T)) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-374))) (-2759 (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1164 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1165) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-1166 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.}"))) @@ -4598,12 +4598,12 @@ NIL NIL (-1167 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."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1168 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}."))) -((-4465 . T) (-4466 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1169 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 @@ -4614,8 +4614,8 @@ NIL NIL (-1171 |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."))) -((-4466 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|)))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121)))) (-1172) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4642,16 +4642,16 @@ NIL NIL (-1178 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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.")) 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4682,9 +4682,9 @@ NIL NIL (-1188 |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. 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3570) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2760 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1491) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2759 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4160) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-1196) ((|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 @@ -4726,8 +4726,8 @@ NIL NIL (-1199 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-6 -4463)) (-4459 . T) (-4460 . T) (-4462 . 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(|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."))) 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T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4439) (|devaluate| |#2|)))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2759 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (QUOTE (-102)))) (-1211 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4786,7 +4786,7 @@ NIL NIL (-1214 |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})}."))) -((-4466 . T)) +((-4465 . T)) NIL (-1215 |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."))) @@ -4826,8 +4826,8 @@ NIL NIL (-1224 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4466 . T) (-4465 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1225 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4836,7 +4836,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1227 R -1962) +(-1227 R -1963) ((|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 @@ -4844,7 +4844,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1229 R -1962) +(-1229 R -1963) ((|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 -626) (LIST (QUOTE -907) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -901) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -901) (|devaluate| |#1|))))) @@ -4854,12 +4854,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-379)))) (-1231 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-1232 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1233 |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 @@ -4872,7 +4872,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) -(-1236 -1962) +(-1236 -1963) ((|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 @@ -4898,7 +4898,7 @@ NIL NIL (-1242) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1243) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4922,7 +4922,7 @@ NIL NIL (-1248 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|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."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1249 S |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)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|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)}."))) @@ -4930,16 +4930,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-1250 |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)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|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| ((|#2| $) "\\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|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1251 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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|#3|) (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1280 |#1| |#2| |#3|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1280 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1280 |#1| |#2| |#3|) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1280 |#1| |#2| |#3|) (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-374)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1280 |#1| |#2| |#3|) (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| (-1280 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1253 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 @@ -4974,8 +4974,8 @@ NIL NIL (-1261 |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}"))) -(((-4467 "*") |has| |#2| (-174)) (-4458 |has| |#2| (-568)) (-4461 |has| |#2| (-374)) (-4463 |has| |#2| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2760 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2760 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2760 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2760 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4460 |has| |#2| (-374)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2759 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2759 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2759 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2759 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) (-1262 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 @@ -4986,15 +4986,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1173)))) (-1264 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}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4463 |has| |#1| (-6 -4463)) (-4460 . T) (-4459 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-1265 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}.")) (|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 -917) (QUOTE (-1197)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3570) (LIST (|devaluate| |#2|) (QUOTE (-1197)))))) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3569) (LIST (|devaluate| |#2|) (QUOTE (-1197)))))) (-1266 |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}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1267 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -5006,7 +5006,7 @@ NIL NIL (-1269 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1270 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.")) (|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)}."))) @@ -5014,24 +5014,24 @@ NIL NIL (-1271 |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.")) (|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)}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1272 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3570) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2760 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1491) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2759 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4160) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-1273 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4463 |has| |#1| (-374)) (-4457 |has| |#1| (-374)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2760 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3570) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2760 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1491) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2759 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2759 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4160) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-1274 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) -(((-4467 "*") |has| (-1273 |#2| |#3| |#4|) (-174)) (-4458 |has| (-1273 |#2| |#3| |#4|) (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-174))) (-2760 (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-568)))) +(((-4466 "*") |has| (-1273 |#2| |#3| |#4|) (-174)) (-4457 |has| (-1273 |#2| |#3| |#4|) (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-174))) (-2759 (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-568)))) (-1275 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4466))) +((|HasAttribute| |#1| (QUOTE -4465))) (-1276 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5043,20 +5043,20 @@ NIL (-1278 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasSignature| |#2| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1491) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1197))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasSignature| |#2| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4160) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1197))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) (-1279 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1280 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4467 "*") |has| |#1| (-174)) (-4458 |has| |#1| (-568)) (-4459 . T) (-4460 . T) (-4462 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2760 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3570) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2760 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1491) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2759 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2759 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4160) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1969) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-1281 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1282 -1962 UP L UTS) +(-1282 -1963 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 (-568)))) @@ -5074,7 +5074,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1286 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) NIL (-1287 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -5082,8 +5082,8 @@ NIL NIL (-1288 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4466 . T) (-4465 . T)) -((-2760 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2760 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2760 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2760 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2759 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2759 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2759 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2759 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-1289) ((|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,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{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\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(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\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|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5110,13 +5110,13 @@ NIL NIL (-1295 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4460 . T) (-4459 . T)) +((-4459 . T) (-4458 . T)) NIL (-1296 R) ((|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 -(-1297 K R UP -1962) +(-1297 K R UP -1963) ((|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{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{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{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{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{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{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5130,56 +5130,56 @@ NIL NIL (-1300 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4460 |has| |#1| (-174)) (-4459 |has| |#1| (-174)) (-4462 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (-1301 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}}."))) -((-4466 . T) (-4465 . T)) +((-4465 . T) (-4464 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1302 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})"))) -((-4459 . T) (-4460 . T) (-4462 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1303 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4462 . T) (-4458 |has| |#2| (-6 -4458)) (-4460 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4458))) +((-4461 . T) (-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4457))) (-1304 R |VarSet| XPOLY) ((|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 (-1305 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4458 |has| |#2| (-6 -4458)) (-4460 . T) (-4459 . T) (-4462 . T)) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1306 S -1962) +(-1306 S -1963) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1307 -1962) +(-1307 -1963) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4457 . T) (-4463 . T) (-4458 . T) ((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-1308 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4458 |has| |#2| (-6 -4458)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4458))) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4457))) (-1309 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4458 |has| |#2| (-6 -4458)) (-4460 . T) (-4459 . T) (-4462 . T)) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-1310 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4458 |has| |#1| (-6 -4458)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4458))) +((-4457 |has| |#1| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4457))) (-1311 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4462 . T) (-4463 |has| |#1| (-6 -4463)) (-4458 |has| |#1| (-6 -4458)) (-4460 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4463)) (|HasAttribute| |#1| (QUOTE -4458))) +((-4461 . T) (-4462 |has| |#1| (-6 -4462)) (-4457 |has| |#1| (-6 -4457)) (-4459 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4457))) (-1312 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4458 |has| |#2| (-6 -4458)) (-4460 . T) (-4459 . T) (-4462 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4458))) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4457))) (-1313) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL @@ -5198,7 +5198,7 @@ NIL NIL (-1317 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4467 "*") . T) (-4459 . T) (-4460 . T) (-4462 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL NIL NIL @@ -5216,4 +5216,4 @@ NIL NIL NIL NIL -((-3 NIL 2294110 2294115 2294120 2294125) (-2 NIL 2294090 2294095 2294100 2294105) (-1 NIL 2294070 2294075 2294080 2294085) (0 NIL 2294050 2294055 2294060 2294065) (-1317 "ZMOD.spad" 2293859 2293872 2293988 2294045) (-1316 "ZLINDEP.spad" 2292925 2292936 2293849 2293854) (-1315 "ZDSOLVE.spad" 2282870 2282892 2292915 2292920) (-1314 "YSTREAM.spad" 2282365 2282376 2282860 2282865) (-1313 "YDIAGRAM.spad" 2281999 2282008 2282355 2282360) (-1312 "XRPOLY.spad" 2281219 2281239 2281855 2281924) (-1311 "XPR.spad" 2279014 2279027 2280937 2281036) (-1310 "XPOLY.spad" 2278569 2278580 2278870 2278939) (-1309 "XPOLYC.spad" 2277888 2277904 2278495 2278564) (-1308 "XPBWPOLY.spad" 2276325 2276345 2277668 2277737) (-1307 "XF.spad" 2274788 2274803 2276227 2276320) (-1306 "XF.spad" 2273231 2273248 2274672 2274677) (-1305 "XFALG.spad" 2270279 2270295 2273157 2273226) (-1304 "XEXPPKG.spad" 2269530 2269556 2270269 2270274) (-1303 "XDPOLY.spad" 2269144 2269160 2269386 2269455) (-1302 "XALG.spad" 2268804 2268815 2269100 2269139) (-1301 "WUTSET.spad" 2264607 2264624 2268414 2268441) (-1300 "WP.spad" 2263806 2263850 2264465 2264532) (-1299 "WHILEAST.spad" 2263604 2263613 2263796 2263801) (-1298 "WHEREAST.spad" 2263275 2263284 2263594 2263599) (-1297 "WFFINTBS.spad" 2260938 2260960 2263265 2263270) (-1296 "WEIER.spad" 2259160 2259171 2260928 2260933) (-1295 "VSPACE.spad" 2258833 2258844 2259128 2259155) (-1294 "VSPACE.spad" 2258526 2258539 2258823 2258828) (-1293 "VOID.spad" 2258203 2258212 2258516 2258521) (-1292 "VIEW.spad" 2255883 2255892 2258193 2258198) (-1291 "VIEWDEF.spad" 2251084 2251093 2255873 2255878) (-1290 "VIEW3D.spad" 2235045 2235054 2251074 2251079) (-1289 "VIEW2D.spad" 2222936 2222945 2235035 2235040) (-1288 "VECTOR.spad" 2221457 2221468 2221708 2221735) (-1287 "VECTOR2.spad" 2220096 2220109 2221447 2221452) (-1286 "VECTCAT.spad" 2218000 2218011 2220064 2220091) (-1285 "VECTCAT.spad" 2215711 2215724 2217777 2217782) (-1284 "VARIABLE.spad" 2215491 2215506 2215701 2215706) (-1283 "UTYPE.spad" 2215135 2215144 2215481 2215486) (-1282 "UTSODETL.spad" 2214430 2214454 2215091 2215096) (-1281 "UTSODE.spad" 2212646 2212666 2214420 2214425) (-1280 "UTS.spad" 2207593 2207621 2211113 2211210) (-1279 "UTSCAT.spad" 2205072 2205088 2207491 2207588) (-1278 "UTSCAT.spad" 2202195 2202213 2204616 2204621) (-1277 "UTS2.spad" 2201790 2201825 2202185 2202190) (-1276 "URAGG.spad" 2196463 2196474 2201780 2201785) (-1275 "URAGG.spad" 2191100 2191113 2196419 2196424) (-1274 "UPXSSING.spad" 2188745 2188771 2190181 2190314) (-1273 "UPXS.spad" 2186041 2186069 2186877 2187026) (-1272 "UPXSCONS.spad" 2183800 2183820 2184173 2184322) (-1271 "UPXSCCA.spad" 2182371 2182391 2183646 2183795) (-1270 "UPXSCCA.spad" 2181084 2181106 2182361 2182366) (-1269 "UPXSCAT.spad" 2179673 2179689 2180930 2181079) (-1268 "UPXS2.spad" 2179216 2179269 2179663 2179668) (-1267 "UPSQFREE.spad" 2177630 2177644 2179206 2179211) (-1266 "UPSCAT.spad" 2175417 2175441 2177528 2177625) (-1265 "UPSCAT.spad" 2172910 2172936 2175023 2175028) (-1264 "UPOLYC.spad" 2167950 2167961 2172752 2172905) (-1263 "UPOLYC.spad" 2162882 2162895 2167686 2167691) (-1262 "UPOLYC2.spad" 2162353 2162372 2162872 2162877) (-1261 "UP.spad" 2159459 2159474 2159846 2159999) (-1260 "UPMP.spad" 2158359 2158372 2159449 2159454) (-1259 "UPDIVP.spad" 2157924 2157938 2158349 2158354) (-1258 "UPDECOMP.spad" 2156169 2156183 2157914 2157919) (-1257 "UPCDEN.spad" 2155378 2155394 2156159 2156164) (-1256 "UP2.spad" 2154742 2154763 2155368 2155373) (-1255 "UNISEG.spad" 2154095 2154106 2154661 2154666) (-1254 "UNISEG2.spad" 2153592 2153605 2154051 2154056) (-1253 "UNIFACT.spad" 2152695 2152707 2153582 2153587) (-1252 "ULS.spad" 2142479 2142507 2143424 2143853) (-1251 "ULSCONS.spad" 2133613 2133633 2133983 2134132) (-1250 "ULSCCAT.spad" 2131350 2131370 2133459 2133608) (-1249 "ULSCCAT.spad" 2129195 2129217 2131306 2131311) (-1248 "ULSCAT.spad" 2127427 2127443 2129041 2129190) (-1247 "ULS2.spad" 2126941 2126994 2127417 2127422) (-1246 "UINT8.spad" 2126818 2126827 2126931 2126936) (-1245 "UINT64.spad" 2126694 2126703 2126808 2126813) (-1244 "UINT32.spad" 2126570 2126579 2126684 2126689) (-1243 "UINT16.spad" 2126446 2126455 2126560 2126565) (-1242 "UFD.spad" 2125511 2125520 2126372 2126441) (-1241 "UFD.spad" 2124638 2124649 2125501 2125506) (-1240 "UDVO.spad" 2123519 2123528 2124628 2124633) (-1239 "UDPO.spad" 2121012 2121023 2123475 2123480) (-1238 "TYPE.spad" 2120944 2120953 2121002 2121007) (-1237 "TYPEAST.spad" 2120863 2120872 2120934 2120939) (-1236 "TWOFACT.spad" 2119515 2119530 2120853 2120858) (-1235 "TUPLE.spad" 2119001 2119012 2119414 2119419) (-1234 "TUBETOOL.spad" 2115868 2115877 2118991 2118996) (-1233 "TUBE.spad" 2114515 2114532 2115858 2115863) (-1232 "TS.spad" 2113114 2113130 2114080 2114177) (-1231 "TSETCAT.spad" 2100241 2100258 2113082 2113109) (-1230 "TSETCAT.spad" 2087354 2087373 2100197 2100202) (-1229 "TRMANIP.spad" 2081720 2081737 2087060 2087065) (-1228 "TRIMAT.spad" 2080683 2080708 2081710 2081715) (-1227 "TRIGMNIP.spad" 2079210 2079227 2080673 2080678) (-1226 "TRIGCAT.spad" 2078722 2078731 2079200 2079205) (-1225 "TRIGCAT.spad" 2078232 2078243 2078712 2078717) (-1224 "TREE.spad" 2076690 2076701 2077722 2077749) (-1223 "TRANFUN.spad" 2076529 2076538 2076680 2076685) (-1222 "TRANFUN.spad" 2076366 2076377 2076519 2076524) (-1221 "TOPSP.spad" 2076040 2076049 2076356 2076361) (-1220 "TOOLSIGN.spad" 2075703 2075714 2076030 2076035) (-1219 "TEXTFILE.spad" 2074264 2074273 2075693 2075698) (-1218 "TEX.spad" 2071410 2071419 2074254 2074259) (-1217 "TEX1.spad" 2070966 2070977 2071400 2071405) (-1216 "TEMUTL.spad" 2070521 2070530 2070956 2070961) (-1215 "TBCMPPK.spad" 2068614 2068637 2070511 2070516) (-1214 "TBAGG.spad" 2067664 2067687 2068594 2068609) (-1213 "TBAGG.spad" 2066722 2066747 2067654 2067659) (-1212 "TANEXP.spad" 2066130 2066141 2066712 2066717) (-1211 "TALGOP.spad" 2065854 2065865 2066120 2066125) (-1210 "TABLE.spad" 2063823 2063846 2064093 2064120) (-1209 "TABLEAU.spad" 2063304 2063315 2063813 2063818) (-1208 "TABLBUMP.spad" 2060107 2060118 2063294 2063299) (-1207 "SYSTEM.spad" 2059335 2059344 2060097 2060102) (-1206 "SYSSOLP.spad" 2056818 2056829 2059325 2059330) (-1205 "SYSPTR.spad" 2056717 2056726 2056808 2056813) (-1204 "SYSNNI.spad" 2055899 2055910 2056707 2056712) (-1203 "SYSINT.spad" 2055303 2055314 2055889 2055894) (-1202 "SYNTAX.spad" 2051509 2051518 2055293 2055298) (-1201 "SYMTAB.spad" 2049577 2049586 2051499 2051504) (-1200 "SYMS.spad" 2045600 2045609 2049567 2049572) (-1199 "SYMPOLY.spad" 2044607 2044618 2044689 2044816) (-1198 "SYMFUNC.spad" 2044108 2044119 2044597 2044602) (-1197 "SYMBOL.spad" 2041611 2041620 2044098 2044103) (-1196 "SWITCH.spad" 2038382 2038391 2041601 2041606) (-1195 "SUTS.spad" 2035430 2035458 2036849 2036946) (-1194 "SUPXS.spad" 2032713 2032741 2033562 2033711) (-1193 "SUP.spad" 2029433 2029444 2030206 2030359) (-1192 "SUPFRACF.spad" 2028538 2028556 2029423 2029428) (-1191 "SUP2.spad" 2027930 2027943 2028528 2028533) (-1190 "SUMRF.spad" 2026904 2026915 2027920 2027925) (-1189 "SUMFS.spad" 2026541 2026558 2026894 2026899) (-1188 "SULS.spad" 2016312 2016340 2017270 2017699) (-1187 "SUCHTAST.spad" 2016081 2016090 2016302 2016307) (-1186 "SUCH.spad" 2015763 2015778 2016071 2016076) (-1185 "SUBSPACE.spad" 2007878 2007893 2015753 2015758) (-1184 "SUBRESP.spad" 2007048 2007062 2007834 2007839) (-1183 "STTF.spad" 2003147 2003163 2007038 2007043) (-1182 "STTFNC.spad" 1999615 1999631 2003137 2003142) (-1181 "STTAYLOR.spad" 1992250 1992261 1999496 1999501) (-1180 "STRTBL.spad" 1990301 1990318 1990450 1990477) (-1179 "STRING.spad" 1989088 1989097 1989309 1989336) (-1178 "STREAM.spad" 1985889 1985900 1988496 1988511) (-1177 "STREAM3.spad" 1985462 1985477 1985879 1985884) (-1176 "STREAM2.spad" 1984590 1984603 1985452 1985457) (-1175 "STREAM1.spad" 1984296 1984307 1984580 1984585) (-1174 "STINPROD.spad" 1983232 1983248 1984286 1984291) (-1173 "STEP.spad" 1982433 1982442 1983222 1983227) (-1172 "STEPAST.spad" 1981667 1981676 1982423 1982428) (-1171 "STBL.spad" 1979751 1979779 1979918 1979933) (-1170 "STAGG.spad" 1978826 1978837 1979741 1979746) (-1169 "STAGG.spad" 1977899 1977912 1978816 1978821) (-1168 "STACK.spad" 1977139 1977150 1977389 1977416) (-1167 "SREGSET.spad" 1974807 1974824 1976749 1976776) (-1166 "SRDCMPK.spad" 1973368 1973388 1974797 1974802) (-1165 "SRAGG.spad" 1968511 1968520 1973336 1973363) (-1164 "SRAGG.spad" 1963674 1963685 1968501 1968506) (-1163 "SQMATRIX.spad" 1961217 1961235 1962133 1962220) (-1162 "SPLTREE.spad" 1955613 1955626 1960497 1960524) (-1161 "SPLNODE.spad" 1952201 1952214 1955603 1955608) (-1160 "SPFCAT.spad" 1951010 1951019 1952191 1952196) (-1159 "SPECOUT.spad" 1949562 1949571 1951000 1951005) (-1158 "SPADXPT.spad" 1941157 1941166 1949552 1949557) (-1157 "spad-parser.spad" 1940622 1940631 1941147 1941152) (-1156 "SPADAST.spad" 1940323 1940332 1940612 1940617) (-1155 "SPACEC.spad" 1924522 1924533 1940313 1940318) (-1154 "SPACE3.spad" 1924298 1924309 1924512 1924517) (-1153 "SORTPAK.spad" 1923847 1923860 1924254 1924259) (-1152 "SOLVETRA.spad" 1921610 1921621 1923837 1923842) (-1151 "SOLVESER.spad" 1920138 1920149 1921600 1921605) (-1150 "SOLVERAD.spad" 1916164 1916175 1920128 1920133) (-1149 "SOLVEFOR.spad" 1914626 1914644 1916154 1916159) (-1148 "SNTSCAT.spad" 1914226 1914243 1914594 1914621) (-1147 "SMTS.spad" 1912498 1912524 1913791 1913888) (-1146 "SMP.spad" 1909973 1909993 1910363 1910490) (-1145 "SMITH.spad" 1908818 1908843 1909963 1909968) (-1144 "SMATCAT.spad" 1906928 1906958 1908762 1908813) (-1143 "SMATCAT.spad" 1904970 1905002 1906806 1906811) (-1142 "SKAGG.spad" 1903933 1903944 1904938 1904965) (-1141 "SINT.spad" 1902873 1902882 1903799 1903928) (-1140 "SIMPAN.spad" 1902601 1902610 1902863 1902868) (-1139 "SIG.spad" 1901931 1901940 1902591 1902596) (-1138 "SIGNRF.spad" 1901049 1901060 1901921 1901926) (-1137 "SIGNEF.spad" 1900328 1900345 1901039 1901044) (-1136 "SIGAST.spad" 1899713 1899722 1900318 1900323) (-1135 "SHP.spad" 1897641 1897656 1899669 1899674) (-1134 "SHDP.spad" 1885319 1885346 1885828 1885927) (-1133 "SGROUP.spad" 1884927 1884936 1885309 1885314) (-1132 "SGROUP.spad" 1884533 1884544 1884917 1884922) (-1131 "SGCF.spad" 1877672 1877681 1884523 1884528) (-1130 "SFRTCAT.spad" 1876602 1876619 1877640 1877667) (-1129 "SFRGCD.spad" 1875665 1875685 1876592 1876597) (-1128 "SFQCMPK.spad" 1870302 1870322 1875655 1875660) (-1127 "SFORT.spad" 1869741 1869755 1870292 1870297) (-1126 "SEXOF.spad" 1869584 1869624 1869731 1869736) (-1125 "SEX.spad" 1869476 1869485 1869574 1869579) (-1124 "SEXCAT.spad" 1867248 1867288 1869466 1869471) (-1123 "SET.spad" 1865536 1865547 1866633 1866672) (-1122 "SETMN.spad" 1863986 1864003 1865526 1865531) (-1121 "SETCAT.spad" 1863471 1863480 1863976 1863981) (-1120 "SETCAT.spad" 1862954 1862965 1863461 1863466) (-1119 "SETAGG.spad" 1859503 1859514 1862934 1862949) (-1118 "SETAGG.spad" 1856060 1856073 1859493 1859498) (-1117 "SEQAST.spad" 1855763 1855772 1856050 1856055) (-1116 "SEGXCAT.spad" 1854919 1854932 1855753 1855758) (-1115 "SEG.spad" 1854732 1854743 1854838 1854843) (-1114 "SEGCAT.spad" 1853657 1853668 1854722 1854727) (-1113 "SEGBIND.spad" 1853415 1853426 1853604 1853609) (-1112 "SEGBIND2.spad" 1853113 1853126 1853405 1853410) (-1111 "SEGAST.spad" 1852827 1852836 1853103 1853108) (-1110 "SEG2.spad" 1852262 1852275 1852783 1852788) (-1109 "SDVAR.spad" 1851538 1851549 1852252 1852257) (-1108 "SDPOL.spad" 1848871 1848882 1849162 1849289) (-1107 "SCPKG.spad" 1846960 1846971 1848861 1848866) (-1106 "SCOPE.spad" 1846113 1846122 1846950 1846955) (-1105 "SCACHE.spad" 1844809 1844820 1846103 1846108) (-1104 "SASTCAT.spad" 1844718 1844727 1844799 1844804) (-1103 "SAOS.spad" 1844590 1844599 1844708 1844713) (-1102 "SAERFFC.spad" 1844303 1844323 1844580 1844585) (-1101 "SAE.spad" 1841773 1841789 1842384 1842519) (-1100 "SAEFACT.spad" 1841474 1841494 1841763 1841768) (-1099 "RURPK.spad" 1839133 1839149 1841464 1841469) (-1098 "RULESET.spad" 1838586 1838610 1839123 1839128) (-1097 "RULE.spad" 1836826 1836850 1838576 1838581) (-1096 "RULECOLD.spad" 1836678 1836691 1836816 1836821) (-1095 "RTVALUE.spad" 1836413 1836422 1836668 1836673) (-1094 "RSTRCAST.spad" 1836130 1836139 1836403 1836408) (-1093 "RSETGCD.spad" 1832508 1832528 1836120 1836125) (-1092 "RSETCAT.spad" 1822444 1822461 1832476 1832503) (-1091 "RSETCAT.spad" 1812400 1812419 1822434 1822439) (-1090 "RSDCMPK.spad" 1810852 1810872 1812390 1812395) (-1089 "RRCC.spad" 1809236 1809266 1810842 1810847) (-1088 "RRCC.spad" 1807618 1807650 1809226 1809231) (-1087 "RPTAST.spad" 1807320 1807329 1807608 1807613) (-1086 "RPOLCAT.spad" 1786680 1786695 1807188 1807315) (-1085 "RPOLCAT.spad" 1765753 1765770 1786263 1786268) (-1084 "ROUTINE.spad" 1761174 1761183 1763938 1763965) (-1083 "ROMAN.spad" 1760502 1760511 1761040 1761169) (-1082 "ROIRC.spad" 1759582 1759614 1760492 1760497) (-1081 "RNS.spad" 1758485 1758494 1759484 1759577) (-1080 "RNS.spad" 1757474 1757485 1758475 1758480) (-1079 "RNG.spad" 1757209 1757218 1757464 1757469) (-1078 "RNGBIND.spad" 1756369 1756383 1757164 1757169) (-1077 "RMODULE.spad" 1756134 1756145 1756359 1756364) (-1076 "RMCAT2.spad" 1755554 1755611 1756124 1756129) (-1075 "RMATRIX.spad" 1754342 1754361 1754685 1754724) (-1074 "RMATCAT.spad" 1749921 1749952 1754298 1754337) (-1073 "RMATCAT.spad" 1745390 1745423 1749769 1749774) (-1072 "RLINSET.spad" 1745094 1745105 1745380 1745385) (-1071 "RINTERP.spad" 1744982 1745002 1745084 1745089) (-1070 "RING.spad" 1744452 1744461 1744962 1744977) (-1069 "RING.spad" 1743930 1743941 1744442 1744447) (-1068 "RIDIST.spad" 1743322 1743331 1743920 1743925) (-1067 "RGCHAIN.spad" 1741850 1741866 1742752 1742779) (-1066 "RGBCSPC.spad" 1741631 1741643 1741840 1741845) (-1065 "RGBCMDL.spad" 1741161 1741173 1741621 1741626) (-1064 "RF.spad" 1738803 1738814 1741151 1741156) (-1063 "RFFACTOR.spad" 1738265 1738276 1738793 1738798) (-1062 "RFFACT.spad" 1738000 1738012 1738255 1738260) (-1061 "RFDIST.spad" 1736996 1737005 1737990 1737995) (-1060 "RETSOL.spad" 1736415 1736428 1736986 1736991) (-1059 "RETRACT.spad" 1735843 1735854 1736405 1736410) (-1058 "RETRACT.spad" 1735269 1735282 1735833 1735838) (-1057 "RETAST.spad" 1735081 1735090 1735259 1735264) (-1056 "RESULT.spad" 1732679 1732688 1733266 1733293) (-1055 "RESRING.spad" 1732026 1732073 1732617 1732674) (-1054 "RESLATC.spad" 1731350 1731361 1732016 1732021) (-1053 "REPSQ.spad" 1731081 1731092 1731340 1731345) (-1052 "REP.spad" 1728635 1728644 1731071 1731076) (-1051 "REPDB.spad" 1728342 1728353 1728625 1728630) (-1050 "REP2.spad" 1718000 1718011 1728184 1728189) (-1049 "REP1.spad" 1712196 1712207 1717950 1717955) (-1048 "REGSET.spad" 1709957 1709974 1711806 1711833) (-1047 "REF.spad" 1709292 1709303 1709912 1709917) (-1046 "REDORDER.spad" 1708498 1708515 1709282 1709287) (-1045 "RECLOS.spad" 1707281 1707301 1707985 1708078) (-1044 "REALSOLV.spad" 1706421 1706430 1707271 1707276) (-1043 "REAL.spad" 1706293 1706302 1706411 1706416) (-1042 "REAL0Q.spad" 1703591 1703606 1706283 1706288) (-1041 "REAL0.spad" 1700435 1700450 1703581 1703586) (-1040 "RDUCEAST.spad" 1700156 1700165 1700425 1700430) (-1039 "RDIV.spad" 1699811 1699836 1700146 1700151) (-1038 "RDIST.spad" 1699378 1699389 1699801 1699806) (-1037 "RDETRS.spad" 1698242 1698260 1699368 1699373) (-1036 "RDETR.spad" 1696381 1696399 1698232 1698237) (-1035 "RDEEFS.spad" 1695480 1695497 1696371 1696376) (-1034 "RDEEF.spad" 1694490 1694507 1695470 1695475) (-1033 "RCFIELD.spad" 1691676 1691685 1694392 1694485) (-1032 "RCFIELD.spad" 1688948 1688959 1691666 1691671) (-1031 "RCAGG.spad" 1686876 1686887 1688938 1688943) (-1030 "RCAGG.spad" 1684731 1684744 1686795 1686800) (-1029 "RATRET.spad" 1684091 1684102 1684721 1684726) (-1028 "RATFACT.spad" 1683783 1683795 1684081 1684086) (-1027 "RANDSRC.spad" 1683102 1683111 1683773 1683778) (-1026 "RADUTIL.spad" 1682858 1682867 1683092 1683097) (-1025 "RADIX.spad" 1679682 1679696 1681228 1681321) (-1024 "RADFF.spad" 1677421 1677458 1677540 1677696) (-1023 "RADCAT.spad" 1677016 1677025 1677411 1677416) (-1022 "RADCAT.spad" 1676609 1676620 1677006 1677011) (-1021 "QUEUE.spad" 1675840 1675851 1676099 1676126) (-1020 "QUAT.spad" 1674328 1674339 1674671 1674736) (-1019 "QUATCT2.spad" 1673948 1673967 1674318 1674323) (-1018 "QUATCAT.spad" 1672118 1672129 1673878 1673943) (-1017 "QUATCAT.spad" 1670039 1670052 1671801 1671806) (-1016 "QUAGG.spad" 1668866 1668877 1670007 1670034) (-1015 "QQUTAST.spad" 1668634 1668643 1668856 1668861) (-1014 "QFORM.spad" 1668252 1668267 1668624 1668629) (-1013 "QFCAT.spad" 1666954 1666965 1668154 1668247) (-1012 "QFCAT.spad" 1665247 1665260 1666449 1666454) (-1011 "QFCAT2.spad" 1664939 1664956 1665237 1665242) (-1010 "QEQUAT.spad" 1664497 1664506 1664929 1664934) (-1009 "QCMPACK.spad" 1659243 1659263 1664487 1664492) (-1008 "QALGSET.spad" 1655321 1655354 1659157 1659162) (-1007 "QALGSET2.spad" 1653316 1653335 1655311 1655316) (-1006 "PWFFINTB.spad" 1650731 1650753 1653306 1653311) (-1005 "PUSHVAR.spad" 1650069 1650089 1650721 1650726) (-1004 "PTRANFN.spad" 1646196 1646207 1650059 1650064) (-1003 "PTPACK.spad" 1643283 1643294 1646186 1646191) (-1002 "PTFUNC2.spad" 1643105 1643120 1643273 1643278) (-1001 "PTCAT.spad" 1642359 1642370 1643073 1643100) (-1000 "PSQFR.spad" 1641665 1641690 1642349 1642354) (-999 "PSEUDLIN.spad" 1640551 1640561 1641655 1641660) (-998 "PSETPK.spad" 1625984 1626000 1640429 1640434) (-997 "PSETCAT.spad" 1619904 1619927 1625964 1625979) (-996 "PSETCAT.spad" 1613798 1613823 1619860 1619865) (-995 "PSCURVE.spad" 1612781 1612789 1613788 1613793) (-994 "PSCAT.spad" 1611564 1611593 1612679 1612776) (-993 "PSCAT.spad" 1610437 1610468 1611554 1611559) (-992 "PRTITION.spad" 1609135 1609143 1610427 1610432) (-991 "PRTDAST.spad" 1608854 1608862 1609125 1609130) (-990 "PRS.spad" 1598416 1598433 1608810 1608815) (-989 "PRQAGG.spad" 1597851 1597861 1598384 1598411) (-988 "PROPLOG.spad" 1597423 1597431 1597841 1597846) (-987 "PROPFUN2.spad" 1597046 1597059 1597413 1597418) (-986 "PROPFUN1.spad" 1596444 1596455 1597036 1597041) (-985 "PROPFRML.spad" 1595012 1595023 1596434 1596439) (-984 "PROPERTY.spad" 1594500 1594508 1595002 1595007) (-983 "PRODUCT.spad" 1592182 1592194 1592466 1592521) (-982 "PR.spad" 1590574 1590586 1591273 1591400) (-981 "PRINT.spad" 1590326 1590334 1590564 1590569) (-980 "PRIMES.spad" 1588579 1588589 1590316 1590321) (-979 "PRIMELT.spad" 1586660 1586674 1588569 1588574) (-978 "PRIMCAT.spad" 1586287 1586295 1586650 1586655) (-977 "PRIMARR.spad" 1585139 1585149 1585317 1585344) (-976 "PRIMARR2.spad" 1583906 1583918 1585129 1585134) (-975 "PREASSOC.spad" 1583288 1583300 1583896 1583901) (-974 "PPCURVE.spad" 1582425 1582433 1583278 1583283) (-973 "PORTNUM.spad" 1582200 1582208 1582415 1582420) (-972 "POLYROOT.spad" 1581049 1581071 1582156 1582161) (-971 "POLY.spad" 1578384 1578394 1578899 1579026) (-970 "POLYLIFT.spad" 1577649 1577672 1578374 1578379) (-969 "POLYCATQ.spad" 1575767 1575789 1577639 1577644) (-968 "POLYCAT.spad" 1569237 1569258 1575635 1575762) (-967 "POLYCAT.spad" 1562045 1562068 1568445 1568450) (-966 "POLY2UP.spad" 1561497 1561511 1562035 1562040) (-965 "POLY2.spad" 1561094 1561106 1561487 1561492) (-964 "POLUTIL.spad" 1560035 1560064 1561050 1561055) (-963 "POLTOPOL.spad" 1558783 1558798 1560025 1560030) (-962 "POINT.spad" 1557468 1557478 1557555 1557582) (-961 "PNTHEORY.spad" 1554170 1554178 1557458 1557463) (-960 "PMTOOLS.spad" 1552945 1552959 1554160 1554165) (-959 "PMSYM.spad" 1552494 1552504 1552935 1552940) (-958 "PMQFCAT.spad" 1552085 1552099 1552484 1552489) (-957 "PMPRED.spad" 1551564 1551578 1552075 1552080) (-956 "PMPREDFS.spad" 1551018 1551040 1551554 1551559) (-955 "PMPLCAT.spad" 1550098 1550116 1550950 1550955) (-954 "PMLSAGG.spad" 1549683 1549697 1550088 1550093) (-953 "PMKERNEL.spad" 1549262 1549274 1549673 1549678) (-952 "PMINS.spad" 1548842 1548852 1549252 1549257) (-951 "PMFS.spad" 1548419 1548437 1548832 1548837) (-950 "PMDOWN.spad" 1547709 1547723 1548409 1548414) (-949 "PMASS.spad" 1546719 1546727 1547699 1547704) (-948 "PMASSFS.spad" 1545686 1545702 1546709 1546714) (-947 "PLOTTOOL.spad" 1545466 1545474 1545676 1545681) (-946 "PLOT.spad" 1540389 1540397 1545456 1545461) (-945 "PLOT3D.spad" 1536853 1536861 1540379 1540384) (-944 "PLOT1.spad" 1536010 1536020 1536843 1536848) (-943 "PLEQN.spad" 1523300 1523327 1536000 1536005) (-942 "PINTERP.spad" 1522922 1522941 1523290 1523295) (-941 "PINTERPA.spad" 1522706 1522722 1522912 1522917) (-940 "PI.spad" 1522315 1522323 1522680 1522701) (-939 "PID.spad" 1521285 1521293 1522241 1522310) (-938 "PICOERCE.spad" 1520942 1520952 1521275 1521280) (-937 "PGROEB.spad" 1519543 1519557 1520932 1520937) (-936 "PGE.spad" 1511160 1511168 1519533 1519538) (-935 "PGCD.spad" 1510050 1510067 1511150 1511155) (-934 "PFRPAC.spad" 1509199 1509209 1510040 1510045) (-933 "PFR.spad" 1505862 1505872 1509101 1509194) (-932 "PFOTOOLS.spad" 1505120 1505136 1505852 1505857) (-931 "PFOQ.spad" 1504490 1504508 1505110 1505115) (-930 "PFO.spad" 1503909 1503936 1504480 1504485) (-929 "PF.spad" 1503483 1503495 1503714 1503807) (-928 "PFECAT.spad" 1501165 1501173 1503409 1503478) (-927 "PFECAT.spad" 1498875 1498885 1501121 1501126) (-926 "PFBRU.spad" 1496763 1496775 1498865 1498870) (-925 "PFBR.spad" 1494323 1494346 1496753 1496758) (-924 "PERM.spad" 1490130 1490140 1494153 1494168) (-923 "PERMGRP.spad" 1484900 1484910 1490120 1490125) (-922 "PERMCAT.spad" 1483561 1483571 1484880 1484895) (-921 "PERMAN.spad" 1482093 1482107 1483551 1483556) (-920 "PENDTREE.spad" 1481317 1481327 1481605 1481610) (-919 "PDSPC.spad" 1480130 1480140 1481307 1481312) (-918 "PDSPC.spad" 1478941 1478953 1480120 1480125) (-917 "PDRING.spad" 1478783 1478793 1478921 1478936) (-916 "PDMOD.spad" 1478599 1478611 1478751 1478778) (-915 "PDEPROB.spad" 1477614 1477622 1478589 1478594) (-914 "PDEPACK.spad" 1471654 1471662 1477604 1477609) (-913 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1450360 1450365) (-894 "PARSCURV.spad" 1449324 1449352 1449880 1449885) (-893 "PARSC2.spad" 1449115 1449131 1449314 1449319) (-892 "PARPCURV.spad" 1448577 1448605 1449105 1449110) (-891 "PARPC2.spad" 1448368 1448384 1448567 1448572) (-890 "PARAMAST.spad" 1447496 1447504 1448358 1448363) (-889 "PAN2EXPR.spad" 1446908 1446916 1447486 1447491) (-888 "PALETTE.spad" 1445878 1445886 1446898 1446903) (-887 "PAIR.spad" 1444865 1444878 1445466 1445471) (-886 "PADICRC.spad" 1442106 1442124 1443277 1443370) (-885 "PADICRAT.spad" 1440014 1440026 1440235 1440328) (-884 "PADIC.spad" 1439709 1439721 1439940 1440009) (-883 "PADICCT.spad" 1438258 1438270 1439635 1439704) (-882 "PADEPAC.spad" 1436947 1436966 1438248 1438253) (-881 "PADE.spad" 1435699 1435715 1436937 1436942) (-880 "OWP.spad" 1434939 1434969 1435557 1435624) (-879 "OVERSET.spad" 1434512 1434520 1434929 1434934) (-878 "OVAR.spad" 1434293 1434316 1434502 1434507) (-877 "OUT.spad" 1433379 1433387 1434283 1434288) (-876 "OUTFORM.spad" 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280072 280088 280775 280874) (-242 "DIRPCAT.spad" 278892 278910 279597 279602) (-241 "DIOSP.spad" 277717 277725 278882 278887) (-240 "DIOPS.spad" 276713 276723 277697 277712) (-239 "DIOPS.spad" 275683 275695 276669 276674) (-238 "DIFRING.spad" 275521 275529 275663 275678) (-237 "DIFFSPC.spad" 275100 275108 275511 275516) (-236 "DIFFSPC.spad" 274677 274687 275090 275095) (-235 "DIFFMOD.spad" 274166 274176 274645 274672) (-234 "DIFFDOM.spad" 273331 273342 274156 274161) (-233 "DIFFDOM.spad" 272494 272507 273321 273326) (-232 "DIFEXT.spad" 272313 272323 272474 272489) (-231 "DIAGG.spad" 271943 271953 272293 272308) (-230 "DIAGG.spad" 271581 271593 271933 271938) (-229 "DHMATRIX.spad" 269776 269786 270921 270948) (-228 "DFSFUN.spad" 263416 263424 269766 269771) (-227 "DFLOAT.spad" 260147 260155 263306 263411) (-226 "DFINTTLS.spad" 258378 258394 260137 260142) (-225 "DERHAM.spad" 256292 256324 258358 258373) (-224 "DEQUEUE.spad" 255499 255509 255782 255809) (-223 "DEGRED.spad" 255116 255130 255489 255494) (-222 "DEFINTRF.spad" 252653 252663 255106 255111) (-221 "DEFINTEF.spad" 251163 251179 252643 252648) (-220 "DEFAST.spad" 250531 250539 251153 251158) (-219 "DECIMAL.spad" 248540 248548 248901 248994) (-218 "DDFACT.spad" 246353 246370 248530 248535) (-217 "DBLRESP.spad" 245953 245977 246343 246348) (-216 "DBASE.spad" 244617 244627 245943 245948) (-215 "DATAARY.spad" 244079 244092 244607 244612) (-214 "D03FAFA.spad" 243907 243915 244069 244074) (-213 "D03EEFA.spad" 243727 243735 243897 243902) (-212 "D03AGNT.spad" 242813 242821 243717 243722) (-211 "D02EJFA.spad" 242275 242283 242803 242808) (-210 "D02CJFA.spad" 241753 241761 242265 242270) (-209 "D02BHFA.spad" 241243 241251 241743 241748) (-208 "D02BBFA.spad" 240733 240741 241233 241238) (-207 "D02AGNT.spad" 235547 235555 240723 240728) (-206 "D01WGTS.spad" 233866 233874 235537 235542) (-205 "D01TRNS.spad" 233843 233851 233856 233861) (-204 "D01GBFA.spad" 233365 233373 233833 233838) (-203 "D01FCFA.spad" 232887 232895 233355 233360) (-202 "D01ASFA.spad" 232355 232363 232877 232882) (-201 "D01AQFA.spad" 231801 231809 232345 232350) (-200 "D01APFA.spad" 231225 231233 231791 231796) (-199 "D01ANFA.spad" 230719 230727 231215 231220) (-198 "D01AMFA.spad" 230229 230237 230709 230714) (-197 "D01ALFA.spad" 229769 229777 230219 230224) (-196 "D01AKFA.spad" 229295 229303 229759 229764) (-195 "D01AJFA.spad" 228818 228826 229285 229290) (-194 "D01AGNT.spad" 224885 224893 228808 228813) (-193 "CYCLOTOM.spad" 224391 224399 224875 224880) (-192 "CYCLES.spad" 221183 221191 224381 224386) (-191 "CVMP.spad" 220600 220610 221173 221178) (-190 "CTRIGMNP.spad" 219100 219116 220590 220595) (-189 "CTOR.spad" 218791 218799 219090 219095) (-188 "CTORKIND.spad" 218394 218402 218781 218786) (-187 "CTORCAT.spad" 217643 217651 218384 218389) (-186 "CTORCAT.spad" 216890 216900 217633 217638) (-185 "CTORCALL.spad" 216479 216489 216880 216885) (-184 "CSTTOOLS.spad" 215724 215737 216469 216474) (-183 "CRFP.spad" 209448 209461 215714 215719) (-182 "CRCEAST.spad" 209168 209176 209438 209443) (-181 "CRAPACK.spad" 208219 208229 209158 209163) (-180 "CPMATCH.spad" 207723 207738 208144 208149) (-179 "CPIMA.spad" 207428 207447 207713 207718) (-178 "COORDSYS.spad" 202437 202447 207418 207423) (-177 "CONTOUR.spad" 201848 201856 202427 202432) (-176 "CONTFRAC.spad" 197598 197608 201750 201843) (-175 "CONDUIT.spad" 197356 197364 197588 197593) (-174 "COMRING.spad" 197030 197038 197294 197351) (-173 "COMPPROP.spad" 196548 196556 197020 197025) (-172 "COMPLPAT.spad" 196315 196330 196538 196543) (-171 "COMPLEX.spad" 191692 191702 191936 192197) (-170 "COMPLEX2.spad" 191407 191419 191682 191687) (-169 "COMPILER.spad" 190956 190964 191397 191402) (-168 "COMPFACT.spad" 190558 190572 190946 190951) (-167 "COMPCAT.spad" 188630 188640 190292 190553) (-166 "COMPCAT.spad" 186430 186442 188094 188099) (-165 "COMMUPC.spad" 186178 186196 186420 186425) (-164 "COMMONOP.spad" 185711 185719 186168 186173) (-163 "COMM.spad" 185522 185530 185701 185706) (-162 "COMMAAST.spad" 185285 185293 185512 185517) (-161 "COMBOPC.spad" 184200 184208 185275 185280) (-160 "COMBINAT.spad" 182967 182977 184190 184195) (-159 "COMBF.spad" 180349 180365 182957 182962) (-158 "COLOR.spad" 179186 179194 180339 180344) (-157 "COLONAST.spad" 178852 178860 179176 179181) (-156 "CMPLXRT.spad" 178563 178580 178842 178847) (-155 "CLLCTAST.spad" 178225 178233 178553 178558) (-154 "CLIP.spad" 174333 174341 178215 178220) (-153 "CLIF.spad" 172988 173004 174289 174328) (-152 "CLAGG.spad" 169493 169503 172978 172983) (-151 "CLAGG.spad" 165869 165881 169356 169361) (-150 "CINTSLPE.spad" 165200 165213 165859 165864) (-149 "CHVAR.spad" 163338 163360 165190 165195) (-148 "CHARZ.spad" 163253 163261 163318 163333) (-147 "CHARPOL.spad" 162763 162773 163243 163248) (-146 "CHARNZ.spad" 162516 162524 162743 162758) (-145 "CHAR.spad" 160390 160398 162506 162511) (-144 "CFCAT.spad" 159718 159726 160380 160385) (-143 "CDEN.spad" 158914 158928 159708 159713) (-142 "CCLASS.spad" 157025 157033 158287 158326) (-141 "CATEGORY.spad" 156067 156075 157015 157020) (-140 "CATCTOR.spad" 155958 155966 156057 156062) (-139 "CATAST.spad" 155576 155584 155948 155953) (-138 "CASEAST.spad" 155290 155298 155566 155571) (-137 "CARTEN.spad" 150657 150681 155280 155285) (-136 "CARTEN2.spad" 150047 150074 150647 150652) (-135 "CARD.spad" 147342 147350 150021 150042) (-134 "CAPSLAST.spad" 147116 147124 147332 147337) (-133 "CACHSET.spad" 146740 146748 147106 147111) (-132 "CABMON.spad" 146295 146303 146730 146735) (-131 "BYTEORD.spad" 145970 145978 146285 146290) (-130 "BYTE.spad" 145397 145405 145960 145965) (-129 "BYTEBUF.spad" 143095 143103 144405 144432) (-128 "BTREE.spad" 142051 142061 142585 142612) (-127 "BTOURN.spad" 140939 140949 141541 141568) (-126 "BTCAT.spad" 140331 140341 140907 140934) (-125 "BTCAT.spad" 139743 139755 140321 140326) (-124 "BTAGG.spad" 139209 139217 139711 139738) (-123 "BTAGG.spad" 138695 138705 139199 139204) (-122 "BSTREE.spad" 137319 137329 138185 138212) (-121 "BRILL.spad" 135516 135527 137309 137314) (-120 "BRAGG.spad" 134456 134466 135506 135511) (-119 "BRAGG.spad" 133360 133372 134412 134417) (-118 "BPADICRT.spad" 131234 131246 131489 131582) (-117 "BPADIC.spad" 130898 130910 131160 131229) (-116 "BOUNDZRO.spad" 130554 130571 130888 130893) (-115 "BOP.spad" 125736 125744 130544 130549) (-114 "BOP1.spad" 123202 123212 125726 125731) (-113 "BOOLE.spad" 122852 122860 123192 123197) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2293911 2293916 2293921 2293926) (-2 NIL 2293891 2293896 2293901 2293906) (-1 NIL 2293871 2293876 2293881 2293886) (0 NIL 2293851 2293856 2293861 2293866) (-1317 "ZMOD.spad" 2293660 2293673 2293789 2293846) (-1316 "ZLINDEP.spad" 2292726 2292737 2293650 2293655) (-1315 "ZDSOLVE.spad" 2282671 2282693 2292716 2292721) (-1314 "YSTREAM.spad" 2282166 2282177 2282661 2282666) (-1313 "YDIAGRAM.spad" 2281800 2281809 2282156 2282161) (-1312 "XRPOLY.spad" 2281020 2281040 2281656 2281725) (-1311 "XPR.spad" 2278815 2278828 2280738 2280837) (-1310 "XPOLY.spad" 2278370 2278381 2278671 2278740) (-1309 "XPOLYC.spad" 2277689 2277705 2278296 2278365) (-1308 "XPBWPOLY.spad" 2276126 2276146 2277469 2277538) (-1307 "XF.spad" 2274589 2274604 2276028 2276121) (-1306 "XF.spad" 2273032 2273049 2274473 2274478) (-1305 "XFALG.spad" 2270080 2270096 2272958 2273027) (-1304 "XEXPPKG.spad" 2269331 2269357 2270070 2270075) (-1303 "XDPOLY.spad" 2268945 2268961 2269187 2269256) (-1302 "XALG.spad" 2268605 2268616 2268901 2268940) (-1301 "WUTSET.spad" 2264408 2264425 2268215 2268242) (-1300 "WP.spad" 2263607 2263651 2264266 2264333) (-1299 "WHILEAST.spad" 2263405 2263414 2263597 2263602) (-1298 "WHEREAST.spad" 2263076 2263085 2263395 2263400) (-1297 "WFFINTBS.spad" 2260739 2260761 2263066 2263071) (-1296 "WEIER.spad" 2258961 2258972 2260729 2260734) (-1295 "VSPACE.spad" 2258634 2258645 2258929 2258956) (-1294 "VSPACE.spad" 2258327 2258340 2258624 2258629) (-1293 "VOID.spad" 2258004 2258013 2258317 2258322) (-1292 "VIEW.spad" 2255684 2255693 2257994 2257999) (-1291 "VIEWDEF.spad" 2250885 2250894 2255674 2255679) (-1290 "VIEW3D.spad" 2234846 2234855 2250875 2250880) (-1289 "VIEW2D.spad" 2222737 2222746 2234836 2234841) (-1288 "VECTOR.spad" 2221258 2221269 2221509 2221536) (-1287 "VECTOR2.spad" 2219897 2219910 2221248 2221253) (-1286 "VECTCAT.spad" 2217801 2217812 2219865 2219892) (-1285 "VECTCAT.spad" 2215512 2215525 2217578 2217583) (-1284 "VARIABLE.spad" 2215292 2215307 2215502 2215507) (-1283 "UTYPE.spad" 2214936 2214945 2215282 2215287) (-1282 "UTSODETL.spad" 2214231 2214255 2214892 2214897) (-1281 "UTSODE.spad" 2212447 2212467 2214221 2214226) (-1280 "UTS.spad" 2207394 2207422 2210914 2211011) (-1279 "UTSCAT.spad" 2204873 2204889 2207292 2207389) (-1278 "UTSCAT.spad" 2201996 2202014 2204417 2204422) (-1277 "UTS2.spad" 2201591 2201626 2201986 2201991) (-1276 "URAGG.spad" 2196264 2196275 2201581 2201586) (-1275 "URAGG.spad" 2190901 2190914 2196220 2196225) (-1274 "UPXSSING.spad" 2188546 2188572 2189982 2190115) (-1273 "UPXS.spad" 2185842 2185870 2186678 2186827) (-1272 "UPXSCONS.spad" 2183601 2183621 2183974 2184123) (-1271 "UPXSCCA.spad" 2182172 2182192 2183447 2183596) (-1270 "UPXSCCA.spad" 2180885 2180907 2182162 2182167) (-1269 "UPXSCAT.spad" 2179474 2179490 2180731 2180880) (-1268 "UPXS2.spad" 2179017 2179070 2179464 2179469) (-1267 "UPSQFREE.spad" 2177431 2177445 2179007 2179012) (-1266 "UPSCAT.spad" 2175218 2175242 2177329 2177426) (-1265 "UPSCAT.spad" 2172711 2172737 2174824 2174829) (-1264 "UPOLYC.spad" 2167751 2167762 2172553 2172706) (-1263 "UPOLYC.spad" 2162683 2162696 2167487 2167492) (-1262 "UPOLYC2.spad" 2162154 2162173 2162673 2162678) (-1261 "UP.spad" 2159260 2159275 2159647 2159800) (-1260 "UPMP.spad" 2158160 2158173 2159250 2159255) (-1259 "UPDIVP.spad" 2157725 2157739 2158150 2158155) (-1258 "UPDECOMP.spad" 2155970 2155984 2157715 2157720) (-1257 "UPCDEN.spad" 2155179 2155195 2155960 2155965) (-1256 "UP2.spad" 2154543 2154564 2155169 2155174) (-1255 "UNISEG.spad" 2153896 2153907 2154462 2154467) (-1254 "UNISEG2.spad" 2153393 2153406 2153852 2153857) (-1253 "UNIFACT.spad" 2152496 2152508 2153383 2153388) (-1252 "ULS.spad" 2142280 2142308 2143225 2143654) (-1251 "ULSCONS.spad" 2133414 2133434 2133784 2133933) (-1250 "ULSCCAT.spad" 2131151 2131171 2133260 2133409) (-1249 "ULSCCAT.spad" 2128996 2129018 2131107 2131112) (-1248 "ULSCAT.spad" 2127228 2127244 2128842 2128991) (-1247 "ULS2.spad" 2126742 2126795 2127218 2127223) (-1246 "UINT8.spad" 2126619 2126628 2126732 2126737) (-1245 "UINT64.spad" 2126495 2126504 2126609 2126614) (-1244 "UINT32.spad" 2126371 2126380 2126485 2126490) (-1243 "UINT16.spad" 2126247 2126256 2126361 2126366) (-1242 "UFD.spad" 2125312 2125321 2126173 2126242) (-1241 "UFD.spad" 2124439 2124450 2125302 2125307) (-1240 "UDVO.spad" 2123320 2123329 2124429 2124434) (-1239 "UDPO.spad" 2120813 2120824 2123276 2123281) (-1238 "TYPE.spad" 2120745 2120754 2120803 2120808) (-1237 "TYPEAST.spad" 2120664 2120673 2120735 2120740) (-1236 "TWOFACT.spad" 2119316 2119331 2120654 2120659) (-1235 "TUPLE.spad" 2118802 2118813 2119215 2119220) (-1234 "TUBETOOL.spad" 2115669 2115678 2118792 2118797) (-1233 "TUBE.spad" 2114316 2114333 2115659 2115664) (-1232 "TS.spad" 2112915 2112931 2113881 2113978) (-1231 "TSETCAT.spad" 2100042 2100059 2112883 2112910) (-1230 "TSETCAT.spad" 2087155 2087174 2099998 2100003) (-1229 "TRMANIP.spad" 2081521 2081538 2086861 2086866) (-1228 "TRIMAT.spad" 2080484 2080509 2081511 2081516) (-1227 "TRIGMNIP.spad" 2079011 2079028 2080474 2080479) (-1226 "TRIGCAT.spad" 2078523 2078532 2079001 2079006) (-1225 "TRIGCAT.spad" 2078033 2078044 2078513 2078518) (-1224 "TREE.spad" 2076491 2076502 2077523 2077550) (-1223 "TRANFUN.spad" 2076330 2076339 2076481 2076486) (-1222 "TRANFUN.spad" 2076167 2076178 2076320 2076325) (-1221 "TOPSP.spad" 2075841 2075850 2076157 2076162) (-1220 "TOOLSIGN.spad" 2075504 2075515 2075831 2075836) (-1219 "TEXTFILE.spad" 2074065 2074074 2075494 2075499) (-1218 "TEX.spad" 2071211 2071220 2074055 2074060) (-1217 "TEX1.spad" 2070767 2070778 2071201 2071206) (-1216 "TEMUTL.spad" 2070322 2070331 2070757 2070762) (-1215 "TBCMPPK.spad" 2068415 2068438 2070312 2070317) (-1214 "TBAGG.spad" 2067465 2067488 2068395 2068410) (-1213 "TBAGG.spad" 2066523 2066548 2067455 2067460) (-1212 "TANEXP.spad" 2065931 2065942 2066513 2066518) (-1211 "TALGOP.spad" 2065655 2065666 2065921 2065926) (-1210 "TABLE.spad" 2063624 2063647 2063894 2063921) (-1209 "TABLEAU.spad" 2063105 2063116 2063614 2063619) (-1208 "TABLBUMP.spad" 2059908 2059919 2063095 2063100) (-1207 "SYSTEM.spad" 2059136 2059145 2059898 2059903) (-1206 "SYSSOLP.spad" 2056619 2056630 2059126 2059131) (-1205 "SYSPTR.spad" 2056518 2056527 2056609 2056614) (-1204 "SYSNNI.spad" 2055700 2055711 2056508 2056513) (-1203 "SYSINT.spad" 2055104 2055115 2055690 2055695) (-1202 "SYNTAX.spad" 2051310 2051319 2055094 2055099) (-1201 "SYMTAB.spad" 2049378 2049387 2051300 2051305) (-1200 "SYMS.spad" 2045401 2045410 2049368 2049373) (-1199 "SYMPOLY.spad" 2044408 2044419 2044490 2044617) (-1198 "SYMFUNC.spad" 2043909 2043920 2044398 2044403) (-1197 "SYMBOL.spad" 2041412 2041421 2043899 2043904) (-1196 "SWITCH.spad" 2038183 2038192 2041402 2041407) (-1195 "SUTS.spad" 2035231 2035259 2036650 2036747) (-1194 "SUPXS.spad" 2032514 2032542 2033363 2033512) (-1193 "SUP.spad" 2029234 2029245 2030007 2030160) (-1192 "SUPFRACF.spad" 2028339 2028357 2029224 2029229) (-1191 "SUP2.spad" 2027731 2027744 2028329 2028334) (-1190 "SUMRF.spad" 2026705 2026716 2027721 2027726) (-1189 "SUMFS.spad" 2026342 2026359 2026695 2026700) (-1188 "SULS.spad" 2016113 2016141 2017071 2017500) (-1187 "SUCHTAST.spad" 2015882 2015891 2016103 2016108) (-1186 "SUCH.spad" 2015564 2015579 2015872 2015877) (-1185 "SUBSPACE.spad" 2007679 2007694 2015554 2015559) (-1184 "SUBRESP.spad" 2006849 2006863 2007635 2007640) (-1183 "STTF.spad" 2002948 2002964 2006839 2006844) (-1182 "STTFNC.spad" 1999416 1999432 2002938 2002943) (-1181 "STTAYLOR.spad" 1992051 1992062 1999297 1999302) (-1180 "STRTBL.spad" 1990102 1990119 1990251 1990278) (-1179 "STRING.spad" 1988889 1988898 1989110 1989137) (-1178 "STREAM.spad" 1985690 1985701 1988297 1988312) (-1177 "STREAM3.spad" 1985263 1985278 1985680 1985685) (-1176 "STREAM2.spad" 1984391 1984404 1985253 1985258) (-1175 "STREAM1.spad" 1984097 1984108 1984381 1984386) (-1174 "STINPROD.spad" 1983033 1983049 1984087 1984092) (-1173 "STEP.spad" 1982234 1982243 1983023 1983028) (-1172 "STEPAST.spad" 1981468 1981477 1982224 1982229) (-1171 "STBL.spad" 1979552 1979580 1979719 1979734) (-1170 "STAGG.spad" 1978627 1978638 1979542 1979547) (-1169 "STAGG.spad" 1977700 1977713 1978617 1978622) (-1168 "STACK.spad" 1976940 1976951 1977190 1977217) (-1167 "SREGSET.spad" 1974608 1974625 1976550 1976577) (-1166 "SRDCMPK.spad" 1973169 1973189 1974598 1974603) (-1165 "SRAGG.spad" 1968312 1968321 1973137 1973164) (-1164 "SRAGG.spad" 1963475 1963486 1968302 1968307) (-1163 "SQMATRIX.spad" 1961018 1961036 1961934 1962021) (-1162 "SPLTREE.spad" 1955414 1955427 1960298 1960325) (-1161 "SPLNODE.spad" 1952002 1952015 1955404 1955409) (-1160 "SPFCAT.spad" 1950811 1950820 1951992 1951997) (-1159 "SPECOUT.spad" 1949363 1949372 1950801 1950806) (-1158 "SPADXPT.spad" 1940958 1940967 1949353 1949358) (-1157 "spad-parser.spad" 1940423 1940432 1940948 1940953) (-1156 "SPADAST.spad" 1940124 1940133 1940413 1940418) (-1155 "SPACEC.spad" 1924323 1924334 1940114 1940119) (-1154 "SPACE3.spad" 1924099 1924110 1924313 1924318) (-1153 "SORTPAK.spad" 1923648 1923661 1924055 1924060) (-1152 "SOLVETRA.spad" 1921411 1921422 1923638 1923643) (-1151 "SOLVESER.spad" 1919939 1919950 1921401 1921406) (-1150 "SOLVERAD.spad" 1915965 1915976 1919929 1919934) (-1149 "SOLVEFOR.spad" 1914427 1914445 1915955 1915960) (-1148 "SNTSCAT.spad" 1914027 1914044 1914395 1914422) (-1147 "SMTS.spad" 1912299 1912325 1913592 1913689) (-1146 "SMP.spad" 1909774 1909794 1910164 1910291) (-1145 "SMITH.spad" 1908619 1908644 1909764 1909769) (-1144 "SMATCAT.spad" 1906729 1906759 1908563 1908614) (-1143 "SMATCAT.spad" 1904771 1904803 1906607 1906612) (-1142 "SKAGG.spad" 1903734 1903745 1904739 1904766) (-1141 "SINT.spad" 1902674 1902683 1903600 1903729) (-1140 "SIMPAN.spad" 1902402 1902411 1902664 1902669) (-1139 "SIG.spad" 1901732 1901741 1902392 1902397) (-1138 "SIGNRF.spad" 1900850 1900861 1901722 1901727) (-1137 "SIGNEF.spad" 1900129 1900146 1900840 1900845) (-1136 "SIGAST.spad" 1899514 1899523 1900119 1900124) (-1135 "SHP.spad" 1897442 1897457 1899470 1899475) (-1134 "SHDP.spad" 1885120 1885147 1885629 1885728) (-1133 "SGROUP.spad" 1884728 1884737 1885110 1885115) (-1132 "SGROUP.spad" 1884334 1884345 1884718 1884723) (-1131 "SGCF.spad" 1877473 1877482 1884324 1884329) (-1130 "SFRTCAT.spad" 1876403 1876420 1877441 1877468) (-1129 "SFRGCD.spad" 1875466 1875486 1876393 1876398) (-1128 "SFQCMPK.spad" 1870103 1870123 1875456 1875461) (-1127 "SFORT.spad" 1869542 1869556 1870093 1870098) (-1126 "SEXOF.spad" 1869385 1869425 1869532 1869537) (-1125 "SEX.spad" 1869277 1869286 1869375 1869380) (-1124 "SEXCAT.spad" 1867049 1867089 1869267 1869272) (-1123 "SET.spad" 1865337 1865348 1866434 1866473) (-1122 "SETMN.spad" 1863787 1863804 1865327 1865332) (-1121 "SETCAT.spad" 1863272 1863281 1863777 1863782) (-1120 "SETCAT.spad" 1862755 1862766 1863262 1863267) (-1119 "SETAGG.spad" 1859304 1859315 1862735 1862750) (-1118 "SETAGG.spad" 1855861 1855874 1859294 1859299) (-1117 "SEQAST.spad" 1855564 1855573 1855851 1855856) (-1116 "SEGXCAT.spad" 1854720 1854733 1855554 1855559) (-1115 "SEG.spad" 1854533 1854544 1854639 1854644) (-1114 "SEGCAT.spad" 1853458 1853469 1854523 1854528) (-1113 "SEGBIND.spad" 1853216 1853227 1853405 1853410) (-1112 "SEGBIND2.spad" 1852914 1852927 1853206 1853211) (-1111 "SEGAST.spad" 1852628 1852637 1852904 1852909) (-1110 "SEG2.spad" 1852063 1852076 1852584 1852589) (-1109 "SDVAR.spad" 1851339 1851350 1852053 1852058) (-1108 "SDPOL.spad" 1848672 1848683 1848963 1849090) (-1107 "SCPKG.spad" 1846761 1846772 1848662 1848667) (-1106 "SCOPE.spad" 1845914 1845923 1846751 1846756) (-1105 "SCACHE.spad" 1844610 1844621 1845904 1845909) (-1104 "SASTCAT.spad" 1844519 1844528 1844600 1844605) (-1103 "SAOS.spad" 1844391 1844400 1844509 1844514) (-1102 "SAERFFC.spad" 1844104 1844124 1844381 1844386) (-1101 "SAE.spad" 1841574 1841590 1842185 1842320) (-1100 "SAEFACT.spad" 1841275 1841295 1841564 1841569) (-1099 "RURPK.spad" 1838934 1838950 1841265 1841270) (-1098 "RULESET.spad" 1838387 1838411 1838924 1838929) (-1097 "RULE.spad" 1836627 1836651 1838377 1838382) (-1096 "RULECOLD.spad" 1836479 1836492 1836617 1836622) (-1095 "RTVALUE.spad" 1836214 1836223 1836469 1836474) (-1094 "RSTRCAST.spad" 1835931 1835940 1836204 1836209) (-1093 "RSETGCD.spad" 1832309 1832329 1835921 1835926) (-1092 "RSETCAT.spad" 1822245 1822262 1832277 1832304) (-1091 "RSETCAT.spad" 1812201 1812220 1822235 1822240) (-1090 "RSDCMPK.spad" 1810653 1810673 1812191 1812196) (-1089 "RRCC.spad" 1809037 1809067 1810643 1810648) (-1088 "RRCC.spad" 1807419 1807451 1809027 1809032) (-1087 "RPTAST.spad" 1807121 1807130 1807409 1807414) (-1086 "RPOLCAT.spad" 1786481 1786496 1806989 1807116) (-1085 "RPOLCAT.spad" 1765554 1765571 1786064 1786069) (-1084 "ROUTINE.spad" 1760975 1760984 1763739 1763766) (-1083 "ROMAN.spad" 1760303 1760312 1760841 1760970) (-1082 "ROIRC.spad" 1759383 1759415 1760293 1760298) (-1081 "RNS.spad" 1758286 1758295 1759285 1759378) (-1080 "RNS.spad" 1757275 1757286 1758276 1758281) (-1079 "RNG.spad" 1757010 1757019 1757265 1757270) (-1078 "RNGBIND.spad" 1756170 1756184 1756965 1756970) (-1077 "RMODULE.spad" 1755935 1755946 1756160 1756165) (-1076 "RMCAT2.spad" 1755355 1755412 1755925 1755930) (-1075 "RMATRIX.spad" 1754143 1754162 1754486 1754525) (-1074 "RMATCAT.spad" 1749722 1749753 1754099 1754138) (-1073 "RMATCAT.spad" 1745191 1745224 1749570 1749575) (-1072 "RLINSET.spad" 1744895 1744906 1745181 1745186) (-1071 "RINTERP.spad" 1744783 1744803 1744885 1744890) (-1070 "RING.spad" 1744253 1744262 1744763 1744778) (-1069 "RING.spad" 1743731 1743742 1744243 1744248) (-1068 "RIDIST.spad" 1743123 1743132 1743721 1743726) (-1067 "RGCHAIN.spad" 1741651 1741667 1742553 1742580) (-1066 "RGBCSPC.spad" 1741432 1741444 1741641 1741646) (-1065 "RGBCMDL.spad" 1740962 1740974 1741422 1741427) (-1064 "RF.spad" 1738604 1738615 1740952 1740957) (-1063 "RFFACTOR.spad" 1738066 1738077 1738594 1738599) (-1062 "RFFACT.spad" 1737801 1737813 1738056 1738061) (-1061 "RFDIST.spad" 1736797 1736806 1737791 1737796) (-1060 "RETSOL.spad" 1736216 1736229 1736787 1736792) (-1059 "RETRACT.spad" 1735644 1735655 1736206 1736211) (-1058 "RETRACT.spad" 1735070 1735083 1735634 1735639) (-1057 "RETAST.spad" 1734882 1734891 1735060 1735065) (-1056 "RESULT.spad" 1732480 1732489 1733067 1733094) (-1055 "RESRING.spad" 1731827 1731874 1732418 1732475) (-1054 "RESLATC.spad" 1731151 1731162 1731817 1731822) (-1053 "REPSQ.spad" 1730882 1730893 1731141 1731146) (-1052 "REP.spad" 1728436 1728445 1730872 1730877) (-1051 "REPDB.spad" 1728143 1728154 1728426 1728431) (-1050 "REP2.spad" 1717801 1717812 1727985 1727990) (-1049 "REP1.spad" 1711997 1712008 1717751 1717756) (-1048 "REGSET.spad" 1709758 1709775 1711607 1711634) (-1047 "REF.spad" 1709093 1709104 1709713 1709718) (-1046 "REDORDER.spad" 1708299 1708316 1709083 1709088) (-1045 "RECLOS.spad" 1707082 1707102 1707786 1707879) (-1044 "REALSOLV.spad" 1706222 1706231 1707072 1707077) (-1043 "REAL.spad" 1706094 1706103 1706212 1706217) (-1042 "REAL0Q.spad" 1703392 1703407 1706084 1706089) (-1041 "REAL0.spad" 1700236 1700251 1703382 1703387) (-1040 "RDUCEAST.spad" 1699957 1699966 1700226 1700231) (-1039 "RDIV.spad" 1699612 1699637 1699947 1699952) (-1038 "RDIST.spad" 1699179 1699190 1699602 1699607) (-1037 "RDETRS.spad" 1698043 1698061 1699169 1699174) (-1036 "RDETR.spad" 1696182 1696200 1698033 1698038) (-1035 "RDEEFS.spad" 1695281 1695298 1696172 1696177) (-1034 "RDEEF.spad" 1694291 1694308 1695271 1695276) (-1033 "RCFIELD.spad" 1691477 1691486 1694193 1694286) (-1032 "RCFIELD.spad" 1688749 1688760 1691467 1691472) (-1031 "RCAGG.spad" 1686677 1686688 1688739 1688744) (-1030 "RCAGG.spad" 1684532 1684545 1686596 1686601) (-1029 "RATRET.spad" 1683892 1683903 1684522 1684527) (-1028 "RATFACT.spad" 1683584 1683596 1683882 1683887) (-1027 "RANDSRC.spad" 1682903 1682912 1683574 1683579) (-1026 "RADUTIL.spad" 1682659 1682668 1682893 1682898) (-1025 "RADIX.spad" 1679483 1679497 1681029 1681122) (-1024 "RADFF.spad" 1677222 1677259 1677341 1677497) (-1023 "RADCAT.spad" 1676817 1676826 1677212 1677217) (-1022 "RADCAT.spad" 1676410 1676421 1676807 1676812) (-1021 "QUEUE.spad" 1675641 1675652 1675900 1675927) (-1020 "QUAT.spad" 1674129 1674140 1674472 1674537) (-1019 "QUATCT2.spad" 1673749 1673768 1674119 1674124) (-1018 "QUATCAT.spad" 1671919 1671930 1673679 1673744) (-1017 "QUATCAT.spad" 1669840 1669853 1671602 1671607) (-1016 "QUAGG.spad" 1668667 1668678 1669808 1669835) (-1015 "QQUTAST.spad" 1668435 1668444 1668657 1668662) (-1014 "QFORM.spad" 1668053 1668068 1668425 1668430) (-1013 "QFCAT.spad" 1666755 1666766 1667955 1668048) (-1012 "QFCAT.spad" 1665048 1665061 1666250 1666255) (-1011 "QFCAT2.spad" 1664740 1664757 1665038 1665043) (-1010 "QEQUAT.spad" 1664298 1664307 1664730 1664735) (-1009 "QCMPACK.spad" 1659044 1659064 1664288 1664293) (-1008 "QALGSET.spad" 1655122 1655155 1658958 1658963) (-1007 "QALGSET2.spad" 1653117 1653136 1655112 1655117) (-1006 "PWFFINTB.spad" 1650532 1650554 1653107 1653112) (-1005 "PUSHVAR.spad" 1649870 1649890 1650522 1650527) (-1004 "PTRANFN.spad" 1645997 1646008 1649860 1649865) (-1003 "PTPACK.spad" 1643084 1643095 1645987 1645992) (-1002 "PTFUNC2.spad" 1642906 1642921 1643074 1643079) (-1001 "PTCAT.spad" 1642160 1642171 1642874 1642901) (-1000 "PSQFR.spad" 1641466 1641491 1642150 1642155) (-999 "PSEUDLIN.spad" 1640352 1640362 1641456 1641461) (-998 "PSETPK.spad" 1625785 1625801 1640230 1640235) (-997 "PSETCAT.spad" 1619705 1619728 1625765 1625780) (-996 "PSETCAT.spad" 1613599 1613624 1619661 1619666) (-995 "PSCURVE.spad" 1612582 1612590 1613589 1613594) (-994 "PSCAT.spad" 1611365 1611394 1612480 1612577) (-993 "PSCAT.spad" 1610238 1610269 1611355 1611360) (-992 "PRTITION.spad" 1608936 1608944 1610228 1610233) (-991 "PRTDAST.spad" 1608655 1608663 1608926 1608931) (-990 "PRS.spad" 1598217 1598234 1608611 1608616) (-989 "PRQAGG.spad" 1597652 1597662 1598185 1598212) (-988 "PROPLOG.spad" 1597224 1597232 1597642 1597647) (-987 "PROPFUN2.spad" 1596847 1596860 1597214 1597219) (-986 "PROPFUN1.spad" 1596245 1596256 1596837 1596842) (-985 "PROPFRML.spad" 1594813 1594824 1596235 1596240) (-984 "PROPERTY.spad" 1594301 1594309 1594803 1594808) (-983 "PRODUCT.spad" 1591983 1591995 1592267 1592322) (-982 "PR.spad" 1590375 1590387 1591074 1591201) (-981 "PRINT.spad" 1590127 1590135 1590365 1590370) (-980 "PRIMES.spad" 1588380 1588390 1590117 1590122) (-979 "PRIMELT.spad" 1586461 1586475 1588370 1588375) (-978 "PRIMCAT.spad" 1586088 1586096 1586451 1586456) (-977 "PRIMARR.spad" 1584940 1584950 1585118 1585145) (-976 "PRIMARR2.spad" 1583707 1583719 1584930 1584935) (-975 "PREASSOC.spad" 1583089 1583101 1583697 1583702) (-974 "PPCURVE.spad" 1582226 1582234 1583079 1583084) (-973 "PORTNUM.spad" 1582001 1582009 1582216 1582221) (-972 "POLYROOT.spad" 1580850 1580872 1581957 1581962) (-971 "POLY.spad" 1578185 1578195 1578700 1578827) (-970 "POLYLIFT.spad" 1577450 1577473 1578175 1578180) (-969 "POLYCATQ.spad" 1575568 1575590 1577440 1577445) (-968 "POLYCAT.spad" 1569038 1569059 1575436 1575563) (-967 "POLYCAT.spad" 1561846 1561869 1568246 1568251) (-966 "POLY2UP.spad" 1561298 1561312 1561836 1561841) (-965 "POLY2.spad" 1560895 1560907 1561288 1561293) (-964 "POLUTIL.spad" 1559836 1559865 1560851 1560856) (-963 "POLTOPOL.spad" 1558584 1558599 1559826 1559831) (-962 "POINT.spad" 1557269 1557279 1557356 1557383) (-961 "PNTHEORY.spad" 1553971 1553979 1557259 1557264) (-960 "PMTOOLS.spad" 1552746 1552760 1553961 1553966) (-959 "PMSYM.spad" 1552295 1552305 1552736 1552741) (-958 "PMQFCAT.spad" 1551886 1551900 1552285 1552290) (-957 "PMPRED.spad" 1551365 1551379 1551876 1551881) (-956 "PMPREDFS.spad" 1550819 1550841 1551355 1551360) (-955 "PMPLCAT.spad" 1549899 1549917 1550751 1550756) (-954 "PMLSAGG.spad" 1549484 1549498 1549889 1549894) (-953 "PMKERNEL.spad" 1549063 1549075 1549474 1549479) (-952 "PMINS.spad" 1548643 1548653 1549053 1549058) (-951 "PMFS.spad" 1548220 1548238 1548633 1548638) (-950 "PMDOWN.spad" 1547510 1547524 1548210 1548215) (-949 "PMASS.spad" 1546520 1546528 1547500 1547505) (-948 "PMASSFS.spad" 1545487 1545503 1546510 1546515) (-947 "PLOTTOOL.spad" 1545267 1545275 1545477 1545482) (-946 "PLOT.spad" 1540190 1540198 1545257 1545262) (-945 "PLOT3D.spad" 1536654 1536662 1540180 1540185) (-944 "PLOT1.spad" 1535811 1535821 1536644 1536649) (-943 "PLEQN.spad" 1523101 1523128 1535801 1535806) (-942 "PINTERP.spad" 1522723 1522742 1523091 1523096) (-941 "PINTERPA.spad" 1522507 1522523 1522713 1522718) (-940 "PI.spad" 1522116 1522124 1522481 1522502) (-939 "PID.spad" 1521086 1521094 1522042 1522111) (-938 "PICOERCE.spad" 1520743 1520753 1521076 1521081) (-937 "PGROEB.spad" 1519344 1519358 1520733 1520738) (-936 "PGE.spad" 1510961 1510969 1519334 1519339) (-935 "PGCD.spad" 1509851 1509868 1510951 1510956) (-934 "PFRPAC.spad" 1509000 1509010 1509841 1509846) (-933 "PFR.spad" 1505663 1505673 1508902 1508995) (-932 "PFOTOOLS.spad" 1504921 1504937 1505653 1505658) (-931 "PFOQ.spad" 1504291 1504309 1504911 1504916) (-930 "PFO.spad" 1503710 1503737 1504281 1504286) (-929 "PF.spad" 1503284 1503296 1503515 1503608) (-928 "PFECAT.spad" 1500966 1500974 1503210 1503279) (-927 "PFECAT.spad" 1498676 1498686 1500922 1500927) (-926 "PFBRU.spad" 1496564 1496576 1498666 1498671) (-925 "PFBR.spad" 1494124 1494147 1496554 1496559) (-924 "PERM.spad" 1489931 1489941 1493954 1493969) (-923 "PERMGRP.spad" 1484701 1484711 1489921 1489926) (-922 "PERMCAT.spad" 1483362 1483372 1484681 1484696) (-921 "PERMAN.spad" 1481894 1481908 1483352 1483357) (-920 "PENDTREE.spad" 1481118 1481128 1481406 1481411) (-919 "PDSPC.spad" 1479931 1479941 1481108 1481113) (-918 "PDSPC.spad" 1478742 1478754 1479921 1479926) (-917 "PDRING.spad" 1478584 1478594 1478722 1478737) (-916 "PDMOD.spad" 1478400 1478412 1478552 1478579) (-915 "PDEPROB.spad" 1477415 1477423 1478390 1478395) (-914 "PDEPACK.spad" 1471455 1471463 1477405 1477410) (-913 "PDECOMP.spad" 1470925 1470942 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1433175) (-875 "OUTBFILE.spad" 1421990 1421998 1422562 1422567) (-874 "OUTBCON.spad" 1420996 1421004 1421980 1421985) (-873 "OUTBCON.spad" 1420000 1420010 1420986 1420991) (-872 "OSI.spad" 1419475 1419483 1419990 1419995) (-871 "OSGROUP.spad" 1419393 1419401 1419465 1419470) (-870 "ORTHPOL.spad" 1417878 1417888 1419310 1419315) (-869 "OREUP.spad" 1417331 1417359 1417558 1417597) (-868 "ORESUP.spad" 1416632 1416656 1417011 1417050) (-867 "OREPCTO.spad" 1414489 1414501 1416552 1416557) (-866 "OREPCAT.spad" 1408636 1408646 1414445 1414484) (-865 "OREPCAT.spad" 1402673 1402685 1408484 1408489) (-864 "ORDTYPE.spad" 1401910 1401918 1402663 1402668) (-863 "ORDTYPE.spad" 1401145 1401155 1401900 1401905) (-862 "ORDSTRCT.spad" 1400972 1400987 1401135 1401140) (-861 "ORDSET.spad" 1400672 1400680 1400962 1400967) (-860 "ORDRING.spad" 1400062 1400070 1400652 1400667) (-859 "ORDRING.spad" 1399460 1399470 1400052 1400057) (-858 "ORDMON.spad" 1399315 1399323 1399450 1399455) (-857 "ORDFUNS.spad" 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(-819 "ODEPRIM.spad" 1332966 1332988 1335622 1335627) (-818 "ODEPAL.spad" 1332352 1332376 1332956 1332961) (-817 "ODEPACK.spad" 1319018 1319026 1332342 1332347) (-816 "ODEINT.spad" 1318453 1318469 1319008 1319013) (-815 "ODEIFTBL.spad" 1315848 1315856 1318443 1318448) (-814 "ODEEF.spad" 1311339 1311355 1315838 1315843) (-813 "ODECONST.spad" 1310876 1310894 1311329 1311334) (-812 "ODECAT.spad" 1309474 1309482 1310866 1310871) (-811 "OCT.spad" 1307610 1307620 1308324 1308363) (-810 "OCTCT2.spad" 1307256 1307277 1307600 1307605) (-809 "OC.spad" 1305052 1305062 1307212 1307251) (-808 "OC.spad" 1302573 1302585 1304735 1304740) (-807 "OCAMON.spad" 1302421 1302429 1302563 1302568) (-806 "OASGP.spad" 1302236 1302244 1302411 1302416) (-805 "OAMONS.spad" 1301758 1301766 1302226 1302231) (-804 "OAMON.spad" 1301619 1301627 1301748 1301753) (-803 "OAGROUP.spad" 1301481 1301489 1301609 1301614) (-802 "NUMTUBE.spad" 1301072 1301088 1301471 1301476) (-801 "NUMQUAD.spad" 1289048 1289056 1301062 1301067) (-800 "NUMODE.spad" 1280402 1280410 1289038 1289043) (-799 "NUMINT.spad" 1277968 1277976 1280392 1280397) (-798 "NUMFMT.spad" 1276808 1276816 1277958 1277963) (-797 "NUMERIC.spad" 1268922 1268932 1276613 1276618) (-796 "NTSCAT.spad" 1267430 1267446 1268890 1268917) (-795 "NTPOLFN.spad" 1266981 1266991 1267347 1267352) (-794 "NSUP.spad" 1259934 1259944 1264474 1264627) (-793 "NSUP2.spad" 1259326 1259338 1259924 1259929) (-792 "NSMP.spad" 1255556 1255575 1255864 1255991) (-791 "NREP.spad" 1253934 1253948 1255546 1255551) (-790 "NPCOEF.spad" 1253180 1253200 1253924 1253929) (-789 "NORMRETR.spad" 1252778 1252817 1253170 1253175) (-788 "NORMPK.spad" 1250680 1250699 1252768 1252773) (-787 "NORMMA.spad" 1250368 1250394 1250670 1250675) (-786 "NONE.spad" 1250109 1250117 1250358 1250363) (-785 "NONE1.spad" 1249785 1249795 1250099 1250104) (-784 "NODE1.spad" 1249272 1249288 1249775 1249780) (-783 "NNI.spad" 1248167 1248175 1249246 1249267) (-782 "NLINSOL.spad" 1246793 1246803 1248157 1248162) (-781 "NIPROB.spad" 1245334 1245342 1246783 1246788) (-780 "NFINTBAS.spad" 1242894 1242911 1245324 1245329) (-779 "NETCLT.spad" 1242868 1242879 1242884 1242889) (-778 "NCODIV.spad" 1241084 1241100 1242858 1242863) (-777 "NCNTFRAC.spad" 1240726 1240740 1241074 1241079) (-776 "NCEP.spad" 1238892 1238906 1240716 1240721) (-775 "NASRING.spad" 1238488 1238496 1238882 1238887) (-774 "NASRING.spad" 1238082 1238092 1238478 1238483) (-773 "NARNG.spad" 1237434 1237442 1238072 1238077) (-772 "NARNG.spad" 1236784 1236794 1237424 1237429) (-771 "NAGSP.spad" 1235861 1235869 1236774 1236779) (-770 "NAGS.spad" 1225522 1225530 1235851 1235856) (-769 "NAGF07.spad" 1223953 1223961 1225512 1225517) (-768 "NAGF04.spad" 1218355 1218363 1223943 1223948) (-767 "NAGF02.spad" 1212424 1212432 1218345 1218350) (-766 "NAGF01.spad" 1208185 1208193 1212414 1212419) (-765 "NAGE04.spad" 1201885 1201893 1208175 1208180) (-764 "NAGE02.spad" 1192545 1192553 1201875 1201880) (-763 "NAGE01.spad" 1188547 1188555 1192535 1192540) (-762 "NAGD03.spad" 1186551 1186559 1188537 1188542) (-761 "NAGD02.spad" 1179298 1179306 1186541 1186546) (-760 "NAGD01.spad" 1173591 1173599 1179288 1179293) (-759 "NAGC06.spad" 1169466 1169474 1173581 1173586) (-758 "NAGC05.spad" 1167967 1167975 1169456 1169461) (-757 "NAGC02.spad" 1167234 1167242 1167957 1167962) (-756 "NAALG.spad" 1166775 1166785 1167202 1167229) (-755 "NAALG.spad" 1166336 1166348 1166765 1166770) (-754 "MULTSQFR.spad" 1163294 1163311 1166326 1166331) (-753 "MULTFACT.spad" 1162677 1162694 1163284 1163289) (-752 "MTSCAT.spad" 1160771 1160792 1162575 1162672) (-751 "MTHING.spad" 1160430 1160440 1160761 1160766) (-750 "MSYSCMD.spad" 1159864 1159872 1160420 1160425) (-749 "MSET.spad" 1157786 1157796 1159534 1159573) (-748 "MSETAGG.spad" 1157631 1157641 1157754 1157781) (-747 "MRING.spad" 1154608 1154620 1157339 1157406) (-746 "MRF2.spad" 1154178 1154192 1154598 1154603) (-745 "MRATFAC.spad" 1153724 1153741 1154168 1154173) (-744 "MPRFF.spad" 1151764 1151783 1153714 1153719) (-743 "MPOLY.spad" 1149235 1149250 1149594 1149721) (-742 "MPCPF.spad" 1148499 1148518 1149225 1149230) (-741 "MPC3.spad" 1148316 1148356 1148489 1148494) (-740 "MPC2.spad" 1147962 1147995 1148306 1148311) (-739 "MONOTOOL.spad" 1146313 1146330 1147952 1147957) (-738 "MONOID.spad" 1145632 1145640 1146303 1146308) (-737 "MONOID.spad" 1144949 1144959 1145622 1145627) (-736 "MONOGEN.spad" 1143697 1143710 1144809 1144944) (-735 "MONOGEN.spad" 1142467 1142482 1143581 1143586) (-734 "MONADWU.spad" 1140497 1140505 1142457 1142462) (-733 "MONADWU.spad" 1138525 1138535 1140487 1140492) (-732 "MONAD.spad" 1137685 1137693 1138515 1138520) (-731 "MONAD.spad" 1136843 1136853 1137675 1137680) (-730 "MOEBIUS.spad" 1135579 1135593 1136823 1136838) (-729 "MODULE.spad" 1135449 1135459 1135547 1135574) (-728 "MODULE.spad" 1135339 1135351 1135439 1135444) (-727 "MODRING.spad" 1134674 1134713 1135319 1135334) (-726 "MODOP.spad" 1133339 1133351 1134496 1134563) (-725 "MODMONOM.spad" 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1072855 1072860) (-687 "M3D.spad" 1070047 1070057 1071705 1071710) (-686 "LZSTAGG.spad" 1067285 1067295 1070037 1070042) (-685 "LZSTAGG.spad" 1064521 1064533 1067275 1067280) (-684 "LWORD.spad" 1061226 1061243 1064511 1064516) (-683 "LSTAST.spad" 1061010 1061018 1061216 1061221) (-682 "LSQM.spad" 1059167 1059181 1059561 1059612) (-681 "LSPP.spad" 1058702 1058719 1059157 1059162) (-680 "LSMP.spad" 1057552 1057580 1058692 1058697) (-679 "LSMP1.spad" 1055370 1055384 1057542 1057547) (-678 "LSAGG.spad" 1055039 1055049 1055338 1055365) (-677 "LSAGG.spad" 1054728 1054740 1055029 1055034) (-676 "LPOLY.spad" 1053682 1053701 1054584 1054653) (-675 "LPEFRAC.spad" 1052953 1052963 1053672 1053677) (-674 "LO.spad" 1052354 1052368 1052887 1052914) (-673 "LOGIC.spad" 1051956 1051964 1052344 1052349) (-672 "LOGIC.spad" 1051556 1051566 1051946 1051951) (-671 "LODOOPS.spad" 1050486 1050498 1051546 1051551) (-670 "LODO.spad" 1049870 1049886 1050166 1050205) (-669 "LODOF.spad" 1048916 1048933 1049827 1049832) (-668 "LODOCAT.spad" 1047582 1047592 1048872 1048911) (-667 "LODOCAT.spad" 1046246 1046258 1047538 1047543) (-666 "LODO2.spad" 1045519 1045531 1045926 1045965) (-665 "LODO1.spad" 1044919 1044929 1045199 1045238) (-664 "LODEEF.spad" 1043721 1043739 1044909 1044914) (-663 "LNAGG.spad" 1039868 1039878 1043711 1043716) (-662 "LNAGG.spad" 1035979 1035991 1039824 1039829) (-661 "LMOPS.spad" 1032747 1032764 1035969 1035974) (-660 "LMODULE.spad" 1032515 1032525 1032737 1032742) (-659 "LMDICT.spad" 1031685 1031695 1031949 1031976) (-658 "LLINSET.spad" 1031392 1031402 1031675 1031680) (-657 "LITERAL.spad" 1031298 1031309 1031382 1031387) (-656 "LIST.spad" 1028880 1028890 1030292 1030319) (-655 "LIST3.spad" 1028191 1028205 1028870 1028875) (-654 "LIST2.spad" 1026893 1026905 1028181 1028186) (-653 "LIST2MAP.spad" 1023796 1023808 1026883 1026888) (-652 "LINSET.spad" 1023575 1023585 1023786 1023791) (-651 "LINEXP.spad" 1022318 1022328 1023565 1023570) (-650 "LINDEP.spad" 1021127 1021139 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index afc7c6a5..612c3944 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(204908 . 3486833889) -(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((#0=(-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) #0#) |has| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4301 |#1|) (|:| -4440 |#2|))))) -((((-576)) . T) (($) -2760 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1059 (-419 (-576))))) ((|#1|) . T)) +(204908 . 3486841623) +(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((#0=(-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) #0#) |has| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4439 |#2|))))) +((((-576)) . 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T)) @@ -51,14 +51,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1202)) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-1059 (-576))) (((-419 (-576))) |has| |#1| (-1059 (-419 (-576))))) -(-2760 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) -(-2760 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) -(((|#2| (-494 (-3503 |#1|) (-783))) . T)) -((((-1197)) -2760 (|has| (-419 |#2|) (-917 (-1197))) (|has| (-419 |#2|) (-919 (-1197))))) +(-2759 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) +(-2759 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(((|#2| (-494 (-3502 |#1|) (-783))) . T)) +((((-1197)) -2759 (|has| (-419 |#2|) (-917 (-1197))) (|has| (-419 |#2|) (-919 (-1197))))) (((|#1| (-543 (-1197))) . T)) ((((-1179)) . T) (((-977 (-130))) . T) (((-876)) . T)) ((((-876)) . T)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . 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T)) ((((-419 (-576))) . T) (($) . T)) @@ -227,7 +227,7 @@ (((|#1|) . T)) (|has| |#2| (-374)) ((((-1255 (-576)) $) . T) (((-576) |#1|) . T)) -((($) -2760 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) +((($) -2759 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) (((|#1| |#2|) . T)) ((((-876)) . T)) @@ -240,13 +240,13 @@ ((((-876)) . T)) ((((-876)) . T)) (((|#1| |#1|) . T)) -(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . T) (($ $) -2760 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928)))) -((($ $) -2760 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . 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T) (($) -2759 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928)))) +((($) -2759 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +(((|#2|) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070))) (($) |has| |#2| (-1070)) (((-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070)))) ((((-876)) . T)) ((((-876)) . T)) ((((-876)) . T)) @@ -257,10 +257,10 @@ ((((-171 (-227))) |has| |#1| (-1043)) (((-171 (-390))) |has| |#1| (-1043)) (((-548)) |has| |#1| (-626 (-548))) (((-1193 |#1|)) . T) (((-907 (-576))) |has| |#1| (-626 (-907 (-576)))) (((-907 (-390))) |has| |#1| (-626 (-907 (-390))))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (((|#1|) . 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T)) -((((-2 (|:| -3224 |#1|) (|:| -3422 |#2|))) . T) (((-876)) . T)) +((((-2 (|:| -3223 |#1|) (|:| -2508 |#2|))) . T) (((-876)) . T)) ((((-548)) |has| |#1| (-626 (-548))) (((-907 (-390))) |has| |#1| (-626 (-907 (-390)))) (((-907 (-576))) |has| |#1| (-626 (-907 (-576))))) -(((|#4|) -2760 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1070)))) -(((|#3|) -2760 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1070)))) -((((-2 (|:| -3224 |#1|) (|:| -3422 |#2|))) . T)) +(((|#4|) -2759 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1070)))) +(((|#3|) -2759 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1070)))) +((((-2 (|:| -3223 |#1|) (|:| -2508 |#2|))) . T)) ((((-876)) . T)) ((((-876)) . T)) ((((-548)) . T) (((-576)) . T) (((-907 (-576))) . T) (((-390)) . T) (((-227)) . T)) @@ -325,15 +325,15 @@ (((|#1|) . T) (((-576)) |has| |#1| (-1059 (-576))) (((-419 (-576))) |has| |#1| (-1059 (-419 (-576))))) ((($) . 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T)) @@ -347,15 +347,15 @@ (|has| |#1| (-1121)) ((((-929 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T)) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-861)) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-861)) (|has| |#1| (-1121)))) ((((-548)) |has| |#1| (-626 (-548)))) ((((-876)) . T) (((-1202)) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2760 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2759 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) ((((-1202)) . 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T)) (((|#1| (-992)) . T)) ((((-576)) . T) ((|#2|) . T)) @@ -367,7 +367,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1173)) -((((-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))) . T)) +((((-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))) . T)) (|has| (-1274 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1274 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -379,28 +379,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) -((((-1146 |#1| (-1197))) . T) (((-576)) . T) (((-830 (-1197))) . T) (($) -2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1059 (-419 (-576))))) (((-1197)) . T)) +((((-1146 |#1| (-1197))) . T) (((-576)) . T) (((-830 (-1197))) . T) (($) -2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1059 (-419 (-576))))) (((-1197)) . 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T)) -((($) -2760 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-876)) . T)) ((((-876)) . T)) (|has| (-1273 |#2| |#3| |#4|) (-148)) @@ -411,18 +411,18 @@ ((((-876)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2760 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-917 (-1197))) (|has| |#1| (-1070))) +(-2759 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-917 (-1197))) (|has| |#1| (-1070))) (((|#1|) . T)) ((($) . T)) ((((-576) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) . 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T)) ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) (|has| |#1| (-374)) -(-2760 (-12 (|has| (-1280 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) +(-2759 (-12 (|has| (-1280 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-374)) (|has| |#1| (-15 * (|#1| (-783) |#1|))) @@ -447,23 +447,23 @@ ((((-1255 (-576)) $) . T) (((-576) |#1|) . T)) ((((-876)) . T)) (((|#2|) . T)) -(-2760 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) +(-2759 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) ((((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) ((($) |has| |#1| (-568)) (((-576)) . T)) (|has| |#2| (-805)) (|has| |#2| (-805)) -((((-1280 |#1| |#2| |#3|)) . 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T)) -((($ (-1197)) -2760 (|has| (-419 |#2|) (-917 (-1197))) (|has| (-419 |#2|) (-919 (-1197))))) +((($ (-1197)) -2759 (|has| (-419 |#2|) (-917 (-1197))) (|has| (-419 |#2|) (-919 (-1197))))) (((#0=(-711) (-1193 #0#)) . T)) ((((-593 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) ((((-419 (-576))) . T) (($) . T)) @@ -471,18 +471,18 @@ ((((-876)) . T) (((-1288 |#3|)) . T)) ((((-593 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) ((($) . T) (((-419 (-576))) . T)) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2760 (|has| |#1| (-174)) (|has| |#1| (-568)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2759 (|has| |#1| (-174)) (|has| |#1| (-568)))) ((($) |has| |#1| (-568)) ((|#1|) . T)) ((((-876)) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) ((($) . 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T) (($) -2759 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) (((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374)))) (((|#3|) |has| |#3| (-1070))) -((($) -2760 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) -((($ $) -2760 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($ $) -2759 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) (|has| (-1115 |#1|) (-1121)) (((|#2| (-831 |#1|)) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) . T)) @@ -490,20 +490,20 @@ (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1|) . 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T)) -((($) -2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-419 $) (-419 $)) |has| |#1| (-568)) (($ $) . T) ((|#1| |#1|) . T)) -((($) -2760 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((#0=(-1103) |#2|) . T) ((#0# $) . T) (($ $) . T)) ((((-876)) . T)) ((((-929 |#1|)) . T)) @@ -512,22 +512,22 @@ ((((-245 |#1| |#2|) |#2|) . T)) ((((-876)) . T)) (((|#3|) |has| |#3| (-1121)) (((-576)) -12 (|has| |#3| (-1059 (-576))) (|has| |#3| (-1121))) (((-419 (-576))) -12 (|has| |#3| (-1059 (-419 (-576)))) (|has| |#3| (-1121)))) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#1|) . T)) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-861)) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-861)) (|has| |#1| (-1121)))) ((((-548)) |has| |#1| (-626 (-548)))) (((|#1|) |has| |#1| (-174))) -((((-2 (|:| -4301 (-1197)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4300 (-1197)) (|:| -4439 (-52)))) . T)) (|has| |#1| (-374)) ((((-1202)) . T)) (((|#1|) . T)) -(-2760 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2759 (|has| |#1| (-21)) (|has| |#1| (-860))) ((($) . T)) ((((-1197) |#1|) |has| |#1| (-526 (-1197) |#1|)) ((|#1| |#1|) |has| |#1| (-319 |#1|))) (|has| |#2| (-832)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-860)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1| |#2| |#3| (-543 |#3|)) . T)) ((((-876)) . T)) @@ -536,15 +536,15 @@ (|has| |#1| (-379)) ((((-419 (-576))) . T)) (((|#1|) . T)) -(-2760 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) +(-2759 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) ((((-419 (-576))) . T)) ((((-1179) |#1|) . T)) (|has| |#1| (-379)) ((((-576)) . T)) ((((-576)) . T)) (((|#1|) . T) (((-576)) . T)) -(-2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) -(-2760 (|has| |#1| (-861)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(-2759 (|has| |#1| (-861)) (|has| |#1| (-1121))) ((((-876)) . T)) (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) ((((-1197)) -12 (|has| |#1| (-374)) (|has| |#1| (-917 (-1197))))) @@ -558,12 +558,12 @@ ((((-576) |#3|) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) (|has| |#2| (-1070)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) -(-2760 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) +(-2759 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) ((((-876)) . T)) ((((-1274 |#1| |#2| |#3| |#4|)) . T)) ((((-419 (-576))) . T) (((-576)) . T)) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) @@ -572,9 +572,9 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) ((((-576)) . T)) ((((-576)) . T)) -((($) . T) (((-576)) . 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T)) (|has| (-419 |#2|) (-148)) (|has| (-419 |#2|) (-146)) @@ -892,15 +892,15 @@ (|has| |#1| (-568)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) ((((-876)) . T)) -((((-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))) . T)) +((((-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))) . T)) (|has| |#1| (-38 (-419 (-576)))) -((((-400) (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))) . T)) +((((-400) (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#2| (-1173)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-568))) ((((-876)) . T) (((-1202)) . T)) ((((-876)) . T) (((-1202)) . T)) ((((-1202)) . T)) @@ -918,7 +918,7 @@ ((((-400) (-1179)) . T)) (|has| |#1| (-568)) ((((-1255 (-576)) $) . T) (((-576) |#1|) . T)) -(-2760 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(-2759 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) . T)) @@ -936,7 +936,7 @@ ((((-656 |#1|)) . T)) ((((-876)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -(-2760 (|has| |#1| (-861)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-861)) (|has| |#1| (-1121))) (((|#2|) |has| |#2| (-319 |#2|))) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -947,14 +947,14 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) (|has| |#2| (-379)) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-861)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-861)) (|has| |#1| (-1121))) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . 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T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) -((($) . T) (((-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) +((($) . T) (((-419 (-576))) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) ((((-876)) . T)) ((((-1195 |#1| |#2| |#3|) $) -12 (|has| (-1195 |#1| |#2| |#3|) (-296 (-1195 |#1| |#2| |#3|) (-1195 |#1| |#2| |#3|))) (|has| |#1| (-374))) (($ $) . T) (((-576) |#1|) . T)) ((($ $) . T) (((-419 (-576)) |#1|) . T)) @@ -975,7 +975,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-576)) . T) (($) . T)) -((($) -2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((($) . T) (((-576)) . T) ((|#2|) . T)) ((((-576)) . T) (($) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) ((((-419 (-576))) . T) (((-576)) . T)) @@ -984,29 +984,29 @@ (((|#1|) . T)) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) -(-2760 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1070))) +(-2759 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1070))) ((((-112)) . T)) ((((-548)) |has| |#1| (-626 (-548))) (((-227)) . #0=(|has| |#1| (-1043))) (((-390)) . #0#)) ((((-876)) . T)) (((|#1|) . 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T)) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) (((|#1| (-992)) . T)) (((|#1| |#1|) . T)) ((($) . T)) @@ -1035,23 +1035,23 @@ (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) -(-2760 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-738)) (|has| |#2| (-738)))) +(-2759 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-738)) (|has| |#2| (-738)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-174)) ((|#4|) . T) (((-576)) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) ((((-876)) . T)) -(-2760 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2759 (|has| |#1| (-238)) (|has| |#1| (-237))) (|has| |#1| (-360)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-419 (-576))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-419 (-576))) . T)) -((($) . T) (((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#1|) . T)) +((($) . T) (((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#1|) . T)) (|has| |#1| (-840)) ((((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) (((-576)) |has| |#1| (-1059 (-576))) ((|#1|) . T)) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) (((|#1| $) |has| |#1| (-296 |#1| |#1|))) ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) ((($) |has| |#1| (-568))) @@ -1059,8 +1059,8 @@ (((|#4|) |has| |#4| (-1121))) (((|#3|) |has| |#3| (-1121))) (|has| |#3| (-379)) -((($) |has| |#1| (-568)) ((|#1|) . T) (((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1059 (-419 (-576))))) (((-576)) . 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T)) (((|#1|) . T)) ((((-419 (-576))) . T) (((-576)) . T) (($) . T)) ((((-1197)) . T)) (|has| |#1| (-568)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-568)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) @@ -1121,7 +1121,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#1| (-148)) -(((|#2| (-245 (-3503 |#1|) (-783)) (-878 |#1|)) . T)) +(((|#2| (-245 (-3502 |#1|) (-783)) (-878 |#1|)) . T)) (((|#1| (-543 |#3|) |#3|) . T)) (|has| |#1| (-146)) (((#0=(-419 (-576)) #0#) |has| |#2| (-374)) (($ $) . T)) @@ -1135,12 +1135,12 @@ (|has| |#1| (-146)) ((((-419 (-576))) |has| |#2| (-374)) (($) . 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T)) -(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) (((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4301 |#1|) (|:| -4440 |#2|))))) -(((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121))) (((-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))) |has| (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|)) (-319 (-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))))) +(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) (((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) |has| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4439 |#2|))))) +(((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121))) (((-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))) |has| (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|)) (-319 (-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))))) ((((-876)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) ((((-1197) (-52)) . T)) -((((-1197)) -2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197))))) +((((-1197)) -2759 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-878 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-840)) @@ -1203,10 +1203,10 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T)) ((((-576)) . T) (($) . T) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (|has| (-1115 |#1|) (-1121)) -(((|#2| |#2|) -2760 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070)))) -(((|#2|) -2760 (|has| |#2| (-174)) (|has| |#2| (-374)))) -((((-576) (-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2760 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070)))) +(((|#2| |#2|) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070)))) +(((|#2|) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)))) +((((-576) (-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070)))) ((((-576)) . T)) ((((-1202)) . T)) ((((-783)) . T)) @@ -1225,34 +1225,34 @@ (((|#1|) . T)) ((((-419 (-576))) . T) (($) . T)) ((($) . T) (((-419 (-576))) . T)) -(-2760 (|has| |#1| (-174)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-174)) (|has| |#1| (-568))) ((((-1202)) . T)) -(-2760 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2760 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((((-576)) . T)) -(-2760 (|has| |#1| (-174)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-174)) (|has| |#1| (-568))) (|has| |#1| (-146)) ((((-576)) . 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T)) -((($) -2760 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) -((($) -2760 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) +((($) -2759 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) -2759 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) ((((-576) |#2|) . T)) -((($ (-1197)) -2760 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) +((($ (-1197)) -2759 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-379)) @@ -1271,42 +1271,42 @@ ((((-876)) . 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T)) (((|#1|) |has| |#1| (-319 |#1|))) @@ -1316,21 +1316,21 @@ (|has| |#1| (-379)) ((((-1197) $) |has| |#1| (-526 (-1197) $)) (($ $) |has| |#1| (-319 $)) ((|#1| |#1|) |has| |#1| (-319 |#1|)) (((-1197) |#1|) |has| |#1| (-526 (-1197) |#1|))) ((((-1197)) |has| |#1| (-917 (-1197)))) -(-2760 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2759 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-400) |#1|) . T)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) (((|#2|) . T) (((-876)) . T)) ((((-876)) . T)) (((|#2|) . T)) ((((-929 |#1|)) . T)) ((((-876)) . T) (((-1202)) . T)) ((((-1202)) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2760 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) -2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2759 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) -2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) @@ -1339,7 +1339,7 @@ (((|#1|) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) (((|#1| |#1|) . T)) (((#0=(-884 |#1|)) |has| #0# (-319 #0#))) -((((-576)) . T) (($) -2760 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1059 (-419 (-576))))) ((|#1|) . T)) +((((-576)) . T) (($) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2759 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1059 (-419 (-576))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-805)) (|has| |#2| (-805)) @@ -1348,7 +1348,7 @@ (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (|has| |#2| (-1070)) ((($) . T) (((-576)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1223)) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) @@ -1362,7 +1362,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-419 (-576)) #0#) . T)) (|has| |#1| (-374)) ((((-576)) . T) (((-419 (-576))) . T) (($) . 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T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) +((($) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) ((((-576)) |has| #0=(-419 |#2|) (-651 (-576))) ((#0#) . T)) ((($) . T) (((-576)) . T)) ((((-576) (-145)) . T)) -((((-576) (-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T) ((|#1| |#2|) . T)) +((((-576) (-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T) ((|#1| |#2|) . T)) ((((-419 (-576))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) ((((-876)) . T)) ((((-929 |#1|)) . T)) (|has| |#1| (-374)) @@ -1410,11 +1410,11 @@ (|has| |#1| (-374)) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-860)) -((($) -2760 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) -2759 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) (|has| |#1| (-374)) (((|#1|) . T) (($) . T)) (|has| |#1| (-860)) -((($) . T) (((-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) . T) (((-419 (-576))) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) ((((-1197)) |has| |#1| (-917 (-1197)))) (|has| |#1| (-860)) ((((-518)) . T)) @@ -1430,7 +1430,7 @@ ((((-548)) . T)) ((((-876)) . T)) ((($) . T)) -((((-576) (-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T) (((-1255 (-576)) $) . T) ((|#1| |#2|) . T)) +((((-576) (-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T) (((-1255 (-576)) $) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-174))) @@ -1440,22 +1440,22 @@ (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (((|#3|) . 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T)) -(((|#2|) -2760 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070)))) +(((|#2|) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070)))) (|has| $ (-148)) ((((-419 |#2|)) . T)) ((((-419 (-576))) |has| #0=(-419 |#2|) (-1059 (-419 (-576)))) (((-576)) |has| #0# (-1059 (-576))) ((#0#) . T)) @@ -1557,11 +1557,11 @@ (|has| |#2| (-148)) (|has| |#1| (-148)) (|has| |#1| (-146)) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) (((|#1|) . T)) (|has| |#2| (-238)) @@ -1598,9 +1598,9 @@ ((((-876)) . T)) ((((-876)) . T)) ((((-1020 |#1|)) . T) ((|#1|) . T)) -((((-1197)) -2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197)))) (((-830 (-1197))) . 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T)) (|has| |#2| (-148)) (|has| |#1| (-485)) -(-2760 (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-917 (-1197))) (|has| |#1| (-1070))) +(-2759 (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-917 (-1197))) (|has| |#1| (-1070))) (|has| |#1| (-374)) ((((-876)) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -1756,8 +1756,8 @@ (|has| |#1| (-860)) ((((-876)) . T)) (((|#2|) . T)) -((((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2760 (|has| |#1| (-374)) (|has| |#1| (-568))) (((-1280 |#1| |#2| |#3|)) |has| |#1| (-374)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2760 (|has| |#1| (-374)) (|has| |#1| (-568)))) +((((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2759 (|has| |#1| (-374)) (|has| |#1| (-568))) (((-1280 |#1| |#2| |#3|)) |has| |#1| (-374)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2759 (|has| |#1| (-374)) (|has| |#1| (-568)))) ((($) |has| |#1| (-568)) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#2|) . T) (((-576)) . T) (((-831 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1766,8 +1766,8 @@ ((((-929 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) ((((-876)) . T)) ((((-876)) . T)) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) -(((|#2| (-494 (-3503 |#1|) (-783)) (-878 |#1|)) . T)) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(((|#2| (-494 (-3502 |#1|) (-783)) (-878 |#1|)) . T)) ((((-419 (-576))) . #0=(|has| |#2| (-374))) (($) . #0#)) (((|#1| (-543 (-1197)) (-1197)) . T)) (((|#1|) . T)) @@ -1787,19 +1787,19 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -4301 (-1197)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4300 (-1197)) (|:| -4439 (-52)))) . T)) ((((-1195 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1195 |#1| |#2| |#3|)) |has| |#1| (-374))) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) ((((-1197) (-52)) . 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T) (((-576)) |has| |#1| (-1059 (-576))) (((-419 (-576))) |has| |#1| (-1059 (-419 (-576))))) (|has| |#1| (-861)) (|has| |#1| (-861)) @@ -1820,15 +1820,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1121)))) (((|#1|) |has| |#1| (-174))) (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1121)))) -(((|#3|) -2760 (|has| |#3| (-174)) (|has| |#3| (-374)))) -((($) -2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) -(-2760 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-928))) -((($) -2760 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +(((|#3|) -2759 (|has| |#3| (-174)) (|has| |#3| (-374)))) +((($) -2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +(-2759 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-928))) +((($) -2759 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((($ |#2|) . T)) -((($ (-1197)) -2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197)))) (($ (-1103)) . T)) +((($ (-1197)) -2759 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197)))) (($ (-1103)) . T)) ((($ $) . T) ((#0=(-419 (-576)) #0#) . T)) ((((-576) |#2|) . T)) -(((|#2|) -2760 (|has| |#2| (-174)) (|has| |#2| (-374)))) +(((|#2|) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)))) (|has| |#1| (-360)) (((|#3| |#3|) -12 (|has| |#3| (-319 |#3|)) (|has| |#3| (-1121)))) (((|#2|) . T) (((-576)) . T)) @@ -1837,7 +1837,7 @@ (|has| |#1| (-832)) (|has| |#1| (-832)) (((|#1|) . T)) -(-2760 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-860)) (|has| |#1| (-860)) (|has| |#1| (-860)) @@ -1846,14 +1846,14 @@ ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) ((((-1197)) |has| |#1| (-917 (-1197))) (((-1103)) . T)) (((|#1|) . T)) (|has| |#1| (-860)) -(((#0=(-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) #0#) |has| (-2 (|:| -4301 (-1179)) (|:| -4440 (-52))) (-319 (-2 (|:| -4301 (-1179)) (|:| -4440 (-52)))))) +(((#0=(-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) #0#) |has| (-2 (|:| -4300 (-1179)) (|:| -4439 (-52))) (-319 (-2 (|:| -4300 (-1179)) (|:| -4439 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (|has| |#1| (-1121)) ((((-876)) . T) (((-1202)) . T)) @@ -1877,14 +1877,14 @@ (((|#1| (-783) (-1103)) . T)) (((|#3|) . T)) ((((-145)) . T)) -((((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) (((-576)) -2760 (|has| |#1| (-860)) (|has| |#1| (-1059 (-576)))) ((|#1|) . T)) +((((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) (((-576)) -2759 (|has| |#1| (-860)) (|has| |#1| (-1059 (-576)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-145)) . 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T)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -1903,31 +1903,31 @@ ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) ((($) |has| |#1| (-568))) (((|#2|) . T)) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2760 (|has| |#1| (-174)) (|has| |#1| (-568)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2759 (|has| |#1| (-174)) (|has| |#1| (-568)))) ((($) |has| |#1| (-568)) ((|#1|) . T)) ((($) |has| |#1| (-860))) ((((-1195 |#1| |#2| |#3|)) |has| |#1| (-374))) (|has| |#1| (-928)) ((((-1197)) . T)) ((((-876)) . T)) -((($) -2760 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) (((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1280 |#1| |#2| |#3|)) |has| |#1| (-374)) ((|#1|) . 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T)) +((((-2 (|:| -4300 (-1197)) (|:| -4439 (-52)))) . T)) ((((-576)) |has| #0=(-419 |#2|) (-651 (-576))) ((#0#) . T) (((-419 (-576))) . T) (($) . T)) ((((-684 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1961,7 +1961,7 @@ ((((-876)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) ((((-876)) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2760 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2759 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) ((((-1202)) . T)) ((((-419 (-576))) . T) (($) . T) (((-419 |#1|)) . T) ((|#1|) . T) (((-576)) . T)) (((|#3|) . T) (((-576)) . T) (((-624 $)) . T)) @@ -1969,12 +1969,12 @@ ((((-876)) . T)) ((((-876)) . T)) (((|#2|) . 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T)) ((($) |has| |#1| (-238))) @@ -2228,12 +2228,12 @@ (|has| |#1| (-146)) ((($) |has| |#1| (-568)) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#1|) |has| |#1| (-174))) -((($) -2760 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-576)) . T) ((|#1|) . T) (($) . T) (((-419 (-576))) . T) (((-1197)) |has| |#1| (-1059 (-1197)))) (((|#1| |#2|) . T)) -((((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) (((-576)) -2760 (|has| |#1| (-860)) (|has| |#1| (-1059 (-576)))) ((|#1|) . T)) -(-2760 (-12 (|has| |#4| (-238)) (|has| |#4| (-1070))) (-12 (|has| |#4| (-237)) (|has| |#4| (-1070)))) -(-2760 (-12 (|has| |#3| (-238)) (|has| |#3| (-1070))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1070)))) +((((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) (((-576)) -2759 (|has| |#1| (-860)) (|has| |#1| (-1059 (-576)))) ((|#1|) . T)) +(-2759 (-12 (|has| |#4| (-238)) (|has| |#4| (-1070))) (-12 (|has| |#4| (-237)) (|has| |#4| (-1070)))) +(-2759 (-12 (|has| |#3| (-238)) (|has| |#3| (-1070))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1070)))) ((((-145)) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) @@ -2244,13 +2244,13 @@ ((((-876)) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) ((($) . T) (((-576)) |has| |#1| (-651 (-576))) ((|#1|) . 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T) (($ (-1197)) -12 (|has| |#1| (-15 * (|#1| (-783) |#1|))) (|has| |#1| (-917 (-1197))))) (|has| |#1| (-928)) @@ -2258,7 +2258,7 @@ (((|#2|) |has| |#2| (-1070))) (|has| |#1| (-374)) ((($) . T)) -(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) (((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4301 |#1|) (|:| -4440 |#2|))))) +(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) (((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) |has| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4439 |#2|))))) (((|#1|) |has| |#1| (-174))) ((($ (-878 |#1|)) . T)) (((|#1| |#1|) . T)) @@ -2269,7 +2269,7 @@ (((|#1|) . T)) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-656 $)) . T) (((-1179)) . T) (((-1197)) . T) (((-576)) . T) (((-227)) . T) (((-876)) . T)) -((((-576)) -2760 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1070))) ((|#3|) -2760 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-738)) (|has| |#3| (-1070))) (($) |has| |#3| (-1070))) +((((-576)) -2759 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1070))) ((|#3|) -2759 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-738)) (|has| |#3| (-1070))) (($) |has| |#3| (-1070))) ((((-419 (-576))) . T) (((-576)) . T) (((-624 $)) . T)) (((|#1|) . T)) ((((-876)) . T)) @@ -2284,7 +2284,7 @@ (((|#1| (-419 (-576)) (-1103)) . T)) (((|#1| (-783) (-1103)) . T)) (((#0=(-419 |#2|) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-576)) -2760 (|has| (-419 (-576)) (-1059 (-576))) (|has| |#1| (-1059 (-576)))) (((-419 (-576))) . T)) +(((|#1|) . T) (((-576)) -2759 (|has| (-419 (-576)) (-1059 (-576))) (|has| |#1| (-1059 (-576)))) (((-419 (-576))) . T)) (((|#1| (-614 |#1| |#3|) (-614 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2304,37 +2304,37 @@ ((((-711)) . T)) ((((-711)) . T)) (((|#2|) |has| |#2| (-174))) -(-2760 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2759 (|has| |#1| (-238)) (|has| |#1| (-237))) ((((-576)) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-1059 (-419 (-576))))) -((((-112)) |has| |#1| (-1121)) (((-876)) -2760 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-917 (-1197))) (|has| |#1| (-1070)) (|has| |#1| (-1133)) (|has| |#1| (-1121)))) +((((-112)) |has| |#1| (-1121)) (((-876)) -2759 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-917 (-1197))) (|has| |#1| (-1070)) (|has| |#1| (-1133)) (|has| |#1| (-1121)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . 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T) (((-419 (-576))) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) ((((-576) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) (((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4301 |#1|) (|:| -4440 |#2|))))) +(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) (((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) |has| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4439 |#2|))))) ((((-390)) . T)) ((((-711)) . T)) ((((-419 (-576))) . #0=(|has| |#2| (-374))) (($) . #0#)) (((|#1|) |has| |#1| (-174))) ((((-419 (-971 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2760 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) -(-2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(-2759 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) +(-2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1070))) @@ -2346,7 +2346,7 @@ ((((-1197)) |has| |#2| (-917 (-1197)))) (|has| |#1| (-861)) ((((-876)) . T)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (|has| |#1| (-803)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-485)) @@ -2354,8 +2354,8 @@ (|has| |#1| (-379)) (|has| |#1| (-379)) (|has| |#1| (-374)) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1070)) (|has| |#1| (-1133))) -((($) -2760 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-360)))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1070)) (|has| |#1| (-1133))) +((($) -2759 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-360)))) ((((-117 |#1|)) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-360)) @@ -2366,7 +2366,7 @@ (|has| |#1| (-38 (-419 (-576)))) (((|#2|) . T) (((-876)) . T)) (((|#2|) . T) (((-876)) . T)) -((($ (-1197)) -2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197))))) +((($ (-1197)) -2759 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197))))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) @@ -2377,18 +2377,18 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-861)) -((((-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))) . T)) +((((-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) |has| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)))) ((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121)))) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) |has| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)))) ((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121)))) (((|#2|) . 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T)) @@ -2626,13 +2626,13 @@ ((((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((|#1|) . T) (((-576)) . T)) (|has| |#2| (-146)) (|has| |#2| (-148)) -(-2760 (|has| |#2| (-832)) (|has| |#2| (-861))) +(-2759 (|has| |#2| (-832)) (|has| |#2| (-861))) ((((-929 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) ((((-576)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-576)) . T)) (((|#2|) . T)) -((((-1197)) -2760 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) +((((-1197)) -2759 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-374))) ((((-419 |#2|)) . T)) @@ -2641,10 +2641,10 @@ ((((-876)) . T)) ((((-876)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) ((((-1197) |#1|) |has| |#1| (-526 (-1197) |#1|)) ((|#1| |#1|) |has| |#1| (-319 |#1|))) -(((|#1|) -2760 (|has| |#1| (-174)) (|has| |#1| (-374)))) +(((|#1|) -2759 (|has| |#1| (-174)) (|has| |#1| (-374)))) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) ((((-576)) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) @@ -2654,14 +2654,14 @@ (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) |has| |#2| (-374))) -((($) -2760 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) (((|#2|) . T)) ((((-419 (-576))) . T) (((-711)) . T) (($) . T)) -((($) . T) (((-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) . T) (((-419 (-576))) -2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) -(-2760 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2759 (|has| |#1| (-238)) (|has| |#1| (-237))) (((#0=(-792 |#1| (-878 |#2|)) #0#) |has| (-792 |#1| (-878 |#2|)) (-319 (-792 |#1| (-878 |#2|))))) -((($) -2760 (|has| |#1| (-238)) (|has| |#1| (-237)))) +((($) -2759 (|has| |#1| (-238)) (|has| |#1| (-237)))) ((((-576)) . T) (($) . T)) ((((-878 |#1|)) . T)) (((|#2|) |has| |#2| (-174))) @@ -2670,7 +2670,7 @@ ((((-1197)) |has| |#1| (-917 (-1197))) (((-1103)) . T)) ((((-1197)) |has| |#1| (-917 (-1197))) (((-1109 (-1197))) . T)) (((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121)))) -((($ (-1197)) -2760 (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))))) +((($ (-1197)) -2759 (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))))) ((((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (|has| |#1| (-38 (-419 (-576)))) @@ -2679,13 +2679,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((($ $) . 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T)) -(((|#2|) |has| |#2| (-6 (-4467 "*")))) +(((|#2|) |has| |#2| (-6 (-4466 "*")))) (((|#1|) . T)) (((|#1|) . T)) ((($) . T)) @@ -2705,37 +2705,37 @@ (((|#1|) . T)) (((|#3|) . T) (((-576)) . T)) ((((-1273 |#2| |#3| |#4|)) . T) (((-576)) . T) (((-1274 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-419 (-576))) . T)) -((((-48)) -12 (|has| |#1| (-568)) (|has| |#1| (-1059 (-576)))) (((-576)) -2760 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1059 (-576))) (|has| |#1| (-1070))) ((|#1|) . T) (((-624 $)) . T) (($) |has| |#1| (-568)) (((-419 (-576))) -2760 (|has| |#1| (-568)) (|has| |#1| (-1059 (-419 (-576))))) (((-419 (-971 |#1|))) |has| |#1| (-568)) (((-971 |#1|)) |has| |#1| (-1070)) (((-1197)) . T)) +((((-48)) -12 (|has| |#1| (-568)) (|has| |#1| (-1059 (-576)))) (((-576)) -2759 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1059 (-576))) (|has| |#1| (-1070))) ((|#1|) . T) (((-624 $)) . 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T)) +((((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2759 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((|#1|) . T)) (|has| |#1| (-374)) -((($) |has| |#1| (-860)) (((-576)) -2760 (|has| |#1| (-21)) (|has| |#1| (-860)))) -((($) -2760 (-12 (|has| (-1280 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1280 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|))))) +((($) |has| |#1| (-860)) (((-576)) -2759 (|has| |#1| (-21)) (|has| |#1| (-860)))) +((($) -2759 (-12 (|has| (-1280 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1280 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|))))) ((($) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|)))) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -2753,16 +2753,16 @@ (((|#2| |#3|) . T)) (((|#1| (-543 |#2|)) . T)) (((|#1| (-783)) . T)) -(-2760 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) +(-2759 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) (((|#1| (-543 (-1109 (-1197)))) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (|has| |#2| (-928)) -(-2760 (|has| |#2| (-805)) (|has| |#2| (-861))) +(-2759 (|has| |#2| (-805)) (|has| |#2| (-861))) ((((-876)) . T)) -(((|#2|) -2760 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-738)))) -(((|#2|) -2760 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-738)) (|has| |#2| (-1070)))) -((($ (-1197)) -2760 (-12 (|has| |#3| (-917 (-1197))) (|has| |#3| (-1070))) (-12 (|has| |#3| (-919 (-1197))) (|has| |#3| (-1070))))) +(((|#2|) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-738)))) +(((|#2|) -2759 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-738)) (|has| |#2| (-1070)))) +((($ (-1197)) -2759 (-12 (|has| |#3| (-917 (-1197))) (|has| |#3| (-1070))) (-12 (|has| |#3| (-919 (-1197))) (|has| |#3| (-1070))))) ((($ $) . T) ((#0=(-1273 |#2| |#3| |#4|) #0#) . T) ((#1=(-419 (-576)) #1#) |has| #0# (-38 (-419 (-576))))) ((((-929 |#1|)) . T)) (-12 (|has| |#1| (-374)) (|has| |#2| (-832))) @@ -2770,14 +2770,14 @@ ((((-876)) . T)) ((($) . T) (((-576)) . T)) ((($) . T)) -(-2760 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-374)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1273 |#2| |#3| |#4|)) . T) (((-419 (-576))) |has| #0# (-38 (-419 (-576))))) ((((-1195 |#1| |#2| |#3|)) |has| |#1| (-374))) -(-2760 (-12 (|has| |#1| (-317)) (|has| |#1| (-928))) (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-1070))) +(-2759 (-12 (|has| |#1| (-317)) (|has| |#1| (-928))) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-917 (-1197))) (|has| |#1| (-1070))) ((((-576)) |has| |#1| (-651 (-576))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-876)) . T)) @@ -2815,7 +2815,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . 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T) (((-576)) . T)) -((((-2 (|:| -4301 (-1179)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4300 (-1179)) (|:| -4439 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) ((((-876)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) (((|#1| (-419 (-576))) . T)) (((|#1|) . T)) -(-2760 (|has| |#1| (-300)) (|has| |#1| (-374))) +(-2759 (|has| |#1| (-300)) (|has| |#1| (-374))) ((((-145)) . T)) ((((-576)) |has| #0=(-419 |#2|) (-651 (-576))) ((#0#) . T) (((-419 (-576))) . T) (($) . T)) (|has| |#1| (-860)) @@ -2863,7 +2863,7 @@ ((((-876)) . T)) ((((-876)) . T)) ((((-189)) . T) (((-876)) . T)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-876)) . T)) ((((-876)) . T)) @@ -2880,8 +2880,8 @@ (|has| |#1| (-861)) ((((-876)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))) . T)) -((($) -2760 (-12 (|has| (-1195 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1195 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|))))) +((((-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))) . T)) +((($) -2759 (-12 (|has| (-1195 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1195 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|))))) ((((-876)) . T)) (((|#2|) |has| |#2| (-374))) ((((-876)) . T)) @@ -2896,19 +2896,19 @@ (|has| |#3| (-1070)) (|has| |#1| (-1121)) ((((-1197) (-52)) . T)) -(-2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(-2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . 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T) (($ $) . T)) ((((-576)) . T)) (((|#1|) . T)) @@ -2920,12 +2920,12 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) (|has| |#1| (-832)) (((#0=(-929 |#1|) #0#) . T) (($ $) . T) ((#1=(-419 (-576)) #1#) . T)) ((((-419 |#2|)) . T)) (|has| |#1| (-860)) -((((-1224 |#1|)) . T) (((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) +((((-1224 |#1|)) . T) (((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) (((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) . T) ((#1=(-576) #1#) . T) (($ $) . T)) ((((-929 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) |has| |#2| (-1070)) (((-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070)))) @@ -2942,35 +2942,35 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) -((((-2 (|:| -4301 (-1197)) (|:| -4440 (-52)))) . T)) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) +((((-2 (|:| -4300 (-1197)) (|:| -4439 (-52)))) . T)) ((((-576) |#3|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -4301 (-1197)) (|:| -4440 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -4300 (-1197)) (|:| -4439 #0#))) . T)) (|has| |#1| (-360)) ((((-576)) . T)) ((((-876)) . T)) (((|#1|) . 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T)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-360))) (((#0=(-419 (-576)) #0#) . T) ((#1=(-711) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) |has| |#1| (-374))) ((((-876)) . T)) (|has| |#1| (-1121)) (((|#1|) . T)) -(((|#1|) -2760 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) -(((|#1|) -2760 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) +(((|#1|) -2759 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) +(((|#1|) -2759 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) (((|#2|) . T)) ((((-419 (-576))) . T) (((-711)) . T) (($) . T)) ((((-591)) . T)) (((|#3| |#3|) . T)) -((($ (-1197)) -2760 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) +((($ (-1197)) -2759 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) (|has| |#1| (-861)) (|has| |#2| (-238)) ((((-878 |#1|)) . T)) @@ -2991,10 +2991,10 @@ (|has| |#1| (-1121)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2760 (|has| |#1| (-238)) (|has| |#1| (-237)))) +((($) -2759 (|has| |#1| (-238)) (|has| |#1| (-237)))) ((((-576)) . T)) (((|#2|) . T) (((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((|#1|) . T) (($) . T) (((-576)) . T)) -(-2760 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(-2759 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) (((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3037,7 +3037,7 @@ (|has| |#2| (-1043)) ((($) . T)) (|has| |#1| (-928)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3047,32 +3047,32 @@ (|has| |#1| (-374)) ((((-929 |#1|)) . T)) ((($) . T) (((-576)) . T) ((|#1|) . T) (((-419 (-576))) . 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T)) -(((#0=(-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) #0#) |has| (-2 (|:| -4301 (-1197)) (|:| -4440 (-52))) (-319 (-2 (|:| -4301 (-1197)) (|:| -4440 (-52)))))) +(((#0=(-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) #0#) |has| (-2 (|:| -4300 (-1197)) (|:| -4439 (-52))) (-319 (-2 (|:| -4300 (-1197)) (|:| -4439 (-52)))))) ((((-1179)) . T)) (|has| |#1| (-928)) (|has| |#2| (-374)) (((|#1|) . T) (($) . T) (((-576)) . T)) -(-2760 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1070))) +(-2759 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1070))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-876)) . T)) (((|#1|) . T)) @@ -3089,11 +3089,11 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2760 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (-12 (|has| |#1| (-557)) (|has| |#1| (-840))) ((((-876)) . T)) -((((-1197)) -2760 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1197)))))) +((((-1197)) -2759 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1197)))))) (|has| |#1| (-374)) ((((-1197)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-917 (-1197))))) (|has| |#1| (-374)) @@ -3106,13 +3106,13 @@ ((((-576) |#1|) . T)) ((((-1197)) |has| |#1| (-917 (-1197)))) (((|#1|) . T)) -(-2760 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2759 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#2|) |has| |#1| (-374))) (((|#2|) |has| |#1| (-374))) -(-2760 (|has| |#4| (-805)) (|has| |#4| (-861))) -(-2760 (|has| |#3| (-805)) (|has| |#3| (-861))) +(-2759 (|has| |#4| (-805)) (|has| |#4| (-861))) +(-2759 (|has| |#3| (-805)) (|has| |#3| (-861))) ((((-576)) . T) (($) . T)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) @@ -3147,32 +3147,32 @@ ((((-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-901 (-390)))) (((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-901 (-576))))) (((|#1|) . T)) ((($) . T) (((-576)) . T) ((|#2|) . T)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-568))) (((|#3|) . 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T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (|has| |#1| (-38 (-419 (-576)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-419 (-576)))) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) ((($) . T)) (|has| |#1| (-148)) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) ((($) . T)) ((((-593 |#1|)) . T)) @@ -3188,7 +3188,7 @@ ((((-419 (-576))) |has| |#2| (-1059 (-576))) (((-576)) |has| |#2| (-1059 (-576))) (((-1197)) |has| |#2| (-1059 (-1197))) ((|#2|) . T)) (((#0=(-419 |#2|) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2760 (|has| |#1| (-146)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-146)) (|has| |#1| (-360))) (|has| |#1| (-148)) ((((-876)) . T)) ((($) . T)) @@ -3208,15 +3208,15 @@ ((((-419 |#2|)) . T)) ((((-876)) . T)) (((|#1|) . T)) -((((-1197)) -2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197))))) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) +((((-1197)) -2759 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197))))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) (|has| |#1| (-803)) (|has| |#1| (-803)) ((((-876)) . T)) ((((-929 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-876)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-861)) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-861)) (|has| |#1| (-1121)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3225,7 +3225,7 @@ ((((-1274 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568)) (((-419 (-576))) |has| |#1| (-568))) ((((-876)) . T)) -(-2760 (-12 (|has| |#2| (-238)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1070)))) +(-2759 (-12 (|has| |#2| (-238)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1070)))) ((((-876)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3238,10 +3238,10 @@ ((((-876)) . T)) (((|#2|) . T)) ((((-576)) . T)) -((((-1197)) -2760 (|has| (-419 |#2|) (-917 (-1197))) (|has| (-419 |#2|) (-919 (-1197))))) +((((-1197)) -2759 (|has| (-419 |#2|) (-917 (-1197))) (|has| (-419 |#2|) (-919 (-1197))))) ((((-876)) . T)) ((((-576)) . T)) -(-2760 (|has| |#2| (-805)) (|has| |#2| (-861))) +(-2759 (|has| |#2| (-805)) (|has| |#2| (-861))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-876)) . T)) ((((-876)) . T)) @@ -3253,10 +3253,10 @@ (((|#1|) . T) (($) . T) (((-419 (-576))) . 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T)) @@ -3266,20 +3266,20 @@ (((#0=(-117 |#1|) $) |has| #0# (-296 #0# #0#))) (((|#1|) |has| |#1| (-174))) ((((-326 |#1|)) . T) (((-576)) . T)) -(-2760 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2759 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) ((((-876)) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-876)) . T)) -((((-1197)) -2760 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) +((((-1197)) -2759 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) (((|#1|) |has| |#1| (-319 |#1|))) ((((-576) |#1|) . T) (((-1255 (-576)) $) . T)) (((|#1| |#2|) . T)) ((((-1197) |#1|) . T)) -(((|#1|) -2760 (|has| |#1| (-174)) (|has| |#1| (-374)))) +(((|#1|) -2759 (|has| |#1| (-174)) (|has| |#1| (-374)))) (((|#1|) . T)) ((($ (-1197)) . T)) -(((|#1|) -2760 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-1070)))) +(((|#1|) -2759 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-1070)))) ((((-576)) . T) (((-419 (-576))) . T)) (((|#1|) . T)) (|has| |#1| (-568)) @@ -3288,15 +3288,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-568)) ((($) . T)) (|has| |#1| (-1121)) ((((-792 |#1| (-878 |#2|))) |has| (-792 |#1| (-878 |#2|)) (-319 (-792 |#1| (-878 |#2|))))) -(-2760 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) +(-2759 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3305,17 +3305,17 @@ (((|#1| (-783)) . T)) (|has| |#1| (-238)) (((|#1| (-543 (-1109 (-1197)))) . T)) -((($) -2760 (-12 (|has| |#2| (-238)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))))) +((($) -2759 (-12 (|has| |#2| (-238)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))))) ((((-593 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-576)) . T) (((-419 (-576))) . T) (($) . T)) -((((-2 (|:| -4301 (-1179)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4300 (-1179)) (|:| -4439 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-576)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (|has| |#2| (-374)) ((((-876)) . T)) ((((-876)) . T)) -(-2760 (|has| |#3| (-805)) (|has| |#3| (-861))) +(-2759 (|has| |#3| (-805)) (|has| |#3| (-861))) ((((-876)) . T)) ((((-1141)) . T) (((-876)) . T)) ((((-548)) . T) (((-876)) . T)) @@ -3326,14 +3326,14 @@ ((((-576)) . T)) (((|#3|) . T)) ((((-876)) . T)) -(-2760 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) -((((-576)) . 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T) (((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1059 (-419 (-576))))) (((-1197)) . T)) +((((-1146 |#1| (-1197))) . T) (((-576)) . T) (((-1109 (-1197))) . T) (($) -2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) . T) (((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1059 (-419 (-576))))) (((-1197)) . T)) (((|#1|) |has| |#1| (-174))) (((|#1| (-1288 |#1|) (-1288 |#1|)) . T)) ((((-593 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) @@ -3343,12 +3343,12 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-419 (-576))) . T)) -(((|#2|) |has| |#2| (-6 (-4467 "*")))) +(((|#2|) |has| |#2| (-6 (-4466 "*")))) (((|#1|) . T)) ((((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((|#1|) . T) (((-576)) . T)) (((|#1|) . T)) ((((-876)) . T)) -(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . T) (($ $) -2760 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) +(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . T) (($ $) -2759 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-304 |#3|)) . T)) (((|#1|) . T)) @@ -3357,30 +3357,30 @@ (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) -((($ $) -2760 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) -((($ $) -2760 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +((($ $) -2759 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1| |#1|) . 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T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-876)) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -4301 (-1179)) (|:| -4440 |#1|))) . T)) +((((-2 (|:| -4300 (-1179)) (|:| -4439 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2760 (|has| |#2| (-805)) (|has| |#2| (-861))) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(-2759 (|has| |#2| (-805)) (|has| |#2| (-861))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) ((((-1197)) . T) ((|#1|) . T)) @@ -3392,15 +3392,15 @@ (((#0=(-419 (-576)) #0#) . T)) ((((-419 (-576))) . T)) (((|#1|) |has| |#1| (-174))) -(-2760 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070))) +(-2759 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1070))) (((|#1|) . T)) (((|#1|) . 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T) (($) -2759 (|has| |#1| (-174)) (|has| |#1| (-568)))) (|has| |#1| (-568)) (((|#1|) |has| |#1| (-374))) ((((-576)) . T)) ((((-1197) #0=(-117 |#1|)) |has| #0# (-526 (-1197) #0#)) ((#0# #0#) |has| #0# (-319 #0#))) (|has| |#1| (-803)) (|has| |#1| (-803)) -((((-1197)) -2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197))))) +((((-1197)) -2759 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197))))) (((|#2|) . T) (((-576)) |has| |#2| (-1059 (-576))) (((-419 (-576))) |has| |#2| (-1059 (-419 (-576))))) ((((-1103)) . T) ((|#2|) . T) (((-576)) |has| |#2| (-1059 (-576))) (((-419 (-576))) |has| |#2| (-1059 (-419 (-576))))) (((|#1|) . T)) @@ -3449,11 +3449,11 @@ ((($) |has| |#1| (-379))) (|has| |#2| (-832)) (|has| |#2| (-832)) -((((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) (((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2|) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) +((((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) (((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2|) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) ((($ (-1197)) |has| |#1| (-917 (-1197)))) (((|#1|) . T) (((-576)) |has| |#1| (-1059 (-576))) (((-419 (-576))) |has| |#1| (-1059 (-419 (-576))))) -((($) -2760 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360)))) -(((|#1|) . T) (((-419 (-576))) -2760 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) . T)) +((($) -2759 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360)))) +(((|#1|) . T) (((-419 (-576))) -2759 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) ((((-576)) |has| |#1| (-901 (-576))) (((-390)) |has| |#1| (-901 (-390)))) (((|#1|) . T)) @@ -3468,7 +3468,7 @@ (|has| |#1| (-374)) (|has| |#1| (-374)) (((|#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1121)))) -(((|#2|) -2760 (|has| |#2| (-6 (-4467 "*"))) (|has| |#2| (-174)))) +(((|#2|) -2759 (|has| |#2| (-6 (-4466 "*"))) (|has| |#2| (-174)))) (((|#2|) . T)) (|has| |#1| (-374)) (((|#2|) . T)) @@ -3482,12 +3482,12 @@ (((|#2| (-783)) . T)) ((((-1197)) . T)) ((((-884 |#1|)) . T)) -(-2760 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1070))) -(-2760 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-805)) (|has| |#3| (-1070))) +(-2759 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1070))) +(-2759 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-805)) (|has| |#3| (-1070))) ((((-876)) . T)) (((|#1|) . T)) -(-2760 (|has| |#2| (-805)) (|has| |#2| (-861))) -(-2760 (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (-12 (|has| |#1| (-861)) (|has| |#2| (-861)))) +(-2759 (|has| |#2| (-805)) (|has| |#2| (-861))) +(-2759 (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (-12 (|has| |#1| (-861)) (|has| |#2| (-861)))) ((((-884 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-379)) @@ -3505,7 +3505,7 @@ (((|#1|) . T)) ((((-876)) . T)) ((($) . T) ((|#2|) . T) (((-419 (-576))) . T) (((-576)) |has| |#2| (-651 (-576)))) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) @@ -3514,7 +3514,7 @@ (((|#1|) . T)) ((((-876)) . T)) (|has| |#2| (-928)) -((((-2 (|:| -4301 (-1197)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4300 (-1197)) (|:| -4439 (-52)))) . T)) ((((-548)) |has| |#2| (-626 (-548))) (((-907 (-390))) |has| |#2| (-626 (-907 (-390)))) (((-907 (-576))) |has| |#2| (-626 (-907 (-576))))) ((((-876)) . T)) ((((-876)) . T)) @@ -3525,7 +3525,7 @@ ((((-1193 |#1|)) . T) (((-876)) . T)) ((((-876)) . T)) ((((-419 (-576))) |has| |#2| (-1059 (-419 (-576)))) (((-576)) |has| |#2| (-1059 (-576))) ((|#2|) . T) (((-878 |#1|)) . T)) -((((-1197)) -2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197)))) (((-1103)) . T)) +((((-1197)) -2759 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197)))) (((-1103)) . T)) ((((-117 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) ((((-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) (((-576)) |has| |#1| (-1059 (-576))) ((|#1|) . T) (((-1197)) . T)) ((((-876)) . T)) @@ -3544,10 +3544,10 @@ ((((-656 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|)))) ((($) . T) (((-576)) . T) (((-1274 |#1| |#2| |#3| |#4|)) . T) (((-419 (-576))) . 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T)) @@ -3561,16 +3561,16 @@ ((((-419 |#2|) |#3|) . T)) ((((-876)) . T)) (((|#1|) . T)) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) -(((|#2| (-494 (-3503 |#1|) (-783))) . T)) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(((|#2| (-494 (-3502 |#1|) (-783))) . T)) ((((-576) |#1|) . T)) ((((-1179)) . T) (((-876)) . T)) (((|#2| |#2|) . T)) (((|#1| (-543 (-1197))) . T)) -(-2760 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1070))) +(-2759 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1070))) ((((-576)) . T)) (((|#2|) . T)) -((($) -2760 (-12 (|has| |#2| (-238)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))))) +((($) -2759 (-12 (|has| |#2| (-238)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))))) (((|#2|) . T)) ((((-1197)) |has| |#1| (-917 (-1197))) (((-1103)) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) @@ -3579,9 +3579,9 @@ ((($) . T) (((-419 (-576))) . T)) ((($) . T)) ((($) . T)) -(-2760 (|has| |#1| (-861)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-861)) (|has| |#1| (-1121))) (((|#1|) . T)) -((($) -2760 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-876)) . T)) ((((-145)) . T)) (((|#1|) . T) (((-419 (-576))) . T)) @@ -3590,7 +3590,7 @@ ((((-876)) . T)) (((|#1|) . T)) (|has| |#1| (-1173)) -((($ (-1197)) -2760 (|has| (-419 |#2|) (-917 (-1197))) (|has| (-419 |#2|) (-919 (-1197))))) +((($ (-1197)) -2759 (|has| (-419 |#2|) (-917 (-1197))) (|has| (-419 |#2|) (-919 (-1197))))) (((|#1|) . T)) (((|#1| (-543 (-878 |#2|)) (-878 |#2|) (-792 |#1| (-878 |#2|))) . T)) ((((-419 $) (-419 $)) |has| |#1| (-568)) (($ $) . T) ((|#1| |#1|) . T)) @@ -3615,44 +3615,44 @@ (|has| |#1| (-1121)) (|has| |#1| (-1121)) (|has| |#2| (-374)) -(((|#1|) . T) (($) -2760 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) +(((|#1|) . T) (($) -2759 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) (|has| |#1| (-374)) (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576)))) -((($) -2760 (|has| |#2| (-238)) (|has| |#2| (-237)))) +((($) -2759 (|has| |#2| (-238)) (|has| |#2| (-237)))) ((((-576)) . T)) (|has| |#1| (-1121)) -((($ (-1197)) -2760 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) +((($ (-1197)) -2759 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) ((((-1197)) -12 (|has| |#4| (-917 (-1197))) (|has| |#4| (-1070)))) ((((-1197)) -12 (|has| |#3| (-917 (-1197))) (|has| |#3| (-1070)))) (((|#1|) . T)) (|has| |#1| (-238)) -(((|#2| (-245 (-3503 |#1|) (-783))) . T)) +(((|#2| (-245 (-3502 |#1|) (-783))) . 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T)) (((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-419 (-576))) . T) (($) . T)) @@ -3855,7 +3855,7 @@ ((((-876)) . T)) ((((-876)) . T)) ((((-876)) . T)) -(-2760 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2759 (|has| |#1| (-238)) (|has| |#1| (-237))) (((|#1|) . T) (((-876)) . T) (((-1202)) . T)) ((((-1202)) . T)) ((((-876)) . T)) @@ -3864,21 +3864,21 @@ ((($) . T) (((-576)) . T) (((-117 |#1|)) . T) (((-419 (-576))) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (((|#1| (-543 (-878 |#2|)) (-878 |#2|) (-792 |#1| (-878 |#2|))) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2760 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2759 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) ((($) . T) (((-576)) . T)) -((($) -2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-1125)) . T)) ((((-876)) . T)) ((((-1202)) . T) (((-876)) . T)) ((((-1202)) . T) (((-876)) . T)) ((((-1202)) . T)) ((((-1202)) . T)) -((($) -2760 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((($) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) ((($) . T) (((-576)) . T)) -((($) -2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (|has| |#2| (-928)) (((|#1| |#2| (-245 |#1| |#2|) (-245 |#1| |#2|)) . T)) ((((-876)) . T)) @@ -3894,9 +3894,9 @@ (((|#1| |#1|) |has| |#1| (-174))) ((((-711)) . T)) ((((-711)) . T)) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) ((((-1202)) . T)) -(-2760 (|has| |#2| (-805)) (|has| |#2| (-861))) +(-2759 (|has| |#2| (-805)) (|has| |#2| (-861))) (((|#1|) |has| |#1| (-174))) ((((-1202)) . T)) ((((-1274 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-419 (-576))) . T)) @@ -3906,20 +3906,20 @@ (((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-568)) (($) |has| |#1| (-568))) ((((-419 (-576))) . T) (($) . T)) (((|#1| (-576)) . T)) -((($ (-1197)) -2760 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197)))) (($ (-1103)) . T)) +((($ (-1197)) -2759 (|has| |#1| (-917 (-1197))) (|has| |#1| (-919 (-1197)))) (($ (-1103)) . T)) ((((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1|) |has| |#1| (-174))) ((((-1202)) . T)) ((((-1202)) . T)) ((((-1202)) . T)) ((((-1202)) . T)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-1202)) . T)) ((((-1202)) . T)) (|has| |#1| (-374)) (|has| |#1| (-374)) -(-2760 (|has| |#1| (-174)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-174)) (|has| |#1| (-568))) (((|#1| (-576)) . T)) (((|#1| (-419 (-576))) . T)) (((|#1| (-783)) . T)) @@ -3927,24 +3927,24 @@ (((|#1| (-543 |#2|) |#2|) . T)) ((((-576) |#1|) . T)) ((((-576) |#1|) . T)) -(-2760 (|has| |#1| (-102)) (|has| |#1| (-1121))) -(-2760 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237))) +(-2759 (|has| |#1| (-102)) (|has| |#1| (-1121))) +(-2759 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237))) ((((-576) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-907 (-390))) . T) (((-907 (-576))) . T) (((-1197)) . T) (((-548)) . T)) -(-2760 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1070))) -(-2760 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-805)) (|has| |#2| (-805)))) +(-2759 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1070))) +(-2759 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-805)) (|has| |#2| (-805)))) ((((-876)) . T)) ((((-576)) . T)) ((((-576)) . T)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1197)) -12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) (|has| |#2| (-1070)) -(-2760 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-738)) (|has| |#2| (-738)))) +(-2759 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-738)) (|has| |#2| (-738)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-374)) @@ -3977,7 +3977,7 @@ (((|#1| |#2|) . T)) ((((-576)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-576)) . T)) -(-2760 (|has| |#1| (-360)) (|has| |#1| (-379))) +(-2759 (|has| |#1| (-360)) (|has| |#1| (-379))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-419 (-576))) . T) (($) . T) (((-576)) . T)) @@ -3986,11 +3986,11 @@ ((($) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) ((($) . T) (((-576)) |has| |#1| (-651 (-576))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#2|) |has| |#2| (-1121)) (((-576)) -12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121))) (((-419 (-576))) -12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121)))) -(-2760 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2759 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) (((|#1|) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-861)) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-861)) (|has| |#1| (-1121)))) ((((-576) $) . T) (((-656 (-576)) $) . T)) ((($) . T) (((-419 (-576))) . T)) (|has| |#1| (-928)) @@ -4002,14 +4002,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-576)) . T)) ((((-1202)) . T)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2760 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2759 (|has| |#1| (-21)) (|has| |#1| (-860))) (((|#2|) . T)) -(-2760 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2759 (|has| |#1| (-21)) (|has| |#1| (-860))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-876)) -2760 (-12 (|has| |#1| (-625 (-876))) (|has| |#2| (-625 (-876)))) (-12 (|has| |#1| (-1121)) (|has| |#2| (-1121))))) +((((-876)) -2759 (-12 (|has| |#1| (-625 (-876))) (|has| |#2| (-625 (-876)))) (-12 (|has| |#1| (-1121)) (|has| |#2| (-1121))))) ((((-419 |#2|) |#3|) . T)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -4018,7 +4018,7 @@ ((($) . T) (((-576)) . T)) (|has| (-419 |#2|) (-148)) (|has| (-419 |#2|) (-146)) -(-2760 (|has| |#3| (-805)) (|has| |#3| (-861))) +(-2759 (|has| |#3| (-805)) (|has| |#3| (-861))) ((($) . T)) ((((-711)) . T)) (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) @@ -4034,7 +4034,7 @@ ((((-1202)) . T)) ((((-576)) . T)) (((|#2|) . T)) -((((-1197)) -2760 (-12 (|has| (-1195 |#1| |#2| |#3|) (-917 (-1197))) (|has| |#1| (-374))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197)))))) +((((-1197)) -2759 (-12 (|has| (-1195 |#1| |#2| |#3|) (-917 (-1197))) (|has| |#1| (-374))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197)))))) ((((-1197)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-917 (-1197))))) ((((-1197)) -12 (|has| |#1| (-15 * (|#1| (-783) |#1|))) (|has| |#1| (-917 (-1197))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4050,11 +4050,11 @@ ((((-1195 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1161 |#1| |#2|)) . T)) ((((-1195 |#1| |#2| |#3|)) |has| |#1| (-374))) -(((|#2|) . T) (((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) -((((-2 (|:| -4301 (-1197)) (|:| -4440 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) +((((-2 (|:| -4300 (-1197)) (|:| -4439 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1043)) -(((|#2|) . T) (((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) ((($) . T)) ((((-876)) . T)) ((((-548)) |has| |#2| (-626 (-548))) (((-907 (-576))) |has| |#2| (-626 (-907 (-576)))) (((-907 (-390))) |has| |#2| (-626 (-907 (-390)))) (((-390)) . #0=(|has| |#2| (-1043))) (((-227)) . #0#)) @@ -4063,7 +4063,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-1197)) -2760 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) +((((-1197)) -2759 (|has| |#2| (-917 (-1197))) (|has| |#2| (-919 (-1197))))) ((((-876)) . T)) (((|#2|) . T)) ((((-876)) . T)) @@ -4073,15 +4073,15 @@ ((((-1195 |#1| |#2| |#3|)) . T)) ((((-1195 |#1| |#2| |#3|)) . T) (((-1188 |#1| |#2| |#3|)) . T)) ((((-876)) . T)) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) ((((-576) |#1|) . T)) ((((-1195 |#1| |#2| |#3|)) |has| |#1| (-374))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-374)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2760 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1070))) (($) |has| |#4| (-1070)) (((-576)) -12 (|has| |#4| (-651 (-576))) (|has| |#4| (-1070)))) -(((|#2|) . T) ((|#3|) -2760 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1070))) (($) |has| |#3| (-1070)) (((-576)) -12 (|has| |#3| (-651 (-576))) (|has| |#3| (-1070)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2759 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1070))) (($) |has| |#4| (-1070)) (((-576)) -12 (|has| |#4| (-651 (-576))) (|has| |#4| (-1070)))) +(((|#2|) . T) ((|#3|) -2759 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1070))) (($) |has| |#3| (-1070)) (((-576)) -12 (|has| |#3| (-651 (-576))) (|has| |#3| (-1070)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -4095,7 +4095,7 @@ ((((-189)) . T) (((-876)) . T)) ((((-876)) . T)) (((|#1|) . T)) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) ((((-130)) . T) (((-876)) . T)) ((((-576) |#1|) . T) (((-1255 (-576)) $) . T)) ((((-130)) . T)) @@ -4104,14 +4104,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) (($ $) . T) (((-576) |#1|) . T)) ((($ $) . T) (((-419 (-576)) |#1|) . T)) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-928))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-928))) ((($ (-1197)) |has| |#1| (-1070))) -(-2760 (|has| |#1| (-861)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-861)) (|has| |#1| (-1121))) ((((-876)) . T)) ((((-876)) . T)) ((((-876)) . T)) (((|#1| (-543 |#2|)) . T)) -((((-2 (|:| -4301 (-1197)) (|:| -4440 (-52)))) . T)) +((((-2 (|:| -4300 (-1197)) (|:| -4439 (-52)))) . T)) ((((-576) (-130)) . T)) (((|#1| (-576)) . T)) (((|#1| (-419 (-576))) . T)) @@ -4126,8 +4126,8 @@ ((((-1202)) . T)) ((((-876)) . T) (((-1202)) . T)) ((((-876)) . T) (((-1202)) . T)) -(-2760 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) -(-2760 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) +(-2759 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) +(-2759 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-928))) ((($) . T)) (((|#2| (-543 (-878 |#1|))) . T)) ((((-1202)) . T)) @@ -4142,7 +4142,7 @@ ((((-1202)) . T)) ((((-876)) . T) (((-1202)) . T)) ((((-1202)) . T)) -((((-876)) -2760 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) +((((-876)) -2759 (|has| |#1| (-625 (-876))) (|has| |#1| (-1121)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1179) |#1|) . T)) @@ -4150,7 +4150,7 @@ ((((-419 |#2|)) . T)) (|has| |#1| (-568)) (|has| |#1| (-568)) -((((-2 (|:| -4301 |#1|) (|:| -4440 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4439 |#2|))) . T)) (((|#2| (-783)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-419 (-576))) . T)) @@ -4160,14 +4160,14 @@ ((((-576)) . T) (($) . T)) (((|#2| $) |has| |#2| (-296 |#2| |#2|))) (((|#1| (-656 |#1|)) |has| |#1| (-860))) -(-2760 (|has| |#1| (-238)) (|has| |#1| (-360))) -(-2760 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-238)) (|has| |#1| (-360))) +(-2759 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-1284 |#1|)) . T) (((-576)) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-1059 (-419 (-576))))) (|has| |#1| (-1121)) (((|#1|) . T)) ((((-419 (-576))) . T) (($) . T)) -((((-1284 |#1|)) . T) (((-576)) . T) (($) -2760 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) (((-1103)) . T) ((|#2|) . T) (((-419 (-576))) -2760 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1059 (-419 (-576)))))) -((((-1020 |#1|)) . T) ((|#1|) . T) (((-576)) -2760 (|has| (-1020 |#1|) (-1059 (-576))) (|has| |#1| (-1059 (-576)))) (((-419 (-576))) -2760 (|has| (-1020 |#1|) (-1059 (-419 (-576)))) (|has| |#1| (-1059 (-419 (-576)))))) +((((-1284 |#1|)) . T) (((-576)) . T) (($) -2759 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-928))) (((-1103)) . T) ((|#2|) . T) (((-419 (-576))) -2759 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1059 (-419 (-576)))))) +((((-1020 |#1|)) . T) ((|#1|) . T) (((-576)) -2759 (|has| (-1020 |#1|) (-1059 (-576))) (|has| |#1| (-1059 (-576)))) (((-419 (-576))) -2759 (|has| (-1020 |#1|) (-1059 (-419 (-576)))) (|has| |#1| (-1059 (-419 (-576)))))) ((((-929 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) @@ -4184,11 +4184,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1161 |#1| |#2|) #0#) |has| (-1161 |#1| |#2|) (-319 (-1161 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((#0=(-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) #0#) |has| (-2 (|:| -4301 |#1|) (|:| -4440 |#2|)) (-319 (-2 (|:| -4301 |#1|) (|:| -4440 |#2|))))) -(-2760 (|has| |#1| (-238)) (|has| |#1| (-237))) +(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((#0=(-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) #0#) |has| (-2 (|:| -4300 |#1|) (|:| -4439 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4439 |#2|))))) +(-2759 (|has| |#1| (-238)) (|has| |#1| (-237))) (((#0=(-117 |#1|)) |has| #0# (-319 #0#))) ((($ $) . T)) -(-2760 (|has| |#1| (-861)) (|has| |#1| (-1121))) +(-2759 (|has| |#1| (-861)) (|has| |#1| (-1121))) ((($ $) . T) ((#0=(-878 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-238)) ((|#2| |#1|) |has| |#1| (-238)) ((|#3| |#1|) . T) ((|#3| $) . 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201163) ((-326 . -911) 201127) ((-323 . -911) NIL) ((-724 . -464) 201058) ((-48 . -102) T) ((-1272 . -296) 201016) ((-1251 . -296) 200916) ((-656 . -678) 200900) ((-656 . -663) 200884) ((-350 . -21) T) ((-350 . -25) T) ((-40 . -360) NIL) ((-176 . -21) T) ((-176 . -25) T) ((-656 . -384) 200868) ((-617 . -502) 200850) ((-614 . -296) 200802) ((-617 . -625) 200769) ((-400 . -102) T) ((-1141 . -144) T) ((-127 . -625) 200701) ((-888 . -1121) T) ((-670 . -423) 200685) ((-743 . -1238) T) ((-726 . -625) 200667) ((-255 . -625) 200634) ((-189 . -625) 200616) ((-163 . -625) 200598) ((-158 . -625) 200580) ((-1303 . -738) T) ((-1123 . -34) T) ((-885 . -807) NIL) ((-885 . -804) NIL) ((-872 . -861) T) ((-743 . -901) NIL) ((-1312 . -132) T) ((-392 . -132) T) ((-907 . -628) 200548) ((-923 . -102) T) ((-743 . -1059) 200424) ((-1195 . -1238) T) ((-1194 . -1238) T) ((-543 . -132) T) ((-1188 . -1238) T) ((-1108 . -423) 200408) ((-1021 . -501) 200392) ((-118 . -412) 200369) ((-1147 . -1238) T) ((-794 . -423) 200353) ((-792 . -423) 200337) ((-962 . -34) T) ((-706 . -1173) NIL) ((-258 . -660) 200157) ((-257 . -660) 199964) ((-829 . -939) 199943) ((-466 . -423) 199927) ((-614 . -19) 199911) ((-1167 . -1231) 199880) ((-1188 . -901) NIL) ((-1188 . -899) 199832) ((-614 . -616) 199809) ((-108 . -864) T) ((-1224 . -625) 199741) ((-1196 . -625) 199723) ((-62 . -407) T) ((-1194 . -1059) 199658) ((-1188 . -1059) 199624) ((-706 . -38) 199574) ((-40 . -658) 199504) ((-486 . -296) 199462) ((-1244 . -625) 199444) ((-743 . -388) 199428) ((-850 . -625) 199410) ((-670 . -1079) T) ((-635 . -919) 199333) ((-1272 . -1023) 199299) ((-448 . -1238) T) ((-1251 . -1023) 199265) ((-256 . -1238) T) ((-1109 . -628) 199249) ((-1084 . -1214) 199224) ((-1097 . -628) 199201) ((-886 . -626) 199008) ((-886 . -625) 198990) ((-118 . -919) NIL) ((-713 . -234) 198977) ((-1210 . -501) 198914) ((-430 . -1043) 198892) ((-48 . -319) 198879) ((-1084 . -107) 198825) ((-491 . -501) 198762) ((-537 . -1238) T) ((-532 . -1238) T) ((-1188 . -349) 198714) ((-1162 . -501) 198685) ((-1188 . -388) 198637) ((-1108 . -1079) T) ((-449 . -102) T) ((-185 . -1121) T) ((-258 . -34) T) ((-257 . -34) T) ((-1179 . -864) T) ((-862 . -628) 198621) ((-794 . -1079) T) ((-792 . -1079) T) ((-743 . -917) 198598) ((-466 . -1079) T) ((-59 . -501) 198582) ((-1055 . -1077) 198556) ((-531 . -501) 198540) ((-528 . -501) 198524) ((-509 . -501) 198508) ((-508 . -501) 198492) ((-250 . -526) 198425) ((-1055 . -111) 198392) ((-1195 . -917) 198305) ((-1194 . -917) 198211) ((-682 . -1133) T) ((-1188 . -917) 198044) ((-657 . -93) T) ((-1147 . -917) 198028) ((-365 . -1173) T) ((-332 . -1077) 198010) ((-31 . -502) 197991) ((-258 . -806) 197970) ((-258 . -805) 197949) ((-257 . -806) 197928) ((-257 . -805) 197907) ((-31 . -625) 197873) ((-50 . -1079) T) ((-258 . -738) 197851) ((-257 . -738) 197829) ((-1232 . -1121) T) ((-682 . -23) T) ((-593 . -1079) T) ((-530 . -1079) T) ((-390 . -1077) 197794) ((-332 . -111) 197769) ((-73 . -394) T) ((-73 . -407) T) 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195042) ((-337 . -526) 194975) ((-508 . -296) 194927) ((-390 . -248) T) ((-390 . -238) T) ((-848 . -1070) T) ((-839 . -1070) T) ((-724 . -968) 194896) ((-713 . -861) T) ((-624 . -864) T) ((-486 . -625) 194878) ((-1274 . -1072) 194783) ((-592 . -658) 194755) ((-576 . -658) 194727) ((-507 . -658) 194677) ((-839 . -238) 194656) ((-135 . -861) T) ((-1274 . -652) 194548) ((-670 . -1121) T) ((-1210 . -616) 194527) ((-562 . -1214) 194506) ((-347 . -1121) T) ((-329 . -374) 194485) ((-419 . -148) 194464) ((-419 . -146) 194443) ((-983 . -1133) 194342) ((-827 . -1133) 194320) ((-245 . -917) 194252) ((-666 . -866) 194236) ((-491 . -616) 194215) ((-110 . -864) T) ((-536 . -1238) T) ((-562 . -107) 194165) ((-1025 . -388) 194147) ((-1025 . -349) 194129) ((-1197 . -625) 194111) ((-97 . -1121) T) ((-983 . -23) 193922) ((-489 . -21) T) ((-489 . -25) T) ((-827 . -23) 193774) ((-1197 . -626) 193696) ((-59 . -19) 193680) ((-1193 . -738) T) ((-1146 . -738) T) ((-1108 . -1121) T) ((-528 . -19) 193664) ((-508 . -19) 193648) ((-59 . -616) 193625) ((-1024 . -237) 193562) ((-920 . -102) 193512) ((-868 . -738) T) ((-794 . -1121) T) ((-528 . -616) 193489) ((-508 . -616) 193466) ((-792 . -1121) T) ((-792 . -1086) 193433) ((-473 . -1121) T) ((-466 . -1121) T) ((-598 . -729) 193408) ((-661 . -1121) T) ((-1280 . -47) 193385) ((-1274 . -102) T) ((-1273 . -47) 193355) ((-1252 . -47) 193332) ((-1232 . -174) 193283) ((-1194 . -317) 193262) ((-1188 . -317) 193241) ((-1117 . -628) 193222) ((-1111 . -628) 193203) ((-1101 . -568) 193154) ((-1101 . -1242) 193105) ((-1025 . -917) NIL) ((-1094 . -628) 193086) ((-682 . -132) T) ((-639 . -1133) T) ((-1087 . -628) 193067) ((-1057 . -628) 193048) ((-1040 . -628) 193029) ((-726 . -1077) 192999) ((-711 . -658) 192949) ((-284 . -1121) T) ((-85 . -453) T) ((-85 . -407) T) ((-724 . -911) 192852) ((-723 . -174) T) ((-50 . -1121) T) ((-607 . -47) 192829) ((-227 . -660) 192794) ((-593 . -1121) T) ((-530 . -1121) T) ((-499 . -832) T) ((-499 . -939) T) ((-370 . -1242) T) 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190310) ((-355 . -625) 190292) ((-273 . -626) 190040) ((-273 . -625) 190022) ((-253 . -625) 190004) ((-253 . -626) 189865) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1162 . -625) 189847) ((-1141 . -652) 189834) ((-1141 . -1072) 189821) ((-831 . -738) T) ((-831 . -871) T) ((-614 . -298) 189798) ((-593 . -729) 189763) ((-491 . -626) NIL) ((-491 . -625) 189745) ((-530 . -729) 189690) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-929 . -625) 189672) ((-929 . -626) 189654) ((-398 . -738) T) ((-886 . -1077) 189606) ((-886 . -111) 189544) ((-726 . -1070) T) ((-724 . -1264) 189528) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 189460) ((-390 . -807) T) ((-169 . -1238) T) ((-225 . -1121) T) ((-390 . -804) T) ((-59 . -626) 189421) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -625) 189333) ((-227 . -738) T) ((-528 . -626) 189294) ((-528 . -625) 189206) ((-509 . -625) 189138) ((-508 . -626) 189099) ((-508 . -625) 189011) ((-1101 . -374) 188962) ((-40 . -423) 188939) ((-77 . -1238) T) ((-885 . -928) NIL) ((-370 . -339) 188923) ((-370 . -374) T) ((-364 . -339) 188907) ((-364 . -374) T) ((-356 . -339) 188891) ((-356 . -374) T) ((-326 . -294) 188870) ((-108 . -374) T) ((-70 . -1238) T) ((-1252 . -349) 188822) ((-885 . -660) 188767) ((-1252 . -388) 188719) ((-983 . -132) 188574) ((-827 . -132) 188445) ((-45 . -864) NIL) ((-977 . -663) 188429) ((-1108 . -174) 188340) ((-977 . -384) 188324) ((-1083 . -806) T) ((-1083 . -803) T) ((-886 . -628) 188222) ((-794 . -174) 188113) ((-792 . -174) 188024) ((-828 . -47) 187986) ((-1083 . -738) T) ((-337 . -501) 187970) ((-971 . -738) T) ((-1301 . -319) 187908) ((-1280 . -917) 187821) ((-466 . -174) 187732) ((-250 . -296) 187684) ((-1273 . -917) 187590) ((-1272 . -1077) 187425) ((-1252 . -917) 187258) ((-493 . -738) T) ((-1251 . -1077) 187066) ((-1232 . -300) 187045) ((-1207 . -1238) T) ((-1204 . -379) T) ((-1203 . -379) T) ((-1167 . -152) 187029) ((-1141 . -102) T) ((-1139 . -1121) T) ((-1101 . -23) T) ((-1101 . -1133) T) ((-1096 . -102) T) ((-1078 . -625) 186996) ((-1024 . -421) 186968) ((-946 . -974) T) ((-749 . -319) 186906) ((-75 . -1238) T) ((-676 . -393) 186878) ((-171 . -928) 186831) ((-30 . -974) T) ((-112 . -856) T) ((-1 . -625) 186813) ((-1020 . -911) 186734) ((-129 . -663) 186716) ((-50 . -632) 186700) ((-706 . -658) 186635) ((-607 . -917) 186548) ((-450 . -102) T) ((-129 . -384) 186530) ((-142 . -319) NIL) ((-886 . -1070) T) ((-845 . -861) 186509) ((-81 . -1238) T) ((-723 . -300) T) ((-40 . -1079) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 186491) ((-171 . -660) 186365) ((-519 . -625) 186347) ((-362 . -148) 186329) ((-362 . -146) T) ((-370 . -1133) T) ((-364 . -1133) T) ((-356 . -1133) T) ((-1025 . -317) T) ((-933 . -317) T) ((-886 . -248) T) ((-108 . -1133) T) ((-886 . -238) 186308) ((-1272 . -111) 186129) ((-1251 . -111) 185918) ((-250 . -1276) 185902) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 185889) ((-323 . -319) 185830) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1025 . -1043) T) ((-31 . -628) 185811) ((-108 . -23) T) ((-666 . -1072) 185795) ((-250 . -616) 185772) ((-343 . -1121) T) ((-666 . -652) 185742) ((-1274 . -38) 185634) ((-1261 . -928) 185613) ((-112 . -1121) T) ((-828 . -1238) T) ((-425 . -1238) T) ((-1056 . -102) T) ((-1261 . -660) 185502) ((-885 . -806) NIL) ((-869 . -660) 185476) ((-885 . -803) NIL) ((-828 . -901) NIL) ((-885 . -738) T) ((-1108 . -526) 185349) ((-794 . -526) 185296) ((-792 . -526) 185248) ((-583 . -660) 185235) ((-828 . -1059) 185063) ((-466 . -526) 185006) ((-400 . -401) T) ((-1272 . -628) 184819) ((-1251 . -628) 184567) ((-60 . -1238) T) ((-633 . -861) 184546) ((-512 . -673) T) ((-1167 . -997) 184515) ((-1045 . -658) 184452) ((-1024 . -464) T) ((-711 . -860) T) ((-522 . -804) T) ((-486 . -1077) 184287) ((-512 . -113) T) ((-354 . -1121) T) ((-323 . -1173) NIL) ((-299 . -132) T) ((-406 . -1121) T) ((-884 . -1079) T) ((-706 . -381) 184254) ((-365 . -658) 184184) ((-225 . -632) 184161) ((-337 . -296) 184113) ((-486 . -111) 183934) ((-1272 . -1070) T) ((-1251 . -1070) T) ((-828 . -388) 183918) ((-836 . -1238) T) ((-171 . -738) T) ((-1303 . -1238) T) ((-666 . -102) T) ((-1272 . -248) 183897) ((-1272 . -238) 183849) ((-1251 . -238) 183754) ((-1251 . -248) 183733) ((-1024 . -414) NIL) ((-682 . -651) 183681) ((-326 . -38) 183591) ((-323 . -38) 183520) ((-69 . -625) 183502) ((-329 . -505) 183468) ((-48 . -658) 183418) ((-1210 . -298) 183397) ((-1246 . -861) T) ((-1134 . -1133) 183375) ((-83 . -1238) T) ((-61 . -625) 183357) ((-878 . -864) T) ((-491 . -298) 183336) ((-1303 . -1059) 183313) ((-1185 . -1121) T) ((-1134 . -23) 183165) ((-828 . -917) 183101) ((-1261 . -738) T) ((-1123 . -1238) T) ((-486 . -628) 182927) ((-362 . -237) T) ((-1108 . -300) 182858) ((-985 . -1121) T) ((-908 . -102) T) ((-794 . -300) 182769) ((-337 . -19) 182753) ((-59 . -298) 182730) ((-792 . -300) 182661) ((-869 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 182638) ((-337 . -616) 182615) ((-508 . -298) 182592) ((-466 . -300) 182523) ((-1056 . -319) 182374) ((-890 . -502) 182355) ((-890 . -625) 182321) ((-693 . -502) 182302) ((-583 . -738) T) ((-688 . -502) 182283) ((-693 . -625) 182233) ((-688 . -625) 182199) ((-674 . -625) 182181) ((-490 . -502) 182162) ((-490 . -625) 182128) ((-250 . -626) 182089) ((-250 . -502) 182066) ((-139 . -502) 182047) ((-138 . -502) 182028) ((-134 . -502) 182009) ((-250 . -625) 181901) ((-215 . -102) T) ((-139 . -625) 181867) ((-138 . -625) 181833) ((-134 . -625) 181799) ((-1168 . -34) T) ((-962 . -1238) T) ((-354 . -729) 181744) ((-682 . -25) T) ((-682 . -21) T) ((-1197 . -628) 181725) ((-341 . -1238) T) ((-486 . -1070) T) ((-647 . -429) 181690) ((-619 . -429) 181655) ((-1141 . -1173) T) ((-1273 . -317) 181634) ((-724 . -1072) 181457) ((-593 . -300) T) ((-530 . -300) T) ((-1252 . -317) 181436) ((-486 . -238) 181388) ((-486 . -248) 181367) ((-451 . -1238) T) ((-724 . -652) 181196) ((-1252 . -1043) NIL) ((-1101 . -132) T) ((-886 . -807) 181175) ((-145 . -102) T) ((-40 . -1121) T) ((-886 . -804) 181154) ((-656 . -1031) 181138) ((-592 . -1079) T) ((-576 . -1079) T) ((-507 . -1079) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 181122) ((-323 . -412) 181083) ((-364 . -132) T) ((-356 . -132) T) ((-1202 . -1121) T) ((-1141 . -38) 181070) ((-1115 . -625) 181037) ((-108 . -132) T) ((-973 . -1121) T) ((-940 . -1121) T) ((-783 . -1121) T) ((-684 . -1121) T) ((-713 . -148) T) ((-117 . -148) T) ((-1310 . -21) T) ((-1310 . -25) T) ((-1308 . -21) T) ((-1308 . -25) T) ((-676 . -1077) 181021) ((-543 . -861) T) ((-512 . -861) T) ((-376 . -1238) T) ((-366 . -1077) 180973) ((-363 . -1077) 180925) ((-355 . -1077) 180877) ((-258 . -1238) T) ((-257 . -1238) T) ((-273 . -1077) 180720) ((-253 . -1077) 180563) ((-676 . -111) 180542) ((-829 . -1242) 180521) ((-559 . -856) T) ((-326 . -919) 180487) ((-366 . -111) 180425) ((-363 . -111) 180363) ((-355 . -111) 180301) ((-273 . -111) 180130) ((-253 . -111) 179959) ((-323 . -919) NIL) ((-635 . -423) 179943) ((-44 . -21) T) ((-44 . -25) T) ((-924 . -864) 179894) ((-827 . -651) 179800) ((-829 . -568) 179779) ((-499 . -864) T) ((-258 . -1059) 179606) ((-257 . -1059) 179433) ((-127 . -120) 179417) ((-219 . -864) T) ((-929 . -1077) 179382) ((-724 . -102) T) ((-711 . -1079) T) ((-609 . -628) 179363) ((-597 . -628) 179344) ((-548 . -630) 179247) ((-354 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -625) 179229) ((-929 . -111) 179185) ((-40 . -729) 179130) ((-884 . -1121) T) ((-676 . -628) 179107) ((-657 . -628) 179088) ((-366 . -628) 179025) ((-363 . -628) 178962) ((-355 . -628) 178899) ((-559 . -1121) T) ((-337 . -626) 178860) ((-337 . -625) 178772) ((-273 . -628) 178525) ((-253 . -628) 178310) ((-188 . -1238) T) ((-1251 . -804) 178263) ((-1251 . -807) 178216) ((-258 . -388) 178185) ((-257 . -388) 178154) ((-561 . -864) T) ((-666 . -38) 178124) ((-620 . -34) T) ((-494 . -1133) 178102) ((-487 . -34) T) ((-1134 . -132) 177973) ((-983 . -25) 177784) ((-929 . -628) 177734) ((-888 . -625) 177716) ((-983 . -21) 177671) ((-827 . -25) 177504) ((-827 . -21) 177415) ((-1244 . -379) T) ((-635 . -1079) T) ((-1199 . -568) 177394) ((-1193 . -47) 177371) ((-366 . -1070) T) ((-363 . -1070) T) ((-494 . -23) 177223) ((-355 . -1070) T) ((-273 . -1070) T) ((-253 . -1070) T) ((-1146 . -47) 177195) ((-118 . -1079) T) ((-1055 . -660) 177169) ((-977 . -34) T) ((-366 . -238) 177148) ((-366 . -248) T) ((-363 . -238) 177127) ((-363 . -248) T) ((-355 . -238) 177106) ((-355 . -248) T) ((-273 . -336) 177078) ((-253 . -336) 177035) ((-273 . -238) 177014) ((-1178 . -152) 176998) ((-258 . -917) 176930) ((-257 . -917) 176862) ((-1163 . -911) 176783) ((-1103 . -861) T) ((-1255 . -1238) 176761) ((-426 . -1133) T) ((-1075 . -23) T) ((-1045 . -860) T) ((-929 . -1070) T) ((-332 . -660) 176743) ((-713 . -237) T) ((-682 . -234) 176688) ((-1232 . -1023) 176654) ((-1194 . -939) 176633) ((-1188 . -939) 176612) ((-1188 . -832) NIL) ((-1020 . -1072) 176508) ((-986 . -1238) T) ((-929 . -248) T) ((-829 . -374) 176487) ((-396 . -23) T) ((-128 . -1121) 176465) ((-122 . -1121) 176443) ((-929 . -238) T) ((-129 . -34) T) ((-390 . -660) 176408) ((-1020 . -652) 176356) ((-884 . -729) 176343) ((-1317 . -658) 176315) ((-1067 . -152) 176280) ((-1014 . -1238) T) ((-876 . -1238) T) ((-40 . -174) T) ((-706 . -423) 176262) ((-724 . -319) 176249) ((-848 . -660) 176209) ((-839 . -660) 176183) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 176162) ((-592 . -1121) T) ((-576 . -1121) T) ((-507 . -1121) T) ((-1193 . -1238) T) ((-250 . -298) 176139) ((-1146 . -1238) T) ((-868 . -1238) T) ((-323 . -272) 176100) ((-323 . -232) 176061) ((-1243 . -864) T) ((-1193 . -901) NIL) ((-55 . -1121) T) ((-1146 . -901) 175920) ((-130 . -861) T) ((-1193 . -1059) 175800) ((-1146 . -1059) 175683) ((-185 . -625) 175665) ((-868 . -1059) 175561) ((-794 . -296) 175488) ((-829 . -1133) T) ((-1055 . -738) T) ((-1067 . -997) 175417) ((-614 . -663) 175401) ((-1024 . -911) 175308) ((-1020 . -102) T) ((-829 . -23) T) ((-724 . -1173) 175286) ((-706 . -1079) T) ((-614 . -384) 175270) ((-362 . -464) T) ((-354 . -300) T) ((-1289 . -1121) T) ((-254 . -1121) T) ((-411 . -102) T) ((-299 . -21) T) ((-299 . -25) T) ((-372 . -738) T) ((-722 . -1121) T) ((-711 . -1121) T) ((-372 . -485) T) ((-1232 . -625) 175252) ((-1193 . -388) 175236) ((-1146 . -388) 175220) ((-1045 . -423) 175182) ((-142 . -231) 175164) ((-390 . -806) T) ((-390 . -803) T) ((-884 . -174) T) ((-390 . -738) T) ((-723 . -625) 175146) ((-724 . -38) 174975) ((-1288 . -1286) 174959) ((-362 . -414) T) ((-1288 . -1121) 174909) ((-1211 . -1121) T) ((-592 . -729) 174896) ((-576 . -729) 174883) ((-507 . -729) 174848) ((-1274 . -658) 174738) ((-326 . -641) 174717) ((-848 . -738) T) ((-839 . -738) T) ((-1136 . -1238) T) ((-656 . -1238) T) ((-1101 . -651) 174665) ((-1193 . -917) 174608) ((-1146 . -917) 174592) ((-827 . -234) 174483) ((-674 . -1077) 174467) ((-108 . -651) 174449) ((-494 . -132) 174320) ((-1199 . -1133) T) ((-831 . -1238) T) ((-971 . -47) 174289) ((-635 . -1121) T) ((-674 . -111) 174268) ((-503 . -625) 174234) ((-337 . -298) 174211) ((-398 . -1238) T) ((-334 . -1238) T) ((-493 . -47) 174168) ((-1199 . -23) T) ((-118 . -1121) T) ((-103 . -102) 174118) ((-1300 . -1133) T) ((-560 . -861) T) ((-227 . -1238) T) ((-1075 . -132) T) ((-1045 . -1079) T) ((-1300 . -23) T) ((-831 . -1059) 174102) ((-1218 . -625) 174084) ((-1024 . -736) 174056) ((-1141 . -840) T) ((-711 . -729) 174021) ((-598 . -625) 174003) ((-398 . -1059) 173987) ((-365 . -1079) T) ((-396 . -132) T) ((-334 . -1059) 173971) ((-1126 . -1121) T) ((-1101 . -21) T) ((-1101 . -25) T) ((-227 . -901) 173953) ((-1025 . -939) T) ((-91 . -34) T) ((-1025 . -832) T) ((-933 . -939) T) ((-1020 . -319) 173918) ((-890 . -628) 173899) ((-499 . -1242) T) ((-726 . -660) 173859) ((-693 . -628) 173840) ((-688 . -628) 173821) ((-219 . -1242) T) ((-419 . -911) 173742) ((-227 . -1059) 173702) ((-40 . -300) T) ((-499 . -568) T) ((-490 . -628) 173683) ((-370 . -25) T) ((-326 . -658) 173338) ((-323 . -658) 173252) ((-370 . -21) T) ((-364 . -25) T) ((-364 . -21) T) ((-219 . -568) T) ((-356 . -25) T) ((-356 . -21) T) ((-329 . -234) 173198) ((-250 . -628) 173175) ((-139 . -628) 173156) ((-138 . -628) 173137) ((-134 . -628) 173118) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1079) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1083 . -1238) T) ((-971 . -1238) T) ((-725 . -1238) T) ((-670 . -625) 173100) ((-493 . -1238) T) ((-749 . -748) 173084) ((-347 . -625) 173066) ((-68 . -394) T) ((-68 . -407) T) ((-1123 . -107) 173050) ((-1083 . -901) 173032) ((-971 . -901) 172957) ((-665 . -1133) T) ((-635 . -729) 172944) ((-493 . -901) NIL) ((-1167 . -102) T) ((-1115 . -630) 172928) ((-1083 . -1059) 172910) ((-97 . -625) 172892) ((-489 . -148) T) ((-971 . -1059) 172772) ((-118 . -729) 172717) ((-724 . -919) 172624) ((-665 . -23) T) ((-493 . -1059) 172500) ((-1108 . -626) NIL) ((-1108 . -625) 172482) ((-794 . -626) NIL) ((-794 . -625) 172443) ((-792 . -626) 172077) ((-792 . -625) 171991) ((-1134 . -651) 171897) ((-811 . -864) 171876) ((-473 . -625) 171858) ((-466 . -625) 171840) ((-466 . -626) 171701) ((-1056 . -231) 171647) ((-886 . -928) 171626) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 171608) ((-590 . -102) T) ((-366 . -1307) 171592) ((-363 . -1307) 171576) ((-355 . -1307) 171560) ((-122 . -526) 171493) ((-128 . -526) 171426) ((-523 . -804) T) ((-523 . -807) T) ((-522 . -806) T) ((-103 . -319) 171364) ((-224 . -102) 171314) ((-711 . -174) T) ((-706 . -1121) T) ((-886 . -660) 171230) ((-65 . -395) T) ((-284 . -625) 171212) ((-65 . -407) T) ((-971 . -388) 171196) ((-884 . -300) T) ((-50 . -625) 171178) ((-1020 . -38) 171126) ((-1141 . -658) 171098) ((-593 . -625) 171080) ((-493 . -388) 171064) ((-593 . -626) 171046) ((-530 . -625) 171028) ((-929 . -1307) 171015) ((-885 . -1238) T) ((-713 . -464) T) ((-507 . -526) 170981) ((-1299 . -1238) T) ((-1298 . -1238) T) ((-499 . -374) T) ((-366 . -379) 170960) ((-363 . -379) 170939) ((-355 . -379) 170918) ((-726 . -738) T) ((-219 . -374) T) ((-117 . -464) T) ((-1311 . -1302) 170902) ((-885 . -899) 170879) ((-885 . -901) NIL) ((-983 . -861) 170778) ((-827 . -861) 170729) ((-1245 . -102) T) ((-666 . -668) 170713) ((-1224 . -34) T) ((-173 . -625) 170695) ((-1134 . -25) 170528) ((-1134 . -21) 170439) ((-885 . -1059) 170416) ((-971 . -917) 170397) ((-1261 . -47) 170374) ((-929 . -379) T) ((-605 . -864) T) ((-59 . -663) 170358) ((-528 . -663) 170342) ((-493 . -917) 170319) ((-71 . -453) T) ((-71 . -407) T) ((-508 . -663) 170303) ((-59 . -384) 170287) ((-635 . -174) T) ((-528 . -384) 170271) ((-508 . -384) 170255) ((-558 . -1238) T) ((-839 . -720) 170239) ((-1193 . -317) 170218) ((-1199 . -132) T) ((-1163 . -1072) 170202) ((-118 . -174) T) ((-1163 . -652) 170134) ((-1167 . -319) 170072) ((-171 . -1238) T) ((-1300 . -132) T) ((-1273 . -939) 170051) ((-1252 . -939) 170030) ((-1252 . -832) NIL) ((-880 . -1072) 170000) ((-647 . -756) 169984) ((-619 . -756) 169968) ((-1251 . -928) 169921) ((-1045 . -1121) T) ((-924 . -1133) T) ((-880 . -652) 169891) ((-706 . -729) 169841) ((-915 . -1238) T) ((-885 . -388) 169818) ((-885 . -349) 169795) ((-853 . -1238) T) ((-820 . -1238) T) ((-171 . -899) 169779) ((-171 . -901) 169704) ((-781 . -1238) T) ((-689 . -1238) T) ((-1288 . -526) 169637) ((-1272 . -660) 169534) ((-1101 . -234) 169407) ((-499 . -1133) T) ((-365 . -1121) T) ((-219 . -1133) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1059) 169303) ((-304 . -911) 169260) ((-329 . -861) T) ((-1251 . -660) 169068) ((-886 . -806) 169047) ((-886 . -803) 169026) ((-886 . -738) T) ((-499 . -23) T) ((-370 . -234) 168999) ((-364 . -234) 168972) ((-356 . -234) 168945) ((-176 . -464) T) ((-86 . -453) T) ((-224 . -319) 168883) ((-86 . -407) T) ((-225 . -625) 168865) ((-108 . -234) 168852) ((-219 . -23) T) ((-1312 . -1305) 168831) ((-689 . -1059) 168815) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-1261 . -1238) T) ((-137 . -482) 168770) ((-869 . -1238) T) ((-666 . -658) 168729) ((-48 . -1121) T) ((-724 . -272) 168713) ((-724 . -232) 168697) ((-885 . -917) NIL) ((-583 . -1238) T) ((-1261 . -901) NIL) ((-904 . -102) T) ((-900 . -102) T) ((-400 . -1121) T) ((-171 . -388) 168681) ((-171 . -349) 168665) ((-1261 . -1059) 168545) ((-869 . -1059) 168441) ((-1163 . -102) T) ((-1020 . -919) 168364) ((-674 . -804) 168343) ((-665 . -132) T) ((-674 . -807) 168322) ((-118 . -526) 168230) ((-583 . -1059) 168212) ((-304 . -1295) 168182) ((-1188 . -864) NIL) ((-880 . -102) T) ((-982 . -568) 168161) ((-1232 . -1077) 168044) ((-1024 . -1072) 167989) ((-494 . -651) 167895) ((-923 . -1121) T) ((-1045 . -729) 167832) ((-723 . -1077) 167797) ((-1024 . -652) 167742) ((-629 . -102) T) ((-614 . -34) T) ((-1168 . -1238) T) ((-1232 . -111) 167611) ((-486 . -660) 167508) ((-365 . -729) 167453) ((-171 . -917) 167412) ((-711 . -300) T) ((-706 . -174) T) ((-723 . -111) 167368) ((-1317 . -1079) T) ((-1261 . -388) 167352) ((-430 . -1242) 167330) ((-1139 . -625) 167312) ((-323 . -860) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1251 . -803) 167265) ((-1251 . -806) 167218) ((-1272 . -738) T) ((-1251 . -738) T) ((-48 . -729) 167183) ((-227 . -1043) T) ((-1274 . -423) 167149) ((-1261 . -917) 167092) ((-362 . -1295) 167069) ((-1232 . -628) 166951) ((-730 . -738) T) ((-343 . -625) 166933) ((-532 . -864) 166912) ((-1134 . -234) 166803) ((-112 . -625) 166785) ((-112 . -626) 166767) ((-730 . -485) T) ((-723 . -628) 166717) ((-1311 . -1072) 166701) ((-494 . -25) 166534) ((-128 . -501) 166518) ((-122 . -501) 166502) ((-494 . -21) 166413) ((-1311 . -652) 166383) ((-635 . -300) T) ((-598 . -1077) 166358) ((-449 . -1121) T) ((-1083 . -317) T) ((-118 . -300) T) ((-1125 . -102) T) ((-1024 . -102) T) ((-598 . -111) 166326) ((-1232 . -1070) T) ((-1163 . -319) 166264) ((-1083 . -1043) T) ((-1075 . -25) T) ((-66 . -1238) T) ((-907 . -1238) T) ((-1075 . -21) T) ((-723 . -1070) T) ((-396 . -21) T) ((-396 . -25) T) ((-706 . -526) NIL) ((-1045 . -174) T) ((-723 . -248) T) ((-1083 . -557) T) ((-724 . -658) 166174) ((-518 . -102) T) ((-514 . -102) T) ((-365 . -174) T) ((-354 . -625) 166156) ((-419 . -1072) 166108) ((-406 . -625) 166090) ((-1141 . -860) T) ((-486 . -738) T) ((-907 . -1059) 166058) ((-419 . -652) 166010) ((-108 . -861) T) ((-670 . -1077) 165994) ((-499 . -132) T) ((-1274 . -1079) T) ((-219 . -132) T) ((-1178 . -102) 165944) ((-99 . -1121) T) ((-245 . -864) 165895) ((-250 . -678) 165879) ((-250 . -663) 165863) ((-670 . -111) 165842) ((-598 . -628) 165826) ((-326 . -423) 165810) ((-250 . -384) 165794) ((-1180 . -240) 165741) ((-1020 . -272) 165725) ((-1020 . -232) 165709) ((-74 . -1238) T) ((-48 . -174) T) ((-713 . -399) T) ((-713 . -144) T) ((-1311 . -102) T) ((-1219 . -1238) T) ((-1218 . -628) 165691) ((-1109 . -1238) T) ((-1108 . -1077) 165534) ((-1097 . -1238) T) ((-273 . -928) 165513) ((-253 . -928) 165492) ((-794 . -1077) 165315) ((-792 . -1077) 165158) ((-620 . -1238) T) ((-1185 . -625) 165140) ((-1108 . 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163519) ((-593 . -1077) 163484) ((-530 . -1077) 163429) ((-229 . -57) 163387) ((-465 . -23) T) ((-419 . -102) T) ((-1203 . -1238) T) ((-270 . -102) T) ((-110 . -113) T) ((-706 . -300) T) ((-880 . -38) 163357) ((-1108 . -628) 163093) ((-593 . -111) 163049) ((-530 . -111) 162978) ((-430 . -1133) T) ((-326 . -1079) 162868) ((-323 . -1079) T) ((-129 . -1238) T) ((-131 . -1238) T) ((-794 . -628) 162616) ((-792 . -628) 162382) ((-670 . -1070) T) ((-1317 . -1121) T) ((-466 . -628) 162167) ((-171 . -317) 162098) ((-430 . -23) T) ((-40 . -625) 162080) ((-40 . -626) 162064) ((-108 . -1013) 162046) ((-117 . -883) 162030) ((-661 . -628) 162014) ((-48 . -526) 161980) ((-1224 . -1031) 161964) ((-1202 . -625) 161931) ((-1210 . -34) T) ((-973 . -625) 161897) ((-940 . -625) 161879) ((-1134 . -861) 161830) ((-783 . -625) 161812) ((-684 . -625) 161794) ((-529 . -1238) T) ((-1261 . -317) 161773) ((-1178 . -319) 161711) ((-1162 . -34) T) ((-491 . -34) T) ((-1113 . -1238) T) ((-489 . -464) T) ((-1055 . -1238) T) ((-1108 . -1070) T) ((-50 . -628) 161680) ((-794 . -1070) T) ((-792 . -1070) T) ((-659 . -240) 161664) ((-644 . -240) 161610) ((-1199 . -21) T) ((-593 . -628) 161560) ((-530 . -628) 161490) ((-494 . -234) 161381) ((-1199 . -25) T) ((-1108 . -336) 161342) ((-466 . -1070) T) ((-1108 . -238) 161321) ((-794 . -336) 161298) ((-794 . -238) T) ((-792 . -336) 161270) ((-743 . -1242) 161249) ((-531 . -34) T) ((-337 . -663) 161233) ((-528 . -34) T) ((-59 . -34) T) ((-509 . -34) T) ((-508 . -34) T) ((-466 . -336) 161212) ((-337 . -384) 161196) ((-372 . -1238) T) ((-332 . -1238) T) ((-1024 . -1173) NIL) ((-743 . -568) 161127) ((-647 . -102) T) ((-619 . -102) T) ((-366 . -738) T) ((-363 . -738) T) ((-355 . -738) T) ((-273 . -738) T) ((-253 . -738) T) ((-390 . -1238) T) ((-1300 . -21) T) ((-1067 . -319) 161035) ((-1300 . -25) T) ((-920 . -1121) 161013) ((-830 . -234) 161000) ((-50 . -1070) T) ((-1195 . -568) 160979) ((-1194 . -1242) 160958) ((-1194 . -568) 160909) ((-1188 . -1242) 160888) 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. -851) T) ((-282 . -851) T) ((-281 . -851) T) ((-280 . -851) T) ((-48 . -300) T) ((-279 . -851) T) ((-278 . -851) T) ((-277 . -851) T) ((-195 . -799) T) ((-624 . -861) T) ((-666 . -423) 160118) ((-682 . -237) 160069) ((-225 . -628) 160031) ((-110 . -861) T) ((-665 . -21) T) ((-665 . -25) T) ((-1311 . -38) 160001) ((-118 . -296) 159952) ((-1288 . -19) 159936) ((-1252 . -864) NIL) ((-1288 . -616) 159913) ((-1301 . -1121) T) ((-362 . -1072) 159858) ((-1098 . -1121) T) ((-1008 . -1121) T) ((-982 . -132) T) ((-829 . -234) 159845) ((-749 . -1121) T) ((-362 . -652) 159790) ((-747 . -132) T) ((-727 . -132) T) ((-523 . -805) T) ((-523 . -806) T) ((-465 . -132) T) ((-419 . -1173) 159768) ((-225 . -1070) T) ((-304 . -102) 159550) ((-142 . -1121) T) ((-711 . -1023) T) ((-1126 . -296) 159506) ((-91 . -1238) T) ((-128 . -625) 159438) ((-122 . -625) 159370) ((-1317 . -174) T) ((-1194 . -374) 159349) ((-1188 . -374) 159328) ((-326 . -1121) T) ((-430 . -132) T) ((-323 . -1121) T) ((-419 . -38) 159280) 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. -1133) T) ((-1194 . -23) T) ((-527 . -1059) 158566) ((-1188 . -1133) T) ((-1147 . -1133) T) ((-354 . -111) 158495) ((-1025 . -1242) T) ((-127 . -1238) T) ((-933 . -1242) T) ((-1188 . -23) T) ((-1163 . -272) 158479) ((-706 . -296) NIL) ((-726 . -1238) T) ((-1163 . -232) 158463) ((-1147 . -23) T) ((-1096 . -1121) T) ((-1025 . -568) T) ((-933 . -568) T) ((-255 . -1238) T) ((-189 . -1238) T) ((-163 . -1238) T) ((-158 . -1238) T) ((-254 . -625) 158445) ((-827 . -237) 158342) ((-811 . -132) T) ((-722 . -625) 158324) ((-326 . -729) 158234) ((-323 . -729) 158163) ((-711 . -625) 158145) ((-711 . -626) 158090) ((-419 . -412) 158074) ((-450 . -1121) T) ((-499 . -25) T) ((-499 . -21) T) ((-1141 . -1121) T) ((-219 . -25) T) ((-219 . -21) T) ((-724 . -423) 158058) ((-726 . -1059) 158027) ((-1288 . -625) 157939) ((-1288 . -626) 157900) ((-1274 . -174) T) ((-1211 . -625) 157882) ((-250 . -34) T) ((-354 . -628) 157812) ((-406 . -628) 157794) ((-945 . -995) T) ((-1224 . -1238) T) ((-674 . -803) 157773) ((-674 . -806) 157752) ((-410 . -407) T) ((-535 . -102) 157702) ((-1244 . -1238) T) ((-1056 . -1121) T) ((-419 . -919) 157625) ((-224 . -1016) 157609) ((-850 . -1238) T) ((-516 . -102) T) ((-635 . -625) 157591) ((-45 . -861) NIL) ((-635 . -626) 157568) ((-1056 . -622) 157543) ((-920 . -526) 157476) ((-329 . -237) 157428) ((-354 . -1070) T) ((-118 . -626) NIL) ((-118 . -625) 157410) ((-886 . -1238) T) ((-682 . -429) 157394) ((-682 . -1144) 157339) ((-512 . -152) 157321) ((-354 . -238) T) ((-354 . -248) T) ((-40 . -1077) 157266) ((-886 . -899) 157250) ((-886 . -901) 157175) ((-724 . -1079) T) ((-706 . -1023) NIL) ((-1272 . -47) 157145) ((-1251 . -47) 157122) ((-1162 . -1031) 157093) ((-1141 . -729) 157080) ((-3 . |UnionCategory|) T) ((-1126 . -625) 157062) ((-1101 . -148) 157041) ((-1101 . -146) 156992) ((-1025 . -374) T) ((-985 . -628) 156976) ((-227 . -939) T) ((-40 . -111) 156905) ((-886 . -1059) 156769) ((-1024 . -232) 156746) ((-1024 . -272) 156723) ((-713 . -1072) 156710) 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-1242) 155619) ((-362 . -1173) T) ((-337 . -34) T) ((-44 . -429) 155603) ((-1202 . -628) 155539) ((-887 . -1238) T) ((-402 . -756) 155523) ((-1252 . -568) 155474) ((-1251 . -1238) T) ((-1163 . -658) 155433) ((-743 . -132) T) ((-684 . -628) 155417) ((-1251 . -901) 155290) ((-1251 . -899) 155260) ((-1195 . -132) T) ((-1194 . -132) T) ((-1188 . -132) T) ((-1147 . -132) T) ((-321 . -1104) T) ((-1045 . -1023) T) ((-749 . -526) 155193) ((-1025 . -23) T) ((-1025 . -1133) T) ((-908 . -1121) T) ((-145 . -856) T) ((-1024 . -360) NIL) ((-703 . -625) 155175) ((-962 . -864) 155154) ((-535 . -319) 155092) ((-992 . -23) T) ((-142 . -526) NIL) ((-880 . -658) 155037) ((-933 . -1133) T) ((-933 . -23) T) ((-886 . -917) 154996) ((-362 . -38) 154961) ((-884 . -1077) 154948) ((-341 . -864) T) ((-82 . -625) 154930) ((-40 . -1070) T) ((-884 . -111) 154915) ((-730 . -1238) T) ((-713 . -102) T) ((-706 . -625) 154897) ((-614 . -1238) T) ((-608 . -568) 154876) ((-439 . -1133) T) ((-350 . -1072) 154860) ((-215 . 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-660) 150297) ((-1162 . -1238) T) ((-561 . -861) T) ((-473 . -660) 150268) ((-273 . -901) 150127) ((-253 . -901) NIL) ((-118 . -1077) 150072) ((-466 . -660) 149961) ((-676 . -1059) 149938) ((-635 . -111) 149923) ((-402 . -1072) 149907) ((-366 . -1059) 149891) ((-363 . -1059) 149875) ((-355 . -1059) 149859) ((-273 . -1059) 149703) ((-253 . -1059) 149579) ((-929 . -1238) T) ((-118 . -111) 149508) ((-59 . -1238) T) ((-402 . -652) 149492) ((-633 . -1072) 149476) ((-531 . -1238) T) ((-528 . -1238) T) ((-509 . -1238) T) ((-508 . -1238) T) ((-449 . -625) 149458) ((-446 . -625) 149440) ((-633 . -652) 149424) ((-3 . -102) T) ((-1048 . -1231) 149393) ((-845 . -102) T) ((-701 . -57) 149351) ((-711 . -1070) T) ((-647 . -658) 149320) ((-619 . -658) 149289) ((-50 . -660) 149263) ((-299 . -464) T) ((-488 . -1231) 149232) ((0 . -102) T) ((-593 . -660) 149197) ((-530 . -660) 149142) ((-49 . -102) T) ((-929 . -1059) 149129) ((-711 . -248) T) ((-1101 . -421) 149108) ((-743 . -651) 149056) ((-1020 . -1121) T) ((-724 . -174) 148947) ((-635 . -628) 148842) ((-499 . -1013) 148824) ((-430 . -234) 148769) ((-273 . -388) 148753) ((-253 . -388) 148737) ((-411 . -1121) T) ((-1047 . -102) 148715) ((-350 . -38) 148699) ((-219 . -1013) 148681) ((-118 . -628) 148611) ((-176 . -38) 148543) ((-1272 . -317) 148522) ((-1251 . -317) 148501) ((-670 . -738) T) ((-99 . -625) 148483) ((-489 . -1072) 148448) ((-1188 . -651) 148400) ((-489 . -652) 148365) ((-656 . -864) 148344) ((-497 . -25) T) ((-497 . -21) T) ((-1251 . -1043) 148296) ((-1078 . -1238) T) ((-1 . -1238) T) ((-635 . -1070) T) ((-390 . -416) T) ((-402 . -102) T) ((-1126 . -630) 148211) ((-273 . -917) 148157) ((-253 . -917) 148134) ((-118 . -1070) T) ((-1108 . -738) T) ((-828 . -1133) T) ((-831 . -864) T) ((-635 . -238) 148113) ((-633 . -102) T) ((-523 . -1238) T) ((-519 . -1238) T) ((-794 . -738) T) ((-792 . -738) T) ((-1243 . -861) T) ((-425 . -1133) T) ((-118 . -248) T) ((-40 . -379) NIL) ((-118 . -238) NIL) ((-398 . -864) 148092) ((-466 . -738) T) ((-828 . -23) T) ((-743 . -25) T) ((-743 . -21) T) ((-682 . -911) 148013) ((-1098 . -296) 147992) ((-78 . -408) T) ((-78 . -407) T) ((-545 . -779) 147974) ((-227 . -864) T) ((-706 . -1077) 147924) ((-1313 . -102) T) ((-1280 . -132) T) ((-1273 . -132) T) ((-1252 . -132) T) ((-1195 . -25) T) ((-1163 . -423) 147908) ((-647 . -378) 147840) ((-619 . -378) 147772) ((-1178 . -1170) 147756) ((-103 . -1121) 147734) ((-1195 . -21) T) ((-1194 . -21) T) ((-879 . -625) 147716) ((-1020 . -729) 147664) ((-225 . -660) 147631) ((-706 . -111) 147565) ((-50 . -738) T) ((-1194 . -25) T) ((-362 . -360) T) ((-1188 . -21) T) ((-1101 . -464) 147516) ((-1188 . -25) T) ((-724 . -526) 147463) ((-593 . -738) T) ((-530 . -738) T) ((-1147 . -21) T) ((-1147 . -25) T) ((-608 . -132) T) ((-607 . -132) T) ((-304 . -658) 147198) ((-494 . -237) 147095) ((-370 . -464) T) ((-364 . -464) T) ((-356 . -464) T) ((-486 . -317) 147074) ((-1246 . -102) T) ((-323 . -296) 147009) ((-108 . -464) T) ((-79 . -453) T) ((-79 . -407) T) ((-489 . -102) T) ((-703 . -628) 146993) ((-1317 . -625) 146975) ((-1317 . -626) 146957) ((-1101 . -414) 146936) ((-1056 . -501) 146867) ((-137 . -296) 146844) ((-576 . -807) T) ((-576 . -804) T) ((-1084 . -240) 146790) ((-1083 . -864) T) ((-725 . -864) T) ((-370 . -414) 146741) ((-364 . -414) 146692) ((-356 . -414) 146643) ((-1303 . -1133) T) ((-1312 . -1072) 146627) ((-392 . -1072) 146611) ((-1312 . -652) 146581) ((-830 . -237) T) ((-392 . -652) 146551) ((-706 . -628) 146486) ((-1303 . -23) T) ((-1290 . -102) T) ((-350 . -919) 146467) ((-177 . -625) 146449) ((-1163 . -1079) T) ((-559 . -379) T) ((-682 . -756) 146433) ((-1199 . -146) 146412) ((-1199 . -148) 146391) ((-1167 . -1121) T) ((-1167 . -1092) 146360) ((-69 . -1238) T) ((-1045 . -1077) 146297) ((-362 . -658) 146227) ((-880 . -1079) T) ((-245 . -651) 146133) ((-706 . -1070) T) ((-365 . -1077) 146078) ((-61 . -1238) T) ((-1045 . -111) 145994) ((-920 . -625) 145905) ((-706 . -248) T) ((-706 . -238) NIL) ((-855 . -860) 145884) ((-711 . -807) T) ((-711 . -804) T) ((-1024 . -423) 145861) ((-365 . -111) 145790) ((-390 . -939) T) ((-419 . -860) 145769) ((-724 . -300) 145680) ((-225 . -738) T) ((-1280 . -505) 145646) ((-1273 . -505) 145612) ((-1252 . -505) 145578) ((-590 . -1121) T) ((-326 . -1023) 145557) ((-224 . -1121) 145535) ((-1245 . -856) T) ((-329 . -994) 145497) ((-105 . -102) T) ((-48 . -1077) 145462) ((-885 . -864) NIL) ((-1312 . -102) T) ((-392 . -102) T) ((-1274 . -625) 145444) ((-1154 . -1155) 145428) ((-1025 . -651) 145410) ((-890 . -1238) T) ((-48 . -111) 145366) ((-693 . -1238) T) ((-688 . -1238) T) ((-674 . -1238) T) ((-827 . -911) 145233) ((-490 . -1238) T) ((-250 . -1238) T) ((-543 . -102) T) ((-512 . -102) T) ((-153 . -1295) 145217) ((-139 . -1238) T) ((-138 . -1238) T) ((-134 . -1238) T) ((-1237 . -102) T) ((-1045 . -628) 145154) ((-829 . -237) T) ((-1193 . -1242) 145133) ((-365 . -628) 145063) ((-1146 . -1242) 145042) ((-245 . -25) 144875) ((-245 . -21) 144786) ((-128 . -120) 144770) ((-122 . -120) 144754) ((-44 . -756) 144738) ((-1193 . -568) 144649) ((-1146 . -568) 144580) ((-1245 . -1121) T) ((-558 . -864) T) ((-1056 . -296) 144555) ((-1187 . -1104) T) ((-1015 . -1104) T) ((-828 . -132) T) ((-118 . -807) NIL) ((-118 . -804) NIL) ((-366 . -317) T) ((-363 . -317) T) ((-355 . -317) T) ((-1115 . -1238) 144533) ((-258 . -1133) 144511) ((-257 . -1133) 144489) ((-1045 . -1070) T) ((-1024 . -1079) T) ((-48 . -628) 144422) ((-354 . -660) 144367) ((-1301 . -625) 144329) ((-1301 . -626) 144290) ((-633 . -38) 144274) ((-1195 . -234) 144227) ((-1194 . -234) 144173) ((-1098 . -625) 144155) ((-1045 . -248) T) ((-365 . -1070) T) ((-827 . -1295) 144125) ((-258 . -23) T) ((-257 . -23) T) ((-1008 . -625) 144107) ((-1188 . -234) 143924) ((-1180 . -152) 143871) ((-749 . -626) 143832) ((-749 . -625) 143814) ((-1025 . -25) T) ((-811 . -861) 143793) ((-1020 . -526) 143705) ((-689 . -864) T) ((-365 . -238) T) ((-365 . -248) T) ((-400 . -628) 143686) ((-929 . -317) T) ((-142 . -625) 143668) ((-142 . -626) 143627) ((-329 . -911) 143531) ((-1025 . -21) T) ((-992 . -25) T) ((-933 . -21) T) ((-933 . -25) T) ((-439 . -21) T) ((-439 . -25) T) ((-855 . -423) 143515) ((-48 . -1070) T) ((-1310 . -1302) 143499) ((-1308 . -1302) 143483) ((-1056 . -616) 143458) ((-326 . -626) 143319) ((-326 . -625) 143301) ((-323 . -626) NIL) ((-323 . -625) 143283) ((-48 . -248) T) ((-48 . -238) T) ((-666 . -296) 143244) ((-562 . -240) 143194) ((-583 . -864) T) ((-140 . -625) 143161) ((-137 . -625) 143143) ((-115 . -625) 143125) ((-489 . -38) 143090) ((-1312 . -1309) 143069) ((-1303 . -132) T) ((-1311 . -1079) T) ((-1103 . -102) T) ((-88 . -1238) T) ((-512 . -319) NIL) ((-1021 . -107) 143053) ((-904 . -1121) T) ((-900 . -1121) T) ((-1288 . -663) 143037) ((-1288 . -384) 143021) ((-337 . -1238) T) ((-605 . -861) T) ((-1163 . -1121) T) ((-1163 . -1074) 142961) ((-103 . -526) 142894) ((-946 . -625) 142876) ((-354 . -738) T) ((-30 . -625) 142858) ((-880 . -1121) T) ((-855 . -1079) 142837) 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T) ((-783 . -738) T) ((-227 . -374) T) ((-1310 . -1072) 141059) ((-1308 . -1072) 141043) ((-1310 . -652) 141013) ((-1178 . -1121) 140991) ((-885 . -1242) T) ((-1308 . -652) 140961) ((-1109 . -864) T) ((-666 . -625) 140943) ((-885 . -568) T) ((-706 . -379) NIL) ((-44 . -1072) 140927) ((-1317 . -628) 140909) ((-1311 . -1121) T) ((-682 . -102) T) ((-370 . -1295) 140893) ((-364 . -1295) 140877) ((-44 . -652) 140861) ((-356 . -1295) 140845) ((-560 . -102) T) ((-1232 . -1238) T) ((-532 . -861) 140824) ((-723 . -1238) T) ((-977 . -864) 140803) ((-862 . -864) T) ((-499 . -237) T) ((-219 . -237) T) ((-1067 . -1121) T) ((-829 . -464) 140782) ((-153 . -1072) 140766) ((-1067 . -1092) 140695) ((-1048 . -997) 140664) ((-831 . -1133) T) ((-1024 . -729) 140609) ((-153 . -652) 140593) ((-398 . -1133) T) ((-488 . -997) 140562) ((-475 . -997) 140531) ((-1204 . -864) T) ((-110 . -152) 140513) ((-73 . -625) 140495) ((-908 . -625) 140477) ((-1203 . -864) T) ((-1101 . -736) 140456) ((-1317 . -1070) T) ((-828 . -651) 140404) ((-304 . -1079) 140346) ((-171 . -1242) 140251) ((-227 . -1133) T) ((-334 . -23) T) ((-1188 . -1013) 140203) ((-1274 . -1077) 140108) ((-855 . -1121) T) ((-129 . -864) T) ((-1147 . -752) 140087) ((-1272 . -939) 140066) ((-1251 . -939) 140045) ((-884 . -738) T) ((-171 . -568) 139956) ((-592 . -660) 139943) ((-576 . -660) 139915) ((-419 . -1121) T) ((-270 . -1121) T) ((-215 . -625) 139897) ((-507 . -660) 139847) ((-227 . -23) T) ((-1251 . -832) 139800) ((-1310 . -102) T) ((-503 . -1238) T) ((-365 . -1307) 139777) ((-1308 . -102) T) ((-1274 . -111) 139669) ((-1134 . -911) 139536) ((-827 . -1072) 139437) ((-827 . -652) 139359) ((-145 . -625) 139341) ((-1014 . -132) T) ((-44 . -102) T) ((-245 . -861) 139292) ((-598 . -1238) T) ((-1261 . -1242) 139271) ((-103 . -501) 139255) ((-1311 . -729) 139225) ((-1108 . -47) 139186) ((-1083 . -1133) T) ((-971 . -1133) T) ((-128 . -34) T) ((-122 . -34) T) ((-1261 . -568) 139097) ((-794 . -47) 139074) ((-792 . -47) 139046) ((-1218 . -1238) T) ((-1193 . -132) T) ((-365 . -379) T) ((-493 . -1133) T) ((-1146 . -132) T) ((-885 . -374) T) ((-466 . -47) 139025) ((-868 . -132) T) ((-332 . -864) 139004) ((-153 . -102) T) ((-1083 . -23) T) ((-971 . -23) T) ((-583 . -568) T) ((-828 . -25) T) ((-828 . -21) T) ((-1163 . -526) 138937) ((-604 . -1104) T) ((-598 . -1059) 138921) ((-1274 . -628) 138795) ((-493 . -23) T) ((-362 . -1079) T) ((-390 . -864) T) ((-1232 . -917) 138776) ((-682 . -319) 138714) ((-1280 . -234) 138667) ((-1134 . -1295) 138637) ((-711 . -660) 138602) ((-1025 . -861) T) ((-1024 . -174) T) ((-982 . -146) 138581) ((-647 . -1121) T) ((-619 . -1121) T) ((-982 . -148) 138560) ((-747 . -148) 138539) ((-747 . -146) 138518) ((-670 . -1238) T) ((-992 . -861) T) ((-1273 . -234) 138464) ((-1252 . -234) 138281) ((-845 . -658) 138198) ((-486 . -939) 138177) ((-347 . -1238) T) ((-329 . -1072) 138012) ((-326 . -1077) 137922) ((-323 . -1077) 137851) ((-1020 . -296) 137809) ((-419 . -729) 137761) ((-329 . -652) 137602) ((-607 . 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134491) ((-258 . -651) 134397) ((-257 . -651) 134303) ((-329 . -294) 134269) ((-1178 . -526) 134202) ((-489 . -658) 134152) ((-494 . -911) 134019) ((-1154 . -1121) T) ((-227 . -1081) T) ((-827 . -319) 133957) ((-1108 . -917) 133892) ((-794 . -917) 133835) ((-792 . -917) 133819) ((-1310 . -38) 133789) ((-1308 . -38) 133759) ((-1261 . -1133) T) ((-869 . -1133) T) ((-466 . -917) 133736) ((-872 . -1121) T) ((-1261 . -23) T) ((-1141 . -628) 133708) ((-1083 . -132) T) ((-869 . -23) T) ((-583 . -1133) T) ((-635 . -738) T) ((-522 . -864) T) ((-366 . -939) T) ((-363 . -939) T) ((-299 . -102) T) ((-355 . -939) T) ((-991 . -1104) T) ((-971 . -132) T) ((-828 . -234) 133653) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1067 . -526) 133554) ((-706 . -928) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 133505) ((-687 . -319) 133443) ((-225 . -1238) T) ((-647 . -773) T) ((-619 . -773) T) ((-1252 . -861) NIL) ((-1101 . -1072) 133353) ((-1024 . -300) T) ((-706 . -660) 133303) 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130870) ((-908 . -628) 130847) ((-1134 . -652) 130769) ((-1187 . -102) T) ((-1015 . -102) T) ((-1014 . -21) T) ((-128 . -1031) 130753) ((-122 . -1031) 130737) ((-1014 . -25) T) ((-920 . -120) 130721) ((-1179 . -102) T) ((-1261 . -132) T) ((-1251 . -864) 130620) ((-1193 . -25) T) ((-1193 . -21) T) ((-1180 . -319) 130415) ((-354 . -1238) T) ((-1146 . -25) T) ((-869 . -132) T) ((-406 . -1238) T) ((-1146 . -21) T) ((-868 . -25) T) ((-868 . -21) T) ((-794 . -317) 130394) ((-1178 . -501) 130378) ((-1171 . -152) 130328) ((-1167 . -625) 130290) ((-659 . -102) 130240) ((-644 . -102) T) ((-1167 . -626) 130201) ((-583 . -132) T) ((-633 . -860) 130180) ((-1045 . -803) T) ((-1045 . -806) T) ((-1045 . -738) T) ((-827 . -919) 130049) ((-724 . -1077) 129872) ((-614 . -864) 129851) ((-496 . -319) 129789) ((-465 . -429) 129759) ((-362 . -174) T) ((-299 . -38) 129746) ((-258 . -234) 129637) ((-257 . -234) 129528) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) 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T) ((-724 . -1070) T) ((-1083 . -651) 127157) ((-1101 . -38) 127025) ((-971 . -651) 126973) ((-1025 . -148) T) ((-1025 . -146) NIL) ((-390 . -1133) T) ((-334 . -25) T) ((-332 . -23) T) ((-962 . -861) 126952) ((-724 . -336) 126929) ((-493 . -651) 126877) ((-40 . -1059) 126765) ((-724 . -238) T) ((-713 . -729) 126752) ((-350 . -1121) T) ((-176 . -1121) T) ((-341 . -861) T) ((-430 . -464) 126702) ((-390 . -23) T) ((-370 . -38) 126667) ((-364 . -38) 126632) ((-356 . -38) 126597) ((-80 . -453) T) ((-80 . -407) T) ((-227 . -25) T) ((-227 . -21) T) ((-848 . -1133) T) ((-108 . -38) 126547) ((-839 . -1133) T) ((-786 . -1121) T) ((-117 . -729) 126534) ((-684 . -1059) 126518) ((-624 . -102) T) ((-848 . -23) T) ((-839 . -23) T) ((-1178 . -296) 126470) ((-1134 . -319) 126408) ((-494 . -1072) 126309) ((-1123 . -240) 126293) ((-64 . -408) T) ((-64 . -407) T) ((-1172 . -102) T) ((-110 . -102) T) ((-494 . -652) 126215) ((-40 . -388) 126192) ((-96 . -102) T) ((-665 . -866) 126176) ((-1193 . -234) 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T) ((-419 . -296) 124890) ((-245 . -237) 124787) ((-108 . -412) 124769) ((-84 . -395) T) ((-84 . -407) T) ((-713 . -174) T) ((-629 . -625) 124751) ((-99 . -738) T) ((-494 . -102) 124483) ((-99 . -485) T) ((-117 . -174) T) ((-1310 . -658) 124442) ((-1308 . -658) 124401) ((-171 . -651) 124349) ((-1101 . -919) 124220) ((-1075 . -102) T) ((-1020 . -628) 124110) ((-885 . -25) T) ((-827 . -243) 124089) ((-885 . -21) T) ((-830 . -102) T) ((-44 . -658) 124032) ((-1025 . -237) T) ((-426 . -102) T) ((-396 . -102) T) ((-110 . -319) NIL) ((-229 . -102) 123982) ((-128 . -1238) T) ((-122 . -1238) T) ((-108 . -919) NIL) ((-829 . -1072) 123933) ((-59 . -864) 123912) ((-829 . -652) 123854) ((-528 . -864) 123833) ((-508 . -864) 123812) ((-1055 . -132) T) ((-682 . -378) 123796) ((-153 . -658) 123755) ((-1317 . -738) T) ((-647 . -296) 123713) ((-619 . -296) 123671) ((-1280 . -146) 123650) ((-1261 . -651) 123598) ((-1020 . -1070) T) ((-1125 . -625) 123580) ((-1024 . -625) 123562) ((-592 . -1238) T) ((-576 . -1238) T) ((-507 . -1238) T) ((-527 . -23) T) ((-522 . -23) T) ((-354 . -317) T) ((-520 . -23) T) ((-332 . -132) T) ((-3 . -1121) T) ((-1024 . -626) 123546) ((-1020 . -248) 123525) ((-1020 . -238) 123504) ((-1280 . -148) 123483) ((-1273 . -148) 123462) ((-845 . -1121) T) ((-1273 . -146) 123441) ((-1272 . -1242) 123420) ((-1252 . -146) 123327) ((-1252 . -148) 123234) ((-1251 . -1242) 123213) ((-390 . -132) T) ((-227 . -234) 123200) ((-176 . -174) T) ((-576 . -901) 123182) ((0 . -1121) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1238) T) ((-49 . -1121) T) ((-1274 . -660) 123087) ((-1272 . -568) 123038) ((-726 . -1133) T) ((-1251 . -568) 122989) ((-576 . -1059) 122971) ((-607 . -148) 122950) ((-607 . -146) 122929) ((-507 . -1059) 122872) ((-1156 . -1158) T) ((-87 . -395) T) ((-87 . -407) T) ((-886 . -374) T) ((-848 . -132) T) ((-839 . -132) T) ((-983 . -658) 122816) ((-726 . -23) T) ((-518 . -625) 122782) ((-514 . -625) 122764) ((-827 . -658) 122543) ((-1312 . -1079) T) ((-390 . -1081) T) ((-1047 . -1121) 122521) ((-55 . -1059) 122503) ((-920 . -34) T) ((-494 . -319) 122441) ((-604 . -102) T) ((-1178 . -626) 122402) ((-1178 . -625) 122334) ((-1199 . -1072) 122217) ((-45 . -102) T) ((-829 . -102) T) ((-1199 . -652) 122114) ((-1289 . -1238) T) ((-1261 . -25) T) ((-1261 . -21) T) ((-1083 . -234) 122101) ((-869 . -25) T) ((-523 . -864) T) ((-254 . -1238) T) ((-44 . -378) 122085) ((-869 . -21) T) ((-743 . -464) 122036) ((-1311 . -625) 122018) ((-722 . -1238) T) ((-711 . -1238) T) ((-1300 . -1072) 121988) ((-1075 . -319) 121926) ((-683 . -1104) T) ((-618 . -1104) T) ((-402 . -1121) T) ((-583 . -25) T) ((-583 . -21) T) ((-182 . -1104) T) ((-162 . -1104) T) ((-157 . -1104) T) ((-155 . -1104) T) ((-1300 . -652) 121896) ((-633 . -1121) T) ((-711 . -901) 121878) ((-1288 . -1238) T) ((-229 . -319) 121816) ((-145 . -379) T) ((-1211 . -1238) T) ((-1067 . -626) 121758) ((-1067 . -625) 121701) ((-323 . -928) NIL) ((-1246 . -856) T) ((-1134 . -919) 121570) ((-711 . -1059) 121515) ((-723 . -939) T) ((-486 . -1242) 121494) ((-1194 . -464) 121473) ((-1188 . -464) 121452) ((-340 . -102) T) ((-886 . -1133) T) ((-329 . -658) 121334) ((-326 . -660) 121063) ((-323 . -660) 120992) ((-486 . -568) 120943) ((-350 . -526) 120909) ((-562 . -152) 120859) ((-40 . -317) T) ((-855 . -625) 120841) ((-713 . -300) T) ((-886 . -23) T) ((-390 . -505) T) ((-1101 . -272) 120811) ((-1101 . -232) 120781) ((-524 . -102) T) ((-419 . -626) 120588) ((-419 . -625) 120570) ((-270 . -625) 120552) ((-117 . -300) T) ((-1274 . -738) T) ((-635 . -1238) T) ((-1313 . -1121) T) ((-1272 . -374) 120531) ((-1251 . -374) 120510) ((-1301 . -34) T) ((-1246 . -1121) T) ((-118 . -1238) T) ((-108 . -272) 120492) ((-108 . -232) 120474) ((-1199 . -102) T) ((-489 . -1121) T) ((-535 . -501) 120458) ((-749 . -34) T) ((-665 . -1072) 120442) ((-665 . -652) 120412) ((-885 . -234) NIL) ((-142 . -34) T) ((-118 . -899) 120389) ((-118 . -901) NIL) ((-635 . -1059) 120272) ((-1300 . -102) T) ((-1280 . -237) 120231) 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. -234) 118770) ((-884 . -317) T) ((-323 . -806) NIL) ((-323 . -803) NIL) ((-326 . -738) 118619) ((-323 . -738) T) ((-486 . -374) 118598) ((-370 . -360) 118577) ((-364 . -360) 118556) ((-356 . -360) 118535) ((-326 . -485) 118514) ((-1272 . -23) T) ((-1251 . -23) T) ((-730 . -1133) T) ((-726 . -132) T) ((-665 . -102) T) ((-489 . -729) 118479) ((-674 . -864) 118458) ((-45 . -292) 118408) ((-105 . -1121) T) ((-68 . -625) 118390) ((-250 . -864) 118369) ((-991 . -102) T) ((-878 . -102) T) ((-635 . -917) 118328) ((-1312 . -1121) T) ((-392 . -1121) T) ((-1261 . -234) 118315) ((-1237 . -1121) T) ((-82 . -1238) T) ((-1134 . -272) 118284) ((-1083 . -861) T) ((-118 . -917) NIL) ((-794 . -939) 118263) ((-725 . -861) T) ((-543 . -1121) T) ((-512 . -1121) T) ((-366 . -1242) T) ((-363 . -1242) T) ((-355 . -1242) T) ((-273 . -1242) 118242) ((-253 . -1242) 118221) ((-545 . -874) T) ((-1134 . -232) 118190) ((-1179 . -840) T) ((-1163 . -1077) 118174) ((-402 . -773) T) ((-706 . -1238) T) ((-703 . -1059) 118158) ((-366 . -568) T) ((-363 . -568) T) ((-355 . -568) T) ((-273 . -568) 118089) ((-253 . -568) 118020) ((-537 . -1104) T) ((-1163 . -111) 117999) ((-465 . -756) 117969) ((-880 . -1077) 117939) ((-829 . -38) 117881) ((-706 . -899) 117863) ((-706 . -901) 117845) ((-305 . -319) 117649) ((-1178 . -298) 117626) ((-929 . -1242) T) ((-1101 . -658) 117521) ((-1025 . -464) T) ((-682 . -423) 117505) ((-880 . -111) 117470) ((-933 . -464) T) ((-706 . -1059) 117415) ((-929 . -568) T) ((-545 . -625) 117397) ((-593 . -939) T) ((-499 . -1072) 117347) ((-486 . -1133) T) ((-530 . -939) T) ((-494 . -919) 117216) ((-65 . -625) 117198) ((-219 . -1072) 117148) ((-499 . -652) 117098) ((-370 . -658) 117035) ((-364 . -658) 116972) ((-356 . -658) 116909) ((-644 . -231) 116855) ((-219 . -652) 116805) ((-108 . -658) 116755) ((-486 . -23) T) ((-1141 . -806) T) ((-886 . -132) T) ((-1141 . -803) T) ((-1303 . -1305) 116734) ((-1141 . -738) T) ((-666 . -660) 116708) ((-304 . -625) 116449) ((-1163 . -628) 116367) 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. -111) 115516) ((-1195 . -994) 115485) ((-1194 . -994) 115447) ((-532 . -152) 115431) ((-1101 . -381) 115410) ((-362 . -625) 115392) ((-332 . -21) T) ((-365 . -1059) 115369) ((-332 . -25) T) ((-1188 . -994) 115338) ((-48 . -1238) T) ((-76 . -625) 115320) ((-1147 . -994) 115287) ((-711 . -317) T) ((-130 . -856) T) ((-929 . -374) T) ((-390 . -25) T) ((-390 . -21) T) ((-929 . -339) 115274) ((-86 . -625) 115256) ((-711 . -1043) T) ((-689 . -861) T) ((-400 . -1238) T) ((-1272 . -132) T) ((-1251 . -132) T) ((-920 . -1031) 115240) ((-848 . -21) T) ((-48 . -1059) 115183) ((-848 . -25) T) ((-839 . -25) T) ((-839 . -21) T) ((-1134 . -658) 114962) ((-1310 . -1079) T) ((-561 . -102) T) ((-1308 . -1079) T) ((-666 . -738) T) ((-1125 . -630) 114865) ((-1024 . -628) 114795) ((-1311 . -1077) 114779) ((-923 . -1238) T) ((-827 . -423) 114748) ((-103 . -120) 114732) ((-130 . -1121) T) ((-52 . -1121) T) ((-945 . -625) 114714) ((-885 . -1013) 114691) ((-835 . -102) T) ((-1311 . -111) 114670) ((-743 . -911) 114645) ((-665 . -38) 114615) ((-583 . -861) T) ((-366 . -1133) T) ((-363 . -1133) T) ((-355 . -1133) T) ((-273 . -1133) T) ((-253 . -1133) T) ((-1171 . -319) 114419) ((-1109 . -234) 114406) ((-635 . -317) 114385) ((-676 . -23) T) ((-536 . -1104) T) ((-321 . -1121) T) ((-494 . -272) 114354) ((-494 . -232) 114323) ((-153 . -1079) T) ((-366 . -23) T) ((-363 . -23) T) ((-355 . -23) T) ((-118 . -317) T) ((-273 . -23) T) ((-253 . -23) T) ((-1024 . -1070) T) ((-724 . -928) 114302) ((-1195 . -911) 114190) ((-1194 . -911) 114071) ((-1188 . -911) 113807) ((-1178 . -628) 113784) ((-1024 . -238) 113756) ((-1024 . -248) T) ((-1147 . -911) 113738) ((-118 . -1043) NIL) ((-929 . -1133) T) ((-1273 . -464) 113717) ((-1252 . -464) 113696) ((-535 . -625) 113628) ((-724 . -660) 113517) ((-419 . -1077) 113469) ((-516 . -625) 113451) ((-929 . -23) T) ((-499 . -319) NIL) ((-1311 . -628) 113407) ((-486 . -132) T) ((-219 . -319) NIL) ((-419 . -111) 113345) ((-827 . -1079) 113323) ((-749 . -1119) 113307) 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-1121) T) ((-1303 . -1302) 95426) ((-743 . -919) 95403) ((-713 . -807) T) ((-713 . -804) T) ((-1141 . -317) T) ((-390 . -148) T) ((-290 . -625) 95385) ((-289 . -625) 95367) ((-1251 . -1013) 95337) ((-48 . -939) T) ((-687 . -501) 95321) ((-258 . -1295) 95291) ((-257 . -1295) 95261) ((-1109 . -237) T) ((-1197 . -861) T) ((-1141 . -1043) T) ((-1067 . -34) T) ((-848 . -148) 95240) ((-848 . -146) 95219) ((-749 . -107) 95203) ((-624 . -133) T) ((-1199 . -1079) T) ((-494 . -1121) 94955) ((-1195 . -919) 94868) ((-1194 . -919) 94774) ((-1188 . -919) 94535) ((-885 . -464) T) ((-85 . -1238) T) ((-142 . -107) 94517) ((-1147 . -919) 94501) ((-724 . -388) 94485) ((-845 . -628) 94353) ((-1311 . -738) T) ((-1300 . -1079) T) ((-1280 . -102) T) ((-1141 . -557) T) ((-591 . -102) T) ((-130 . -502) 94335) ((-1273 . -102) T) ((-402 . -1077) 94319) ((-1193 . -968) 94288) ((-44 . -296) 94265) ((-130 . -625) 94232) ((-52 . -625) 94214) ((-1146 . -968) 94181) ((-665 . -423) 94165) ((-1252 . -102) T) ((-1179 . 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-146) 90299) ((-118 . -864) NIL) ((-496 . -501) 90283) ((-497 . -346) 90252) ((-524 . -1121) T) ((-1312 . -111) 90231) ((-1020 . -388) 90215) ((-425 . -102) T) ((-392 . -111) 90194) ((-1020 . -349) 90178) ((-288 . -1004) 90162) ((-287 . -1004) 90146) ((-1025 . -919) NIL) ((-1310 . -625) 90128) ((-1308 . -625) 90110) ((-110 . -526) NIL) ((-1193 . -1264) 90094) ((-868 . -866) 90078) ((-1199 . -1121) T) ((-103 . -1238) T) ((-971 . -968) 90039) ((-829 . -729) 89981) ((-1252 . -1173) NIL) ((-493 . -968) 89926) ((-1083 . -144) T) ((-60 . -102) 89876) ((-44 . -625) 89858) ((-78 . -625) 89840) ((-362 . -660) 89785) ((-1300 . -1121) T) ((-523 . -861) T) ((-299 . -296) 89764) ((-354 . -1133) T) ((-305 . -1121) T) ((-1020 . -917) 89723) ((-305 . -622) 89702) ((-1312 . -628) 89651) ((-1280 . -38) 89548) ((-1273 . -38) 89389) ((-1252 . -38) 89185) ((-499 . -1079) T) ((-392 . -628) 89169) ((-219 . -1079) T) ((-354 . -23) T) ((-153 . -625) 89151) ((-845 . -807) 89130) ((-845 . -804) 89109) ((-1237 . -628) 89090) ((-608 . -38) 89063) ((-607 . -38) 88960) ((-884 . -568) T) ((-225 . -132) T) ((-329 . -1023) 88926) ((-79 . -625) 88908) ((-724 . -317) 88887) ((-304 . -738) 88789) ((-836 . -102) T) ((-878 . -856) T) ((-304 . -485) 88768) ((-1303 . -102) T) ((-40 . -374) T) ((-886 . -148) 88747) ((-497 . -658) 88729) ((-886 . -146) 88708) ((-1179 . -501) 88690) ((-1312 . -1070) T) ((-494 . -526) 88623) ((-1167 . -1238) T) ((-983 . -625) 88605) ((-659 . -501) 88589) ((-644 . -501) 88520) ((-827 . -625) 88213) ((-48 . -27) T) ((-1199 . -729) 88110) ((-971 . -911) 88089) ((-665 . -1121) T) ((-875 . -874) T) ((-448 . -375) 88063) ((-743 . -658) 87973) ((-493 . -911) 87948) ((-1123 . -102) T) ((-991 . -1121) T) ((-878 . -1121) T) ((-828 . -319) 87935) ((-545 . -539) T) ((-545 . -588) T) ((-1308 . -393) 87907) ((-706 . -864) T) ((-1075 . -526) 87840) ((-1180 . -296) 87816) ((-245 . -272) 87785) ((-245 . -232) 87754) ((-258 . -1072) 87655) ((-257 . -1072) 87556) ((-1300 . -729) 87526) ((-1187 . -93) T) ((-1015 . -93) T) ((-829 . -174) 87505) ((-258 . -652) 87427) ((-257 . -652) 87349) ((-1235 . -502) 87326) ((-590 . -1238) T) ((-229 . -526) 87259) ((-633 . -807) 87238) ((-633 . -804) 87217) ((-1235 . -625) 87129) ((-224 . -1238) T) ((-687 . -625) 87061) ((-1195 . -658) 86971) ((-1178 . -1031) 86955) ((-962 . -102) 86885) ((-362 . -738) T) ((-875 . -625) 86867) ((-1194 . -658) 86749) ((-1188 . -658) 86586) ((-1147 . -658) 86496) ((-1252 . -412) 86448) ((-1134 . -501) 86432) ((-60 . -319) 86370) ((-341 . -102) T) ((-1232 . -21) T) ((-1232 . -25) T) ((-40 . -1133) T) ((-723 . -21) T) ((-639 . -625) 86352) ((-527 . -333) 86331) ((-723 . -25) T) ((-451 . -102) T) ((-108 . -296) NIL) ((-940 . -1133) T) ((-40 . -23) T) ((-783 . -1133) T) ((-576 . -1242) T) ((-507 . -1242) T) ((-1025 . -272) 86313) ((-329 . -625) 86295) ((-1025 . -232) 86277) ((-171 . -167) 86261) ((-592 . -568) T) ((-576 . -568) T) ((-507 . -568) T) ((-783 . -23) T) ((-1272 . -148) 86240) ((-1272 . -146) 86219) 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-651) 84448) ((-171 . -911) 84369) ((-924 . -922) 84353) ((-390 . -464) T) ((-499 . -1121) T) ((-962 . -319) 84291) ((-713 . -660) 84263) ((-561 . -856) T) ((-219 . -1121) T) ((-326 . -939) 84242) ((-323 . -939) T) ((-323 . -832) NIL) ((-402 . -732) T) ((-884 . -23) T) ((-117 . -660) 84229) ((-486 . -146) 84208) ((-430 . -423) 84192) ((-486 . -148) 84171) ((-110 . -501) 84153) ((-321 . -628) 84134) ((-2 . -625) 84116) ((-188 . -102) T) ((-1179 . -19) 84098) ((-1179 . -616) 84073) ((-670 . -21) T) ((-670 . -25) T) ((-605 . -1165) T) ((-1134 . -296) 84050) ((-347 . -25) T) ((-347 . -21) T) ((-904 . -1238) T) ((-900 . -1238) T) ((-1310 . -1077) 84034) ((-245 . -658) 83813) ((-507 . -374) T) ((-1308 . -1077) 83797) ((-1303 . -38) 83767) ((-1272 . -1223) 83733) ((-1272 . -1226) 83699) ((-1261 . -911) 83602) ((-1193 . -1072) 83425) ((-1163 . -1238) T) ((-1146 . -1072) 83268) ((-868 . -1072) 83252) ((-644 . -616) 83227) ((-1272 . -95) 83193) ((-1272 . -237) 83145) ((-1255 . -102) 83123) 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. -146) 79948) ((-355 . -148) 79927) ((-355 . -146) 79878) ((-273 . -146) 79857) ((-273 . -148) 79836) ((-253 . -148) 79815) ((-118 . -374) T) ((-253 . -146) 79794) ((-1179 . -626) NIL) ((-153 . -111) 79773) ((-1024 . -1059) 79661) ((-1178 . -1238) T) ((-706 . -1242) T) ((-811 . -1079) T) ((-711 . -1133) T) ((-1024 . -388) 79638) ((-518 . -1238) T) ((-514 . -1238) T) ((-929 . -146) T) ((-929 . -148) 79620) ((-884 . -132) T) ((-827 . -1077) 79541) ((-711 . -23) T) ((-706 . -568) T) ((-227 . -1072) 79506) ((-659 . -625) 79438) ((-659 . -626) 79399) ((-644 . -626) NIL) ((-644 . -625) 79381) ((-499 . -174) T) ((-227 . -652) 79346) ((-219 . -174) T) ((-225 . -21) T) ((-225 . -25) T) ((-486 . -1226) 79312) ((-486 . -1223) 79278) ((-283 . -625) 79260) ((-282 . -625) 79242) ((-281 . -625) 79224) ((-280 . -625) 79206) ((-279 . -625) 79188) ((-512 . -663) 79170) ((-278 . -625) 79152) ((-350 . -738) T) ((-277 . -625) 79134) ((-110 . -19) 79116) ((-176 . -738) T) ((-512 . -384) 79098) ((-214 . -625) 79080) ((-532 . -1170) 79064) ((-512 . -124) T) ((-110 . -616) 79039) ((-213 . -625) 79021) ((-486 . -35) 78987) ((-486 . -95) 78953) ((-211 . -625) 78935) ((-210 . -625) 78917) ((-209 . -625) 78899) ((-208 . -625) 78881) ((-205 . -625) 78863) ((-204 . -625) 78845) ((-203 . -625) 78827) ((-202 . -625) 78809) ((-201 . -625) 78791) ((-200 . -625) 78773) ((-199 . -625) 78755) ((-548 . -1124) 78707) ((-198 . -625) 78689) ((-197 . -625) 78671) ((-45 . -501) 78608) ((-196 . -625) 78590) ((-195 . -625) 78572) ((-153 . -628) 78541) ((-1136 . -102) T) ((-827 . -111) 78457) ((-656 . -102) 78387) ((-494 . -296) 78364) ((-1311 . -1059) 78348) ((-1134 . -625) 78041) ((-1122 . -1121) T) ((-1067 . -1238) T) ((-1193 . -319) 78028) ((-1083 . -1072) 78015) ((-1156 . -1121) T) ((-971 . -1072) 77858) ((-1146 . -319) 77845) ((-1117 . -1104) T) ((-635 . -1133) T) ((-1083 . -652) 77832) ((-1111 . -1104) T) ((-971 . -652) 77681) ((-1108 . -234) 77626) ((-493 . -1072) 77469) ((-1094 . -1104) T) ((-1087 . -1104) T) ((-1057 . -1104) T) ((-1040 . -1104) T) ((-118 . -1133) T) ((-493 . -652) 77318) ((-794 . -234) 77305) ((-831 . -102) T) ((-638 . -1104) T) ((-635 . -23) T) ((-1171 . -526) 77097) ((-495 . -1104) T) ((-982 . -1121) T) ((-398 . -102) T) ((-334 . -102) T) ((-220 . -1104) T) ((-855 . -1238) T) ((-153 . -1070) T) ((-743 . -423) 77081) ((-118 . -23) T) ((-1024 . -917) 77033) ((-747 . -1121) T) ((-727 . -1121) T) ((-1280 . -658) 76943) ((-1273 . -658) 76825) ((-465 . -1121) T) ((-419 . -1238) T) ((-326 . -442) 76809) ((-604 . -93) T) ((-1048 . -626) 76770) ((-270 . -1238) T) ((-1045 . -1242) T) ((-227 . -102) T) ((-1048 . -625) 76732) ((-828 . -272) 76716) ((-828 . -232) 76700) ((-827 . -628) 76498) ((-1252 . -658) 76335) ((-1045 . -568) T) ((-845 . -660) 76308) ((-365 . -1242) T) ((-488 . -625) 76270) ((-488 . -626) 76231) ((-475 . -626) 76192) ((-475 . -625) 76154) ((-608 . -658) 76113) ((-419 . -899) 76097) ((-329 . -1077) 75932) ((-419 . -901) 75857) ((-607 . -658) 75767) 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. -414) NIL) ((-118 . -237) NIL) ((-1195 . -628) 34107) ((-1141 . -673) T) ((-885 . -729) 34052) ((-258 . -501) 34036) ((-257 . -501) 34020) ((-1194 . -628) 33763) ((-1188 . -628) 33558) ((-724 . -651) 33506) ((-665 . -660) 33480) ((-1147 . -628) 33362) ((-305 . -34) T) ((-1141 . -113) T) ((-743 . -1070) T) ((-593 . -1295) 33349) ((-530 . -1295) 33326) ((-1261 . -1121) T) ((-1193 . -300) 33237) ((-1146 . -300) 33168) ((-1083 . -174) T) ((-299 . -1238) T) ((-869 . -1121) T) ((-971 . -174) 33079) ((-794 . -1264) 33063) ((-656 . -526) 32996) ((-77 . -625) 32978) ((-743 . -336) 32943) ((-1199 . -738) T) ((-583 . -1121) T) ((-493 . -174) 32854) ((-250 . -319) 32792) ((-1163 . -1133) T) ((-70 . -625) 32774) ((-1300 . -738) T) ((-1195 . -1070) T) ((-1194 . -1070) T) ((-1188 . -1070) T) ((-337 . -102) 32704) ((-1163 . -23) T) ((-2 . -1238) T) ((-1147 . -1070) T) ((-91 . -1142) 32688) ((-880 . -1133) T) ((-1195 . -238) 32647) ((-1194 . -248) 32626) ((-1194 . -238) 32578) ((-1188 . -238) 32465) 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. -238) 13209) ((-1141 . -237) T) ((-40 . -102) T) ((-929 . -1079) T) ((-706 . -911) NIL) ((-1202 . -102) T) ((-129 . -501) 13191) ((-1195 . -738) T) ((-1194 . -738) T) ((-1188 . -738) T) ((-1188 . -803) NIL) ((-1188 . -806) NIL) ((-973 . -102) T) ((-940 . -102) T) ((-884 . -1072) 13178) ((-1147 . -738) T) ((-783 . -102) T) ((-684 . -102) T) ((-884 . -652) 13165) ((-558 . -625) 13147) ((-486 . -1121) T) ((-350 . -1133) T) ((-176 . -1133) T) ((-329 . -939) 13126) ((-1272 . -729) 12967) ((-886 . -174) T) ((-1251 . -729) 12781) ((-855 . -21) 12733) ((-855 . -25) 12685) ((-250 . -1170) 12669) ((-127 . -526) 12602) ((-419 . -25) T) ((-419 . -21) T) ((-350 . -23) T) ((-171 . -626) 12368) ((-171 . -625) 12350) ((-176 . -23) T) ((-656 . -298) 12327) ((-532 . -34) T) ((-915 . -625) 12309) ((-89 . -1238) T) ((-853 . -625) 12291) ((-820 . -625) 12273) ((-781 . -625) 12255) ((-689 . -625) 12237) ((-245 . -660) 12070) ((-629 . -113) T) ((-1197 . -1121) T) ((-1193 . -1077) 11893) ((-216 . -1238) T) 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10413) ((-219 . -901) 10395) ((-619 . -25) T) ((-439 . -660) 10369) ((-1193 . -628) 10138) ((-499 . -1059) 10098) ((-886 . -526) 10010) ((-1146 . -628) 9802) ((-868 . -628) 9720) ((-219 . -1059) 9680) ((-245 . -34) T) ((-1021 . -1121) 9658) ((-592 . -1072) 9645) ((-576 . -1072) 9632) ((-507 . -1072) 9597) ((-1272 . -174) 9528) ((-1251 . -174) 9459) ((-592 . -652) 9446) ((-576 . -652) 9433) ((-507 . -652) 9398) ((-724 . -146) 9377) ((-724 . -148) 9356) ((-130 . -864) T) ((-713 . -132) T) ((-561 . -1238) T) ((-137 . -477) 9333) ((-1168 . -625) 9265) ((-670 . -668) 9249) ((-129 . -296) 9199) ((-117 . -132) T) ((-489 . -1242) T) ((-620 . -616) 9175) ((-487 . -616) 9154) ((-609 . -1121) T) ((-347 . -346) 9123) ((-597 . -1121) T) ((-548 . -1121) T) ((-489 . -568) T) ((-1193 . -1070) T) ((-1146 . -1070) T) ((-868 . -1070) T) ((-835 . -1238) T) ((-245 . -806) 9102) ((-245 . -805) 9081) ((-1193 . -336) 9058) ((-245 . -738) 9036) ((-977 . -19) 9020) ((-499 . -388) 9002) ((-499 . -349) 8984) 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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 709498d4..ce7cca06 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3486833879) -(4468 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3486841613) +(4467 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -488,663 +488,665 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |is?| |direction| |wrregime| - |removeRedundantFactorsInPols| |arg2| |string| |radicalSimplify| - |monomRDEsys| |less?| |monomialIntPoly| |cAtanh| |distFact| |nthr| - |pair?| |mesh?| |deepCopy| |imagi| |normalise| |say| |setClipValue| - |OMgetEndBVar| |OMgetEndAttr| |quoByVar| |shufflein| |isOr| - |conditions| |relationsIdeal| |lazyIntegrate| |setfirst!| - |decreasePrecision| |integralAtInfinity?| |leadingIndex| |e02def| - |quoted?| |oddInfiniteProduct| |title| |match| |imports| |pdct| - |reset| |characteristicSet| |mapdiv| |external?| |hermiteH| - |stoseInvertibleSet| |semiIndiceSubResultantEuclidean| |exponential| - |sum| |baseRDEsys| |tanh2coth| |mirror| |inc| |zeroDim?| - |rootDirectory| |iFTable| |stronglyReduce| |multiplyCoefficients| - |coefChoose| |computeCycleLength| |norm| |write| |redPo| |cycleElt| - |isTimes| |radicalEigenvector| |genericRightNorm| |shuffle| |e| - |curveColorPalette| |bigEndian| |save| |secIfCan| |nullity| |lp| - |raisePolynomial| |d01bbf| |isConnected?| |f02akf| |diophantineSystem| - |coerceImages| |rangePascalTriangle| |recur| |nothing| - |SturmHabichtSequence| |simpleBounds?| |iiasin| |processTemplate| - |normalizeAtInfinity| |variable?| |const| |printStats!| |cylindrical| - |extractProperty| |removeDuplicates| |setDifference| |mindeg| |exp1| - |top| |regularRepresentation| |integer?| |rationalPower| |optpair| - |pole?| |extension| |curry| |makeprod| |lagrange| |continue| - |polarCoordinates| |isAbsolutelyIrreducible?| |permutation| |lprop| - |lex| |quickSort| |readUInt8!| |choosemon| |infRittWu?| |lazyPquo| - |constantKernel| |acscIfCan| |limitedIntegrate| |lllp| |addPoint| - |primlimitedint| |palgLODE| |middle| |iiacoth| ** |hash| |radPoly| - |groebner?| |minGbasis| |isAnd| |viewport3D| |groebner| |elem?| - |generalLambert| |createMultiplicationTable| |count| |localUnquote| - |normalizedAssociate| |component| |primlimintfrac| |uniform01| - |pleskenSplit| |ddFact| |wholeRagits| |generateIrredPoly| |module| - |invertibleSet| |f07adf| |monomRDE| |ridHack1| |byteBuffer| - |trace2PowMod| |d02kef| |lSpaceBasis| |viewDeltaXDefault| |constant| - |patternMatchTimes| |primeFactor| |particularSolution| |aspFilename| - |OMreadStr| |controlPanel| |rotatey| |cscIfCan| |yellow| - |messagePrint| |integrate| |mantissa| |rootBound| |cup| |branchPoint?| - |bombieriNorm| |contractSolve| |c06gsf| |setProperties| |OMclose| - |string?| |iisinh| |scanOneDimSubspaces| |s14abf| |returnTypeOf| - |readIfCan!| |c05adf| |decompose| |pdf2ef| |rdregime| |associative?| - |sPol| |dAndcExp| |partitions| |ode1| |exponential1| |mainExpression| - |meshPar2Var| |localAbs| |s17akf| |OMputEndAttr| |headReduce| - |reducedForm| |rangeIsFinite| |backOldPos| |interactiveEnv| - |separateDegrees| |OMgetString| |numFunEvals3D| |complexElementary| - |gcdPolynomial| |factorByRecursion| |shiftRight| |elaborateFile| - |createPrimitiveElement| |normal?| |zeroMatrix| |isImplies| - |toseSquareFreePart| |lastSubResultant| |find| |axes| |leastMonomial| - |iisin| |status| |intChoose| |showIntensityFunctions| |groebnerIdeal| - |rootNormalize| |maximumExponent| |OMgetBind| |mapUnivariateIfCan| - |permutationGroup| |perfectNthRoot| |OMopenString| |cAcos| |infix| - |complexNumericIfCan| |unitNormalize| |makeSin| |recip| |s18aef| - |linearlyDependentOverZ?| |categories| |OMgetInteger| - |leftExtendedGcd| |insertTop!| |algebraicDecompose| |integral?| - |numer| |iiexp| |retractIfCan| |kovacic| |fixedPoints| |hasSolution?| - |powerAssociative?| |innerEigenvectors| |iiasech| |retractable?| - |insertMatch| |denom| |traverse| |algebraicVariables| - |collectQuasiMonic| |environment| |host| |makeResult| - |stoseInvertibleSetsqfreg| |henselFact| |identity| |legendreP| - |stiffnessAndStabilityOfODEIF| |basis| |smith| |semicolonSeparate| - |iteratedInitials| |inspect| |innerint| |eulerPhi| |pi| - |createZechTable| |cRationalPower| |initiallyReduced?| |idealiser| - |symmetricProduct| |lastSubResultantEuclidean| |elseBranch| - |monomials| |integralDerivationMatrix| |infinity| |approxNthRoot| - |member?| |stronglyReduced?| |rewriteIdealWithQuasiMonicGenerators| - |concat| |step| |extendedIntegrate| |coefficients| |df2mf| |red| - |duplicates| |ode| |stirling1| |OMputObject| |finiteBound| |edf2fi| - |firstUncouplingMatrix| |branchPointAtInfinity?| |indiceSubResultant| - |cyclic| |setRow!| |denominators| |modulus| |negative?| |reopen!| - |OMwrite| |OMgetError| |gderiv| |iifact| |kernel| |karatsubaOnce| - |internalIntegrate0| |maxdeg| |subMatrix| |formula| |ef2edf| - |reducedQPowers| |pade| |linearAssociatedExp| |list| |ptree| |closed?| - |invmultisect| |linearMatrix| |fortranDoubleComplex| |polygon?| |lhs| - |zeroSquareMatrix| |subResultantsChain| |setRealSteps| |subSet| |draw| - |OMreadFile| |digit?| |clearCache| |interReduce| - |permutationRepresentation| |fixPredicate| |rhs| |leftTraceMatrix| - |remove!| |bezoutDiscriminant| |nthFractionalTerm| |cot2trig| |shape| - |solveInField| |cyclicGroup| |gcdprim| |systemSizeIF| |sncndn| - |double?| |safeCeiling| |categoryFrame| |stFuncN| |debug3D| - |composites| |color| |currentEnv| |nrows| |isPlus| |initTable!| - |cartesian| |SturmHabichtCoefficients| |cAsec| |rk4a| |e01sbf| - |laguerreL| |ratpart| |ncols| |parabolic| |addmod| |plus!| - |removeDuplicates!| |makeObject| |qPot| |lieAlgebra?| - |leftAlternative?| |wholeRadix| |outlineRender| |sorted?| - |monomialIntegrate| |stopTableGcd!| |cot2tan| |coef| |tanSum| - |symbolTableOf| |cardinality| |startStats!| |mkIntegral| - |alphanumeric?| |singRicDE| |iiGamma| |modifyPoint| |e04jaf| |curve?| - |freeOf?| |Lazard| |lookupFunction| |readInt8!| |d02raf| - |cyclotomicDecomposition| |makeSUP| |asecIfCan| |iisech| |inRadical?| - |closeComponent| |argument| |rightNorm| |curve| - |LagrangeInterpolation| |back| |solveLinearlyOverQ| |zeroDimPrimary?| - |rischNormalize| |imagK| |d01alf| |kind| |in?| |extend| |eulerE| - |withPredicates| |gbasis| |linears| |toroidal| |groebnerFactorize| - |LyndonBasis| |op| |lieAdmissible?| |omError| |anticoord| - |ReduceOrder| |updatF| |kernels| |leftRemainder| |reduction| - |indicialEquationAtInfinity| |printCode| |write!| |deepestInitial| - |region| |quadratic| |removeCosSq| |tablePow| |oneDimensionalArray| - |anfactor| |minimumExponent| |operator| |leftUnit| - |genericRightTraceForm| |appendPoint| |minrank| |iicoth| |leftPower| - |interval| SEGMENT |inverseLaplace| |scalarMatrix| - |zeroSetSplitIntoTriangularSystems| |droot| |e04naf| |defineProperty| - |leftFactorIfCan| |points| |lazyPseudoRemainder| |sort| |rootsOf| - |exponents| |univariate| |stoseInternalLastSubResultant| |invertIfCan| - |UnVectorise| |OMmakeConn| |factorial| |pseudoQuotient| - |setScreenResolution| |dec| |trivialIdeal?| |size?| |hostByteOrder| - |rotatez| |factorPolynomial| |quasiRegular| |parabolicCylindrical| - |multMonom| |leftScalarTimes!| |cyclicEqual?| |regime| |parent| - |radix| |union| |unknownEndian| |lfextendedint| - |generalizedEigenvector| |epilogue| |laplacian| |binaryTree| |forLoop| - |factor| |idealSimplify| |integralMatrixAtInfinity| |nextNormalPoly| - |clipSurface| |readInt32!| |unvectorise| |reducedDiscriminant| - |random| |modTree| |cTan| |sqrt| |patternMatch| |intcompBasis| - |FormatRoman| |selectFiniteRoutines| |showTheFTable| |qualifier| - |comp| |e01bhf| |irVar| |cyclotomic| |real| |laurentIfCan| - |numericIfCan| |removeConstantTerm| |digamma| |getProperties| |e02bcf| - |leftGcd| |setprevious!| |compound?| |imag| |octon| |supersub| |super| - |properties| |useSingleFactorBound| |s15adf| |extractPoint| - |var2StepsDefault| |reducedContinuedFraction| |copy| |rootSimp| - |directProduct| |matrixGcd| |changeVar| |permanent| |repeating?| - |translate| |tubeRadiusDefault| |randomLC| |exactQuotient!| - |internalSubQuasiComponent?| |hex| |padicFraction| |roughBase?| - |screenResolution3D| |c06gcf| |removeIrreducibleRedundantFactors| - |depth| |HermiteIntegrate| |yCoord| |upperCase?| |gensym| |brace| - |setchildren!| |aQuadratic| |powers| |sparsityIF| |pseudoRemainder| - |lfextlimint| |OMReadError?| |insert!| |dioSolve| |bandedHessian| - |f02bbf| |destruct| |graphs| |listOfLists| |localIntegralBasis| - |palgLODE0| |fixedPointExquo| |OMopenFile| |nand| |edf2ef| - |whatInfinity| |genericRightTrace| |match?| |getMultiplicationMatrix| - |besselK| |conical| |weight| |PollardSmallFactor| |autoCoerce| - |getCurve| |colorFunction| |c06ekf| |position!| |arguments| |subset?| - |list?| |iExquo| |solveLinear| |expandPower| |primitivePart!| - |setTex!| |s19adf| |f02ajf| |enterInCache| |linearAssociatedOrder| - |stopMusserTrials| |product| |ScanRoman| |expand| |mapUp!| - |dualSignature| |monomial| |OMsupportsCD?| |bitLength| |OMgetEndError| - |multiple?| |scan| |binding| |minColIndex| |filterWhile| - |insertBottom!| |multivariate| |graphState| |outputSpacing| |close| - |pascalTriangle| |leastPower| |acotIfCan| F - |solveLinearPolynomialEquation| |eigenvalues| |sumOfKthPowerDivisors| - |filterUntil| |euclideanSize| |flagFactor| |variables| |youngGroup| - |paraboloidal| |overset?| |iilog| |select| |vark| |f04qaf| |display| - |closedCurve?| |rightRankPolynomial| |randomR| |iiacos| |gradient| - |exprToGenUPS| |wordsForStrongGenerators| |imagJ| |complexForm| - |completeHensel| |rst| |fi2df| |setLabelValue| |cSech| - |doublyTransitive?| |rootSplit| |changeThreshhold| |palgintegrate| - |trunc| |critB| |lighting| |quatern| |viewDeltaYDefault| |predicate| - |rightAlternative?| |dimension| |nextPrimitivePoly| |primitiveElement| - |resultantReduit| |perfectSqrt| |internalAugment| |debug| |taylor| - |f02bjf| |measure| |mesh| |members| |karatsubaDivide| |cn| |nullary| - |reflect| |unparse| D |laurent| |input| |extractIndex| |f2df| - |csc2sin| |checkForZero| |c06fqf| |tubeRadius| |addMatch| |rowEchelon| - |puiseux| |library| |rCoord| |OMsend| |noncommutativeJordanAlgebra?| - |fortranLiteralLine| EQ |infieldIntegrate| |sortConstraints| |isExpt| - |buildSyntax| |createThreeSpace| |divisor| |SturmHabicht| |e01saf| - |printTypes| |swap!| |alphabetic| |createPrimitiveNormalPoly| |inv| - |solid?| |unitVector| |mapExpon| |lquo| |exprHasWeightCosWXorSinWX| - |setLegalFortranSourceExtensions| |normalizedDivide| |dihedral| - |commutativeEquality| |ground?| |dimensionsOf| |errorInfo| |slash| - |newSubProgram| |primaryDecomp| |power| |deref| |solveid| |medialSet| - |ground| |set| |intermediateResultsIF| |dark| |cubic| |setleaves!| - |commutator| |fortranDouble| |integralCoordinates| |critMonD1| - |decimal| |leadingMonomial| |OMputEndBind| |jordanAlgebra?| - |symmetricGroup| |accuracyIF| |coercePreimagesImages| |positive?| - |complexExpand| |besselI| |recoverAfterFail| |leadingCoefficient| - |parameters| |extendedSubResultantGcd| |fortranCarriageReturn| - |divideIfCan!| |makeMulti| |airyAi| |size| |tanhIfCan| - |shanksDiscLogAlgorithm| |calcRanges| |standardBasisOfCyclicSubmodule| - |primitiveMonomials| |separant| |isOpen?| |mainVariable?| |numerators| - |makeop| |lflimitedint| |squareFreeFactors| |allRootsOf| - |insertionSort!| |print| |reductum| |corrPoly| |c06fuf| |substring?| - |dot| |iflist2Result| |clipPointsDefault| |nthRoot| |abs| |qfactor| - |virtualDegree| |resolve| |s13aaf| |outputFixed| |trailingCoefficient| - |column| |numberOfPrimitivePoly| |scale| |deepestTail| |squareMatrix| - |figureUnits| |prem| |neglist| |maxIndex| |atrapezoidal| - |setCondition!| |mainCharacterization| |suffix?| |true| |denominator| - |cfirst| |category| |ref| |arrayStack| |alphabetic?| |enumerate| - |c06gqf| |oddintegers| |domain| |float?| - |inverseIntegralMatrixAtInfinity| |preprocess| |trapezoidalo| - |RemainderList| |leastAffineMultiple| |optional| |OMreceive| |delete!| - |numericalIntegration| |f04arf| |nilFactor| |mathieu24| - |lastSubResultantElseSplit| |prefix?| |qinterval| - |countRealRootsMultiple| |package| |numerator| |isNot| |constantRight| - |principalIdeal| |generic?| |insert| |indicialEquation| |signAround| - |numberOfFractionalTerms| |baseRDE| |extractIfCan| |tube| - |useEisensteinCriterion?| |s20adf| |tRange| - |solveLinearPolynomialEquationByFractions| |show| |divideIfCan| - |convergents| |rootOfIrreduciblePoly| |rightTraceMatrix| |addiag| - |fortranComplex| |logIfCan| |commutative?| |nullSpace| |search| - |c05nbf| |listLoops| |cAtan| |quotedOperators| |overlap| |predicates| - |reducedSystem| |node| |clearDenominator| |geometric| |ode2| - |rightLcm| |trace| |clipParametric| |inverseIntegralMatrix| - |setFormula!| |getMatch| |removeRoughlyRedundantFactorsInPol| - |resetNew| |numberOfMonomials| |setButtonValue| |componentUpperBound| - |getSyntaxFormsFromFile| |besselY| |character?| |contains?| - |screenResolution| |removeSuperfluousCases| |leftRank| |d01ajf| - |f04jgf| |sub| |pointData| |mapCoef| |infix?| |sturmSequence| - |mainVariables| |localReal?| |paren| |sinh2csch| |pointPlot| - |createNormalPoly| |nextItem| |polCase| |mask| |imagE| - |setTopPredicate| |chainSubResultants| |unitNormal| |alternatingGroup| - |increase| |areEquivalent?| |chiSquare| |rationalFunction| - |showArrayValues| |flatten| |aLinear| |firstNumer| |deleteRoutine!| - |removeZeroes| |diagonals| |hMonic| |lazyGintegrate| |clipBoolean| - |bytes| |ramified?| |laurentRep| |compose| |shiftLeft| - |rightDiscriminant| |indiceSubResultantEuclidean| |mdeg| |qqq| - |dictionary| |mainCoefficients| |uncouplingMatrices| |isQuotient| - |factorials| |basisOfLeftNucleus| |karatsuba| |leadingSupport| - |setOfMinN| |headRemainder| |entries| |complexLimit| |symmetric?| - |halfExtendedSubResultantGcd2| |s20acf| |computeInt| |e02akf| - |extendedEuclidean| |OMgetEndObject| |fortranLogical| |subHeight| - |solveLinearPolynomialEquationByRecursion| |deriv| |getOperator| - 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|removeSquaresIfCan| |hessian| |OMgetApp| |bits| + |moreAlgebraic?| - |showAllElements| |primintfldpoly| |dmp2rfi| |type| |whileLoop| - |selectODEIVPRoutines| |elementary| |conjunction| |tanQ| |OMlistCDs| - |binaryTournament| |point| - |float| |firstDenom| |generalSqFr| - |supRittWu?| |subResultantGcd| |hypergeometric0F1| |Frobenius| - |zerosOf| |nthCoef| |rightDivide| |variable| |stFunc1| / |leftZero| - |bounds| |mappingAst| |OMputFloat| |iicsc| |scopes| |primextendedint| - |prepareDecompose| |nextsousResultant2| |iterators| |numFunEvals| - |sumSquares| |removeSinhSq| |ListOfTerms| |fractRagits| |nor| - |polyRicDE| |maxrow| |partialDenominators| |rk4qc| |readable?| - |gramschmidt| |series| |basisOfLeftAnnihilator| |f02aff| - |balancedFactorisation| |testDim| |capacity| |eigenMatrix| |newReduc| - |conjug| |polyred| |outputGeneral| |continuedFraction| |showAll?| - |OMUnknownCD?| |doubleDisc| |critM| |radicalRoots| |minPol| |myDegree| - |id| |quadraticForm| |zeroDimensional?| - |selectMultiDimensionalRoutines| |e02daf| |rationalIfCan| |prevPrime| - |value| |constantOperator| |modularFactor| |pushucoef| |symbol| - |relativeApprox| |rightQuotient| |lo| |internalIntegrate| |nary?| - |pointColorDefault| |fixedPoint| |collectUpper| |complexRoots| - |harmonic| |simpsono| |coord| |expression| |lazyResidueClass| |min| - |complete| |d01apf| |s13adf| |showFortranOutputStack| |aQuartic| - |mappingMode| |qroot| |max| |listexp| |integer| |hclf| - |pushNewContour| |physicalLength| GE |OMbindTCP| |cycles| - |constantToUnaryFunction| |divisors| |problemPoints| - |leftCharacteristicPolynomial| |inputOutputBinaryFile| |froot| - |putProperties| |rowEchelonLocal| |bat| GT |makeFloatFunction| - |resize| |createMultiplicationMatrix| |univariatePolynomial| - |generalizedInverse| |charpol| |e04ucf| |real?| |OMunhandledSymbol| - |largest| LE |hdmpToDmp| |selectsecond| |btwFact| |explicitlyFinite?| - |deepExpand| |adaptive3D?| |testModulus| |zCoord| |f01qcf| - |encodingDirectory| LT |se2rfi| |semiSubResultantGcdEuclidean1| - |expandLog| |coefficient| |iiasinh| |invertibleElseSplit?| |cotIfCan| - 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|outputMeasure| |curryRight| |getOperands| |midpoints| |sqfree| - |leftOne| |twoFactor| |rightTrace| |imagj| |optimize| |elliptic| - |OMputApp| |applyRules| |dfRange| |nextNormalPrimitivePoly| |limit| - |precision| |function| |s19abf| |upperCase| |rotatex| |d02ejf| - |zeroOf| RF2UTS |s21bcf| |isPower| |trim| |cExp| - |rightRegularRepresentation| |e04gcf| |index?| |rroot| |iiacosh| - |musserTrials| |monicLeftDivide| |selectSumOfSquaresRoutines| |e02gaf| - |width| |substitute| |computePowers| |redpps| |balancedBinaryTree| - |rules| |diagonalProduct| |subQuasiComponent?| |cycleEntry| |double| - |clearFortranOutputStack| |chineseRemainder| |increasePrecision| - |gcdPrimitive| |sin?| |critT| |rightPower| |getExplanations| - |euclideanNormalForm| UTS2UP |hue| |f01qdf| |completeEchelonBasis| - |extendIfCan| |Nul| |groebgen| |polynomialZeros| - |rewriteSetWithReduction| |s21bbf| |scripted?| |merge| |cAsinh| - |divisorCascade| |leftNorm| |squareTop| |move| |schwerpunkt| - |plotPolar| |specialTrigs| |s14aaf| |makeViewport3D| |f02abf| - 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|Lazard2| |iterationVar| |primintegrate| |unknown| |dilog| |e02bdf| - |legendre| |definingPolynomial| |setStatus| |Or| |more?| |stirling2| - |multiEuclidean| |addPoint2| |birth| |fortranCharacter| |trigs| |sin| - |euclideanGroebner| |univcase| |drawStyle| |characteristicSerie| |Not| - |front| |genus| |minPoints3D| |sample| |Is| |coleman| |cos| |po| - |coHeight| |has?| |invmod| |viewPhiDefault| |useSingleFactorBound?| - |int| |jordanAdmissible?| |resetVariableOrder| |basisOfNucleus| - |maxRowIndex| |tan| |realEigenvectors| |quasiMonicPolynomials| - |pastel| |makeSeries| |comparison| |quadraticNorm| |HenselLift| - |initiallyReduce| |cot| |fractRadix| |bezoutMatrix| - |leftReducedSystem| F2FG |changeNameToObjf| |e02ddf| |order| - |readInt16!| |abelianGroup| |sec| |squareFree| |s17ajf| - |rectangularMatrix| |overbar| |sizeMultiplication| |strongGenerators| - |coth2trigh| |bezoutResultant| |certainlySubVariety?| |csc| - |clearTheIFTable| |var1Steps| |expenseOfEvaluation| |setelt!| - |numberOfComposites| |read!| |romberg| |asin| |univariatePolynomials| - |test| |positiveRemainder| |unitsColorDefault| |bag| - |pointColorPalette| |derivative| |remove| |operation| |integral| - |addBadValue| |selectfirst| |acos| |cCoth| |knownInfBasis| |cAcosh| - |cCos| |d02gbf| |f01brf| |mapmult| |Aleph| |adjoint| |atan| - |minPoints| |recolor| |sn| |trapezoidal| |parts| |sh| |exprToXXP| - |last| |basisOfRightNucleus| |minPoly| |mapUnivariate| |empty?| |acot| - |pushdown| |getButtonValue| |assoc| |cAcsch| |setImagSteps| - |clearTable!| |mkPrim| |pack!| |asec| |s21bdf| |simplifyLog| - |asimpson| |condition| |tower| |pushdterm| |reverse!| |simplifyPower| - |leadingIdeal| |setUnion| |removeZero| |acsc| |characteristic| - |iicsch| |jacobiIdentity?| |associatedSystem| |Beta| |padicallyExpand| - |diagonal?| |divergence| |fortranLinkerArgs| |prefix| |sinh| - |inrootof| |key?| |lazyPseudoQuotient| |mapBivariate| |blankSeparate| - |ratPoly| |iomode| |cosh| |denomRicDE| |sizeLess?| |plenaryPower| - |support| |getVariableOrder| |fracPart| |makeUnit| |complement| - |OMUnknownSymbol?| |obj| |tanh| |triangular?| |eq| |makeVariable| - |KrullNumber| |showRegion| |sizePascalTriangle| |ord| |getConstant| - |conditionsForIdempotents| |subNode?| |cache| |coth| |iter| |s01eaf| - |eq?| |callForm?| |doubleResultant| |complexNumeric| |credPol| |arity| - |fill!| |lazy?| |d01amf| |unprotectedRemoveRedundantFactors| |sech| - |OMputEndError| |att2Result| |moduleSum| |torsionIfCan| |before?| - |lowerCase| |ldf2vmf| |f01rcf| |tan2trig| |getOrder| |csch| |lfunc| - |expPot| |antiCommutator| |setClosed| |permutations| |factorAndSplit| - |mainContent| |opeval| |setEmpty!| |asinh| |nthFlag| |gethi| - |normal01| |thenBranch| |setMinPoints| |OMputVariable| - |LazardQuotient| |meatAxe| |printInfo!| |resetAttributeButtons| - |cAcoth| |acosh| |iisqrt3| |cCsch| |normInvertible?| |ran| |s18adf| - |subscriptedVariables| |primitive?| |stopTable!| |hasTopPredicate?| - |row| |removeSuperfluousQuasiComponents| |lowerCase?| |zeroDimPrime?| - |basisOfRightNucloid| |clip| |s17aef| |factorSquareFreePolynomial| - |traceMatrix| |iiabs| |outputAsTex| |exp| |reseed| |rotate| |closed| - 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|tableForDiscreteLogarithm| |OMputBVar| |returnType!| |e02ahf| - |startTable!| |finiteBasis| |totalfract| |cyclicCopy| |simpson| - |mapSolve| |one?| |leadingCoefficientRicDE| |mapDown!| |dflist| - |failed| |hexDigit| |lifting1| |randnum| |addPointLast| |times!| - |revert| LODO2FUN |readUInt16!| |simplify| |bfKeys| - |associatorDependence| |printingInfo?| |realRoots| |mainMonomials| - |doubleComplex?| |bernoulliB| |equality| |cAsin| |lyndon| - |factorOfDegree| |algebraicOf| |univariateSolve| |incr| - |UpTriBddDenomInv| |rombergo| |determinant| |clearTheFTable| |empty| - |contract| |parametric?| |asinIfCan| |spherical| |hi| |writable?| - |morphism| |ramifiedAtInfinity?| |indices| |LazardQuotient2| - |voidMode| |cyclotomicFactorization| |OMread| |padecf| |left| |e01bff| - |logpart| |mainValue| |binaryFunction| |readLine!| |eigenvectors| - |lexGroebner| |part?| |prime?| |right| |power!| |powerSum| |isAtom| - |schema| |startTableInvSet!| |f07fdf| |cCot| |leftDivide| |cPower| - |root| |readBytes!| |currentScope| |normalElement| |lineColorDefault| - |pToHdmp| |d01fcf| |minRowIndex| |signatureAst| |sylvesterMatrix| - |infLex?| |perfectSquare?| |nextPartition| |elRow2!| |qelt| |initials| - |nthFactor| |weierstrass| |LyndonWordsList1| |qsetelt| |s19aaf| - |characteristicPolynomial| |showTheRoutinesTable| |cTanh| |getRef| - |hexDigit?| |initial| |elements| |coth2tanh| |acoshIfCan| - |noLinearFactor?| |sinhcosh| |lexico| |unexpand| |setPredicates| - |xRange| |next| |functionIsFracPolynomial?| |sort!| |vspace| |round| - |key| |partialQuotients| |slex| |pmintegrate| |OMencodingUnknown| - |singular?| |yRange| |zero?| |solveRetract| |stopTableInvSet!| - |setPrologue!| |df2st| |sdf2lst| |critBonD| |ParCond| |zRange| - |htrigs| |basisOfLeftNucloid| |reorder| |every?| |vconcat| |filename| - |map!| |sts2stst| |moduloP| |digits| |discriminantEuclidean| - |algebraicSort| |sinhIfCan| |setPoly| |expIfCan| |parseString| - |littleEndian| |uniform| |qsetelt!| |charthRoot| - |genericRightMinimalPolynomial| |subTriSet?| |quasiMonic?| - |principal?| |minset| |f02awf| |parse| |replaceKthElement| |exists?| - |realZeros| |rootPower| |normDeriv2| |code| |OMsetEncoding| - |frobenius| |discriminant| |car| |generate| |cosSinInfo| |surface| - |exactQuotient| |universe| |seed| |minimize| |basisOfMiddleNucleus| - |twist| |removeRoughlyRedundantFactorsInPols| |setrest!| |cSec| - |superscript| |subtractIfCan| |multiset| |leadingExponent| - |lazyVariations| |prepareSubResAlgo| |trueEqual| |incrementBy| |iicos| - |semiResultantEuclidean1| |rewriteIdealWithHeadRemainder| - |doubleFloatFormat| |whitePoint| |mulmod| |iidprod| |asechIfCan| - |phiCoord| |fprindINFO| |totolex| |tValues| |airyBi| |f02xef| |acsch| - |brillhartTrials| |mainMonomial| |factorSquareFree| |f02aaf| - |functorData| GF2FG |alternative?| |printInfo| |leviCivitaSymbol| - |squareFreeLexTriangular| |transform| |factorGroebnerBasis| |lookup| - |tab| |jokerMode| |OMParseError?| |quasiComponent| |rightZero| - |f04mcf| |updatD| |createNormalPrimitivePoly| |sechIfCan| - |createLowComplexityTable| |irreducibleFactors| |perfectNthPower?| - |companionBlocks| |getCode| |s19acf| |submod| |irCtor| - |possiblyInfinite?| |options| |irreducible?| |complex?| |inHallBasis?| - |psolve| |mainForm| |tail| |cosIfCan| |dom| |palgint0| |tableau| - |monicRightFactorIfCan| |jacobi| |weights| |leadingBasisTerm| - |semiResultantEuclideannaif| |setColumn!| |packageCall| |arg1| - |saturate| |entry| |purelyAlgebraic?| |rquo| |selectNonFiniteRoutines| - |e04fdf| |s18dcf| |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 + |Record| |Union| |asinhIfCan| |RemainderList| |lazyIntegrate| + |wronskianMatrix| |arg2| |forLoop| |string| |upperCase!| |clikeUniv| + |simpson| |leastAffineMultiple| |legendre| |updateStatus!| |distance| + |setfirst!| |idealSimplify| |prindINFO| |selectOrPolynomials| |say| + |mapSolve| |decreasePrecision| |OMconnectTCP| |OMreceive| |sqfrFactor| + |definingPolynomial| |conditions| |integralMatrixAtInfinity| |belong?| + |writeInt8!| |one?| |delete!| |integralAtInfinity?| |transpose| + |showTheIFTable| |setStatus| |title| |match| |nextNormalPoly| + |hasPredicate?| |reset| |viewWriteDefault| |leadingCoefficientRicDE| + |leadingIndex| |numericalIntegration| |maxrank| |supDimElseRittWu?| + |more?| |sum| |bitTruth| |lfintegrate| |mapDown!| |inc| |stirling2| + |f04arf| |restorePrecision| |e02def| |BumInSepFFE| |outlineRender| + |property| |minordet| |write| |dflist| |logGamma| |nilFactor| + |numberOfComponents| |multiEuclidean| |quoted?| |e| |sorted?| + |putProperty| |save| |crushedSet| |hexDigit| |lp| |diag| |mathieu24| + |repeating| |oddInfiniteProduct| |addPoint2| |monomialIntegrate| + |nothing| |c06gbf| |toseInvertibleSet| |lifting1| |imports| |cAcsc| + |birth| |stopTableGcd!| |goto| |bsolve| |randnum| + |noncommutativeJordanAlgebra?| |aQuartic| |fortranCharacter| + |sequences| |pdct| |cot2tan| |top| |e02zaf| |complexNormalize| + |addPointLast| |fortranLiteralLine| |mappingMode| |expint| |trigs| + |characteristicSet| |tanSum| |continue| |insertRoot!| + |dimensionOfIrreducibleRepresentation| |times!| |infieldIntegrate| + |qroot| |euclideanGroebner| |setMaxPoints| |mapdiv| |symbolTableOf| + |revert| |sortConstraints| |max| |external?| |univcase| |infinite?| + |cardinality| |cSin| |squareFreePrim| ** LODO2FUN |hash| |listexp| + |isExpt| |hermiteH| |bivariatePolynomials| |drawStyle| |startStats!| + |iiatan| |s18def| |readUInt16!| |count| |hclf| |buildSyntax| + |integerIfCan| |stoseInvertibleSet| |characteristicSerie| |mkIntegral| + |e04ycf| |cosh2sech| |simplify| |pushNewContour| |createThreeSpace| + |alphanumeric?| |ratDsolve| |stripCommentsAndBlanks| |bfKeys| + |divisor| |physicalLength| |mix| |changeWeightLevel| |constant| + |singRicDE| |selectOptimizationRoutines| |reduced?| + |associatorDependence| |OMbindTCP| |SturmHabicht| + |useEisensteinCriterion| |lyndon?| |iiGamma| |exprHasAlgebraicWeight| + |numberOfChildren| |mantissa| |printingInfo?| |e01saf| |cycles| + |linearDependence| |B1solve| |modifyPoint| |listConjugateBases| + |f02fjf| |shuffle| |constantToUnaryFunction| |printTypes| + |deleteProperty!| |associates?| |e04jaf| |readUInt32!| |leaf?| + |normInvertible?| |curveColorPalette| |divisors| |swap!| FG2F + |failed?| |curve?| |safeFloor| |increment| |ran| |alphabetic| + |problemPoints| |iitan| |e01sef| |freeOf?| + |stiffnessAndStabilityFactor| |binary| |s18adf| + |createPrimitiveNormalPoly| |leftCharacteristicPolynomial| + |linearlyDependent?| |basicSet| |Lazard| |UP2ifCan| |coordinate| + |subscriptedVariables| |solid?| |inputOutputBinaryFile| + |explicitlyEmpty?| |internalDecompose| |transform| |lookupFunction| + |extract!| |stoseInvertible?| |primitive?| |froot| |unitVector| |pquo| + |primitivePart| |factorGroebnerBasis| |readInt8!| |rightGcd| + |removeCoshSq| |stopTable!| |bigEndian| |putProperties| |mapExpon| + |escape| |startTableGcd!| |lookup| |d02raf| |complexZeros| + |makeGraphImage| |hasTopPredicate?| |secIfCan| |categories| + |rowEchelonLocal| |lquo| |returns| |finite?| |tab| |numer| + |cyclotomicDecomposition| |retractIfCan| |modularGcd| |conjugates| + |row| |exprHasWeightCosWXorSinWX| |bat| |normalizeIfCan| |bumptab| + |jokerMode| |denom| |makeSUP| |d02gaf| |variationOfParameters| + |removeSuperfluousQuasiComponents| |setLegalFortranSourceExtensions| + |makeFloatFunction| |rightScalarTimes!| |mathieu11| |OMParseError?| + |asecIfCan| |e04dgf| |prefixRagits| |lowerCase?| |normalizedDivide| + |resize| |probablyZeroDim?| |modifyPointData| |quasiComponent| |pi| + |iisech| |directSum| |connectTo| |zeroDimPrime?| |dihedral| + |createMultiplicationMatrix| |c02agf| + |purelyAlgebraicLeadingMonomial?| |rightZero| |infinity| |inRadical?| + |weighted| |changeMeasure| |basisOfRightNucloid| |concat| |step| + |commutativeEquality| |univariatePolynomial| |cycleLength| |connect| + |f04mcf| |closeComponent| |noValueMode| |s17acf| |clip| + |generalizedInverse| |dimensionsOf| |doubleRank| |besselJ| |updatD| + |argument| |rur| |stoseInvertible?sqfreg| |s17aef| |charpol| + |errorInfo| |roughBasicSet| |viewZoomDefault| + |createNormalPrimitivePoly| |kernel| |rightNorm| + |genericRightDiscriminant| |incrementKthElement| + |factorSquareFreePolynomial| |formula| |numberOfNormalPoly| |e04ucf| + |slash| |list| |bernoulli| |ptree| |sechIfCan| |curve| + |genericLeftDiscriminant| |just| |traceMatrix| |lhs| |newSubProgram| + |real?| |numberOfFactors| |monicDecomposeIfCan| |draw| + |createLowComplexityTable| |LagrangeInterpolation| |clearCache| + |rewriteSetByReducingWithParticularGenerators| |definingEquations| + |iiabs| |rhs| |primaryDecomp| |OMunhandledSymbol| |alphanumeric| + |d01gaf| |irreducibleFactors| |back| |matrixDimensions| + |extractClosed| |outputAsTex| |power| |largest| |exprToUPS| + |OMputBind| |perfectNthPower?| |solveLinearlyOverQ| + |ellipticCylindrical| |lambert| |reseed| |currentEnv| |nrows| + |hdmpToDmp| |deref| |outputFloating| |palgextint| |companionBlocks| + |zeroDimPrimary?| |cyclePartition| |semiResultantReduitEuclidean| + |rotate| |ncols| |solveid| |selectsecond| |iitanh| |assign| + |makeObject| |getCode| |rischNormalize| |solid| |fintegrate| |closed| + |btwFact| |medialSet| |drawComplex| |singularitiesOf| |s19acf| |coef| + |imagK| |someBasis| |pop!| |fibonacci| |intermediateResultsIF| + |explicitlyFinite?| |var2Steps| |s14baf| |submod| |d01alf| + |seriesSolve| |rowEchLocal| |listRepresentation| |deepExpand| |dark| + |digit| |inconsistent?| |irCtor| |in?| |rightMinimalPolynomial| + |nodes| |rubiksGroup| |adaptive3D?| |cubic| |partialFraction| + |colorDef| |possiblyInfinite?| |extend| |multiEuclideanTree| |dmpToP| + |innerSolve1| |kind| |setleaves!| |testModulus| |push| |invertible?| + |irreducible?| |eulerE| |iiacot| |loopPoints| |swapColumns!| |op| + |commutator| |zCoord| |unit?| |f02aef| |complex?| |kernels| + |withPredicates| |physicalLength!| |radicalEigenvalues| + |showScalarValues| |nullity| |fortranDouble| |f01qcf| |iiatanh| + |outputAsScript| |inHallBasis?| |gbasis| |symmetricRemainder| + |operator| |algebraicCoefficients?| |e02baf| |raisePolynomial| + |encodingDirectory| |integralCoordinates| |palgextint0| |associator| + |psolve| SEGMENT |linears| |completeEval| |fractionPart| |point?| + |critMonD1| |se2rfi| |highCommonTerms| |palglimint0| |mainForm| |sort| + |toroidal| |univariate| |csubst| |sech2cosh| |multiplyExponents| + |decimal| |semiSubResultantGcdEuclidean1| |extendedResultant| |blue| + |cosIfCan| |groebnerFactorize| |dec| |splitLinear| |BasicMethod| + |ceiling| |OMputEndBind| |expandLog| |discreteLog| |rightFactorIfCan| + |palgint0| |LyndonBasis| |rightFactorCandidate| + |stoseInvertibleSetreg| |represents| |union| |jordanAlgebra?| + |coefficient| |OMsupportsSymbol?| |null?| |tableau| |lieAdmissible?| + |fullPartialFraction| |factor| |resultantEuclideannaif| |setAdaptive| + |iiasinh| |symmetricGroup| |bipolar| |errorKind| + |monicRightFactorIfCan| |random| |primextintfrac| |omError| + |bandedJacobian| |sqrt| |setright!| |accuracyIF| + |invertibleElseSplit?| |curveColor| |untab| |jacobi| |comp| + |anticoord| |f01qef| |real| |tubePointsDefault| |shellSort| + |coercePreimagesImages| |cotIfCan| |quotient| |indicialEquations| + |weights| |lazyEvaluate| |ReduceOrder| |imag| |triangSolve| |aCubic| + |super| |properties| |mainDefiningPolynomial| |positive?| |f07aef| + |realEigenvalues| |leadingBasisTerm| |copy| |directProduct| |updatF| + |genericLeftTrace| |complexIntegrate| |pr2dmp| |complexExpand| + |explogs2trigs| |translate| |bubbleSort!| |enterPointData| + |semiResultantEuclideannaif| |leftRemainder| |s17dlf| + |integralLastSubResultant| |drawToScale| |symmetricSquare| |depth| + |besselI| |roman| |removeSinSq| |setColumn!| |reduction| |exprex| + |e01bef| |brace| |superHeight| |nsqfree| |recoverAfterFail| + |expressIdealMember| |subPolSet?| |packageCall| + |indicialEquationAtInfinity| |destruct| |inR?| |lazyPseudoDivide| + |graphStates| |algDsolve| |extendedSubResultantGcd| |pdf2df| + |prinpolINFO| |saturate| |printCode| |factorsOfCyclicGroupSize| + |infinityNorm| |monicDivide| |match?| |fortranCarriageReturn| + |normalized?| |splitConstant| |trigs2explogs| |purelyAlgebraic?| + |autoCoerce| |write!| |rootKerSimp| |tanNa| |oblateSpheroidal| + |principalAncestors| |divideIfCan!| |pile| |arguments| |OMputError| + |rquo| |sturmVariationsOf| |degreeSubResultant| |firstSubsetGray| + |makeMulti| |rename!| |compBound| |userOrdered?| + |selectNonFiniteRoutines| |internalIntegrate0| |expand| |f04maf| + |monomial| |findBinding| |ignore?| |nextsubResultant2| |airyAi| + |startPolynomial| |atom?| |e04fdf| |filterWhile| |maxdeg| |distribute| + |f02adf| |multivariate| |sequence| |close| |categoryMode| |tanhIfCan| + |cos2sec| |s21baf| F |s18dcf| |subMatrix| |filterUntil| + |binarySearchTree| |s15aef| |variables| |isobaric?| |printStatement| + |reverseLex| |ef2edf| |select| |expextendedint| |components| |display| + |evaluateInverse| |euclideanSize| |nextsousResultant2| + |realElementary| |head| |reducedQPowers| |newLine| |identification| + |space| |flagFactor| |numFunEvals| |minimalPolynomial| + |roughEqualIdeals?| |pade| |linkToFortran| |nthExpon| |elaboration| + |sumSquares| |youngGroup| |rootPoly| |subResultantChain| + |linearAssociatedExp| |halfExtendedSubResultantGcd1| |predicate| + |paraboloidal| |removeSinhSq| |leftDiscriminant| |critMTonD1| + |closed?| |sin?| |OMgetEndObject| |debug| |taylor| |reduceLODE| + |ListOfTerms| |overset?| |OMcloseConn| |OMgetAtp| |cn| |invmultisect| + |fortranLogical| |critT| D |laurent| |findConstructor| |input| |iilog| + |fractRagits| |argumentList!| |externalList| |linearMatrix| + |rightPower| |subHeight| |puiseux| |fillPascalTriangle| |library| + |removeDuplicates| |nor| |vark| EQ |fortranDoubleComplex| + |solveLinearPolynomialEquationByRecursion| |getExplanations| |ideal| + |setDifference| |f04qaf| |polyRicDE| |drawComplexVectorField| |latex| + |polygon?| |euclideanNormalForm| |deriv| |inv| |setVariableOrder| + |mindeg| |closedCurve?| |maxrow| |genericLeftNorm| |countRealRoots| + |zeroSquareMatrix| |getOperator| UTS2UP |ground?| |measure2Result| + |exp1| |partialDenominators| |rightRankPolynomial| + |nextIrreduciblePoly| |checkRur| |subResultantsChain| |hue| + |listYoungTableaus| |ground| |set| |regularRepresentation| |rk4qc| + |randomR| |rightMult| |constDsolve| |setRealSteps| |f01qdf| |leftLcm| + |getVariableOrder| |leadingMonomial| |integer?| |iiacos| |readable?| + |explicitEntries?| |rightExtendedGcd| |subSet| |completeEchelonBasis| + |setlast!| |fracPart| |leadingCoefficient| |parameters| + |rationalPower| |gradient| |gramschmidt| + |semiDegreeSubResultantEuclidean| |sinIfCan| |size| |OMreadFile| + |nonLinearPart| |extendIfCan| |makeUnit| |primitiveMonomials| + |optpair| |basisOfLeftAnnihilator| |exprToGenUPS| |s17def| |rootOf| + |digit?| |Nul| |complement| |simplifyExp| |print| |reductum| |f02aff| + |pole?| |wordsForStrongGenerators| |substring?| |mainKernel| |quartic| + |genericRightMinimalPolynomial| |interReduce| |select!| |groebgen| + |resolve| |OMUnknownSymbol?| |extension| |balancedFactorisation| + |imagJ| |factorSquareFreeByRecursion| |taylorRep| |subTriSet?| + |permutationRepresentation| |polynomialZeros| |extensionDegree| + |triangular?| |rootDirectory| |testDim| |curry| |suffix?| + |complexForm| |true| |setPosition| |polyPart| |category| |quasiMonic?| + |fixPredicate| |badValues| |rewriteSetWithReduction| |makeVariable| + |iFTable| |capacity| |makeprod| |domain| |completeHensel| + |numberOfDivisors| |badNum| |principal?| |optional| |leftTraceMatrix| + |s21bbf| |axesColorDefault| |KrullNumber| |rst| |lagrange| + |eigenMatrix| |prefix?| |shrinkable| |dual| |package| |minset| + |remove!| |prime| |scripted?| |showRegion| |insert| |polarCoordinates| + |fi2df| |newReduc| |f02wef| |currentSubProgram| |f02awf| + |bezoutDiscriminant| |groebSolve| |merge| |sizePascalTriangle| |show| + |isAbsolutelyIrreducible?| |setLabelValue| |conjug| |algint| |delay| + |replaceKthElement| |nthFractionalTerm| |yCoordinates| |cAsinh| |ord| + |search| |permutation| |cSech| |polyred| |lepol| |roughUnitIdeal?| + |exists?| |node| |cot2trig| |divisorCascade| |subNodeOf?| + |getConstant| |trace| |lprop| |doublyTransitive?| |outputGeneral| + |duplicates?| |mpsode| |realZeros| |shape| |leftNorm| + |compiledFunction| |conditionsForIdempotents| |lex| |rootSplit| + |continuedFraction| |bringDown| |linGenPos| |rootPower| |solveInField| + |squareTop| |c06fpf| |subNode?| |quickSort| |infix?| + |changeThreshhold| |showAll?| |mvar| |replace| |normDeriv2| + |cyclicGroup| |rewriteIdealWithRemainder| |move| |s01eaf| |readUInt8!| + |mask| |palgintegrate| |OMUnknownCD?| |maxPoints3D| |child?| + |OMsetEncoding| |gcdprim| |schwerpunkt| |linearPart| |eq?| |flatten| + |choosemon| |doubleDisc| |trunc| |biRank| |ksec| |frobenius| + |systemSizeIF| |extractBottom!| |plotPolar| |callForm?| |infRittWu?| + |critM| |critB| |copies| |reduceBasisAtInfinity| |discriminant| + |sncndn| |specialTrigs| |conjugate| |doubleResultant| |isQuotient| + |lazyPquo| |radicalRoots| |lighting| |rarrow| |diagonal| |car| + |double?| |s14aaf| |lazyPremWithDefault| |credPol| |constantKernel| + |minPol| |quatern| |s18aff| |mainVariable| |cosSinInfo| |safeCeiling| + |mergeFactors| |makeViewport3D| |arity| |acscIfCan| |myDegree| + |viewDeltaYDefault| |mergeDifference| |showClipRegion| |surface| + |categoryFrame| |inf| |f02abf| |fill!| |limitedIntegrate| + |rightAlternative?| |quadraticForm| |wordInGenerators| |noKaratsuba| + |directory| |exactQuotient| |stFuncN| |explimitedint| |resultantnaif| + |lazy?| |rootRadius| |lllp| |zeroDimensional?| |dimension| |notelem| + |radicalEigenvector| |universe| |elRow1!| |debug3D| |d01amf| |high| + |height| |units| |nextPrimitivePoly| |log10| |addPoint| + |genericRightNorm| |selectMultiDimensionalRoutines| |LyndonWordsList| + |rk4| |seed| |equation| |composites| |e02aef| |e04mbf| + |unprotectedRemoveRedundantFactors| |primlimitedint| |bitand| |e02daf| + |primitiveElement| |prinb| |generic| |minimize| |color| |chebyshevT| + |upperBound| |OMputEndError| |leaves| |palgLODE| |outerProduct| + |resultantReduit| |bitior| |rationalIfCan| |topPredicate| |routines| + |linear| |basisOfMiddleNucleus| |isPlus| |bottom!| |cross| + |att2Result| |middle| |perfectSqrt| |prevPrime| |repeatUntilLoop| + |mapMatrixIfCan| |twist| |initTable!| |generalizedEigenvectors| + |maxPoints| |macroExpand| |moduleSum| |constantOperator| |iiacoth| + |leftMult| |internalAugment| |OMencodingSGML| |polynomial| + |removeRoughlyRedundantFactorsInPols| |cartesian| |sup| |viewpoint| + |torsionIfCan| |comment| |radPoly| |modularFactor| |f02bjf| |option?| + |collectUnder| |setrest!| |center| |SturmHabichtCoefficients| + |internal?| |before?| |groebner?| |pushucoef| |measure| + |irreducibleFactor| |subspace| |cSec| |cAsec| |singularAtInfinity?| + |truncate| |lowerCase| |minGbasis| |e02bef| |relativeApprox| |mesh| + |rule| |nonQsign| |superscript| |declare| |rk4a| + |generalizedContinuumHypothesisAssumed| |complementaryBasis| |ldf2vmf| + |kroneckerDelta| |isAnd| |rightQuotient| |members| |common| + |lexTriangular| |subtractIfCan| |e01sbf| |s13acf| |OMgetVariable| + |f01rcf| |internalIntegrate| |viewport3D| |length| |karatsubaDivide| + |Ci| |lyndonIfCan| |multiset| |laguerreL| |ptFunc| + |createRandomElement| |tan2trig| |nary?| |groebner| |nullary| + |scripts| |leadingTerm| |OMputEndBVar| |leadingExponent| |ratpart| + |semiIndiceSubResultantEuclidean| |ricDsolve| |Hausdorff| |getOrder| + |elem?| |reflect| |pointColorDefault| |ffactor| + |unrankImproperPartitions1| |lazyVariations| |parabolic| |jacobian| + |exponential| |c05pbf| |matrix| |lfunc| |generalLambert| |unparse| + |fixedPoint| |bivariateSLPEBR| |listBranches| |prepareSubResAlgo| + |addmod| |selectPolynomials| |algebraic?| |expPot| + |createMultiplicationTable| |collectUpper| |extractIndex| + |patternVariable| |setvalue!| |trueEqual| |plus!| |hcrf| |fullDisplay| + |antiCommutator| |localUnquote| |f2df| |complexRoots| |oddlambert| + |var1StepsDefault| |iicos| Y |removeDuplicates!| |e02dff| |midpoint| + |setClosed| |harmonic| |normalizedAssociate| |complexEigenvalues| + |csc2sin| |label| |cycle| |semiResultantEuclidean1| |qPot| + |critpOrder| |exponent| |permutations| |checkForZero| |simpsono| + |goodnessOfFit| |bat1| |rewriteIdealWithHeadRemainder| |lieAlgebra?| + |close!| |taylorQuoByVar| |factorAndSplit| |coord| |c06fqf| + |genericPosition| |symbolIfCan| |doubleFloatFormat| |leftAlternative?| + |clipWithRanges| |f04atf| |mainContent| |tubeRadius| + |lazyResidueClass| |result| |rightCharacteristicPolynomial| + |getDatabase| |whitePoint| |wholeRadix| |logical?| |coerceS| |opeval| + |addMatch| |complete| |getMultiplicationTable| |relerror| |mulmod| + |iipow| |functionIsOscillatory| |setEmpty!| |d01apf| |d02bbf| + |rowEchelon| |numeric| |hdmpToP| |iidprod| |insertMatch| |graeffe| + |powern| |nthFlag| |tubePlot| |s13adf| |rCoord| |radical| |overlabel| + |asechIfCan| |traverse| |radicalOfLeftTraceForm| |vertConcat| + |constructor| |gethi| |showFortranOutputStack| |OMsend| + |gcdcofactprim| |contours| |phiCoord| |algebraicVariables| |coerceL| + |writeUInt8!| |normal01| |bindings| |option| |minimumDegree| + |endSubProgram| |fprindINFO| |symbolTable| |collectQuasiMonic| + |showSummary| |f04asf| |makeYoungTableau| |thenBranch| |OMReadError?| + |equiv| |reify| |endOfFile?| |totolex| |environment| |unravel| + |OMencodingBinary| |setMinPoints| |f04faf| |insert!| |algSplitSimple| + |idealiserMatrix| |tValues| |pushFortranOutputStack| |host| + |getIdentifier| |flexibleArray| |showAttributes| |OMputVariable| + |dioSolve| |torsion?| |makeRecord| |c06ecf| |transcendenceDegree| + |airyBi| |popFortranOutputStack| |makeResult| |LazardQuotient| + |bandedHessian| |adaptive?| |quadratic?| |curryLeft| |f02xef| + |stoseInvertibleSetsqfreg| |outputAsFortran| |computeBasis| |sub| + |meatAxe| |elliptic?| |f02bbf| |name| |parents| + |wordInStrongGenerators| |orthonormalBasis| |brillhartTrials| + |henselFact| |laguerre| |pointData| |rightTrim| |printInfo!| + |LowTriBddDenomInv| |graphs| |body| |definingInequation| |intensity| + |mainMonomial| |identity| |mapCoef| |moebiusMu| + |resetAttributeButtons| |leftTrim| |fTable| |listOfLists| |null| + |factorSquareFree| |legendreP| |compactFraction| |sturmSequence| + |cAcoth| |stack| |outputBinaryFile| |localIntegralBasis| + |OMencodingXML| |pureLex| |f02aaf| |not| + |stiffnessAndStabilityOfODEIF| |collect| |mainVariables| |iisqrt3| BY + |prinshINFO| |palgLODE0| |algintegrate| |setref| |functorData| |and| + |basis| |localReal?| |branchIfCan| |cCsch| |outputList| |exQuo| + |fixedPointExquo| |semiResultantEuclidean2| |degree| GF2FG |or| + |smith| |paren| |symmetricDifference| |OMopenFile| |atoms| + |functionIsContinuousAtEndPoints| |linearDependenceOverZ| + |alternative?| |xor| |semicolonSeparate| |cyclicEntries| |sinh2csch| + |f01ref| |addBadValue| |nand| |ocf2ocdf| |nodeOf?| |e02agf| + |signature| |dim| |leviCivitaSymbol| |case| |any?| |iteratedInitials| + |pointPlot| |assert| |selectfirst| |nextLatticePermutation| |edf2ef| + |port| |subscript| |binomThmExpt| |possiblyNewVariety?| |pattern| + |squareFreeLexTriangular| |Zero| |inspect| |createNormalPoly| + |triangulate| |makeFR| |cCoth| |f01bsf| |whatInfinity| |gcdcofact| + |llprop| |One| |innerint| |edf2df| |nextItem| |knownInfBasis| + |swapRows!| |genericRightTrace| |norm| |t| |viewport2D| |optional?| + |rdHack1| |shift| |infLex?| NOT |outputMeasure| |eulerPhi| |cAcosh| + |polCase| |output| |removeRedundantFactorsInContents| |redPo| + |getMultiplicationMatrix| |writeLine!| |f02agf| |mathieu22| + |perfectSquare?| |leader| OR |createZechTable| |vector| |curryRight| + |imagE| |cCos| |meshFun2Var| |OMgetAttr| |besselK| |even?| |rational?| + |message| |nextPartition| AND |cRationalPower| |differentiate| + |setTopPredicate| |getOperands| |d02gbf| |makeViewport2D| |conical| + |sec2cos| |putGraph| |realSolve| |elRow2!| + |generalizedContinuumHypothesisAssumed?| |initiallyReduced?| + |chainSubResultants| |midpoints| |f01brf| |fortran| |atanh| |weight| + |totalLex| |putColorInfo| |makeEq| |initials| |elt| |idealiser| + |unitNormal| |sqfree| |minus!| |mapmult| |acoth| |PollardSmallFactor| + |queue| |f04mbf| |OMserve| |nthFactor| |is?| |symmetricProduct| + |leftOne| |alternatingGroup| |Aleph| |FormatArabic| |asech| |level| + |iiacsch| |getCurve| |graphImage| |splitNodeOf!| |direction| + |weierstrass| |lastSubResultantEuclidean| |increase| |twoFactor| + |adjoint| |mindegTerm| |colorFunction| |drawCurves| |presuper| + |setScreenResolution3D| |LyndonWordsList1| |wrregime| |elseBranch| + |rightTrace| |areEquivalent?| |rightExactQuotient| |minPoints| + |multiple| |cons| |copyInto!| |c06ekf| |f2st| |bumprow| |s19aaf| + |removeRedundantFactorsInPols| |monomials| |imagj| |chiSquare| + |recolor| |OMputAtp| |applyQuote| |cond| |position!| + |removeSquaresIfCan| |mathieu23| |zoom| |characteristicPolynomial| + |radicalSimplify| |retract| |integralDerivationMatrix| |elliptic| + |rationalFunction| |trapezoidal| |chiSquare1| |hessian| |subset?| + |ldf2lst| |representationType| |monomRDEsys| |showTheRoutinesTable| + |approxNthRoot| |OMputApp| |showArrayValues| |getProperty| |sh| + |cTanh| |f02akf| |OMgetApp| |list?| |s17dhf| |primes| |second| |less?| + * |member?| |applyRules| |aLinear| |exprToXXP| |conditionP| |ruleset| + |domainTemplate| |bits| |monomialIntPoly| |iExquo| |getRef| + |numberOfComputedEntries| |diophantineSystem| |third| + |stronglyReduced?| |dfRange| |firstNumer| |basisOfRightNucleus| + |bumptab1| |solveLinear| |moreAlgebraic?| |numberOfIrreduciblePoly| + |ip4Address| |hexDigit?| |cAtanh| + |rewriteIdealWithQuasiMonicGenerators| |nextNormalPrimitivePoly| + |deleteRoutine!| |minPoly| |makeCos| |source| |void| |showAllElements| + |expandPower| |generalPosition| |f01maf| |distFact| |elements| + |extendedIntegrate| = |limit| |removeZeroes| |mapUnivariate| |euler| + |suchThat| |primintfldpoly| |primitivePart!| |acosIfCan| |lazyPrem| + |nthr| |coth2tanh| |coerceP| |coefficients| |s19abf| |diagonals| + |empty?| |script| |dmp2rfi| |setTex!| |push!| |extractSplittingLeaf| + |acoshIfCan| |pair?| |df2mf| < |hMonic| |upperCase| + |combineFeatureCompatibility| |pushdown| |plusInfinity| |whileLoop| + |s19adf| |eisensteinIrreducible?| |d01aqf| |noLinearFactor?| |mesh?| + |char| > |red| |rotatex| |lazyGintegrate| |getButtonValue| |Ei| + |systemCommand| |minusInfinity| |f02ajf| |selectODEIVPRoutines| + |initializeGroupForWordProblem| |atanIfCan| |sinhcosh| |deepCopy| + |clipBoolean| |duplicates| <= |cAcsch| |d02ejf| |OMgetBVar| |tex| + |target| |elementary| |enterInCache| |iCompose| |getPickedPoints| + |imagi| |lexico| >= |ode| |zeroOf| |bytes| |setImagSteps| + |setEpilogue!| |basisOfRightAnnihilator| |linearAssociatedOrder| + |conjunction| |OMputString| |coerceImages| |normalise| |unexpand| + |expr| |stirling1| |ramified?| RF2UTS |clearTable!| |taylorIfCan| + |setClipValue| |tanQ| |stopMusserTrials| |pow| |linearPolynomials| + |normal| |rangePascalTriangle| |setPredicates| |OMputObject| |s21bcf| + |laurentRep| |mkPrim| |isList| |OMlistCDs| |product| |OMgetSymbol| + |rational| |functionIsFracPolynomial?| |OMgetEndBVar| |finiteBound| + + |isPower| |compose| |pack!| |leftFactor| |type| |binaryTournament| + |ScanRoman| |maxColIndex| |polygamma| |sort!| |OMgetEndAttr| |edf2fi| + |point| - |float| |trim| |shiftLeft| |setIntersection| |s21bdf| + |mapUp!| |firstDenom| |differentialVariables| |d01gbf| |vspace| + |variable| |firstUncouplingMatrix| / |rightDiscriminant| |cExp| + |children| |simplifyLog| |dualSignature| |generalSqFr| + |factorSFBRlcUnit| |terms| |round| |iterators| + |branchPointAtInfinity?| |rightRegularRepresentation| + |indiceSubResultantEuclidean| |leftRegularRepresentation| |asimpson| + |variable?| |OMsupportsCD?| |supRittWu?| |rationalPoints| + |triangularSystems| |partialQuotients| |indiceSubResultant| |series| + |e04gcf| |mdeg| |pushdterm| |changeBase| |bitLength| |subResultantGcd| + |ipow| |denomLODE| |slex| |cyclic| |index?| |qqq| |reverse!| + |toseLastSubResultant| |hypergeometric0F1| |OMgetEndError| |cSinh| + |tab1| |pmintegrate| |id| |setRow!| |dictionary| |simplifyPower| + |rroot| |value| |subresultantVector| |cCosh| |multiple?| |Frobenius| + |symbol| |wholePart| |OMencodingUnknown| |lo| |denominators| |iiacosh| + |mainCoefficients| |associatedEquations| |leadingIdeal| |top!| + |zerosOf| |scan| |expression| |numberOfCycles| |singular?| |min| + |modulus| |uncouplingMatrices| |musserTrials| |setUnion| |symFunc| + |binding| |nthCoef| |integer| |nextSublist| |isEquiv| |zero?| + |quoByVar| |negative?| GE |factorials| |monicLeftDivide| + |rationalApproximation| |removeZero| |rightDivide| |minColIndex| + |factorFraction| |child| |shufflein| |solveRetract| |reopen!| GT + |basisOfLeftNucleus| |selectSumOfSquaresRoutines| |primeFrobenius| + |characteristic| |insertBottom!| |stFunc1| |multinomial| |pointColor| + |stopTableInvSet!| |OMwrite| LE |e02gaf| |karatsuba| |iicsch| + |symmetricPower| |leftZero| |graphState| |listOfMonoms| |nlde| + |setPrologue!| |OMgetError| LT |leadingSupport| |substitute| + |jacobiIdentity?| |OMputEndObject| |outputSpacing| |bounds| + |nextPrimitiveNormalPoly| |infieldint| |df2st| |associatedSystem| + |gderiv| |computePowers| |setOfMinN| |internalZeroSetSplit| |mirror| + |pascalTriangle| |mappingAst| |d02bhf| |selectIntegrationRoutines| + |sdf2lst| |iifact| |nthExponent| |redpps| |headRemainder| |zeroDim?| + |Beta| |leastPower| |keys| |OMputFloat| |monicRightDivide| |split!| + |critBonD| |karatsubaOnce| |balancedBinaryTree| |entries| + |padicallyExpand| |totalGroebner| |iicsc| |acotIfCan| |cLog| |isOp| + |ParCond| |complexLimit| |diagonalProduct| |makeSketch| |diagonal?| + |scopes| |solveLinearPolynomialEquation| |janko2| |monicModulo| + |index| |htrigs| |OMputEndAttr| |symmetric?| |subQuasiComponent?| + |divergence| |light| |eigenvalues| |primextendedint| |mat| + |antiCommutative?| |basisOfLeftNucloid| |headReduce| + |halfExtendedSubResultantGcd2| |cycleEntry| |constantOpIfCan| + |fortranLinkerArgs| |sumOfKthPowerDivisors| |prepareDecompose| + |rowEch| |rischDE| |reorder| |reducedForm| |clearFortranOutputStack| + |s20acf| |inrootof| |fortranInteger| |quote| |factorset| |every?| + |pair| |rangeIsFinite| |tree| |open| |computeInt| |chineseRemainder| + |key?| |LyndonCoordinates| |bright| |cycleTail| |clipSurface| |e01sff| + |dequeue!| |vconcat| |backOldPos| |increasePrecision| |e02akf| + |normalize| |lazyPseudoQuotient| |readInt32!| |outputArgs| + |tracePowMod| |iiacsc| |sts2stst| |interactiveEnv| |extendedEuclidean| + |gcdPrimitive| |mapBivariate| |minIndex| |eval| |unvectorise| + |lowerCase!| |commaSeparate| |tensorProduct| |moduloP| + |separateDegrees| |innerSolve| |blankSeparate| |normalDeriv| + |reducedDiscriminant| |heapSort| |chebyshevU| |digits| |basisOfCenter| + |OMgetString| |operations| |lastSubResultantElseSplit| |ratPoly| + |numericalOptimization| |modTree| |OMgetEndAtp| |SturmHabichtMultiple| + |showTheSymbolTable| |discriminantEuclidean| |numFunEvals3D| + |qinterval| |moebius| |setErrorBound| |iomode| |interpret| |error| + |element?| |cTan| |varselect| |fmecg| |algebraicSort| + |complexElementary| |rightUnits| |countRealRootsMultiple| |denomRicDE| + |OMgetEndBind| |ParCondList| |patternMatch| |sinhIfCan| + |gcdPolynomial| |numerator| |polygon| |sizeLess?| |sylvesterSequence| + |optimize| |intcompBasis| |leftRecip| |adaptive| |hspace| |precision| + |setPoly| |function| |factorByRecursion| |isNot| |completeSmith| + |plenaryPower| |nthRootIfCan| |createIrreduciblePoly| |FormatRoman| + |tan2cot| |limitPlus| |expIfCan| |shiftRight| |optAttributes| + |constantRight| |s17aff| |support| |selectFiniteRoutines| + |decomposeFunc| |npcoef| |integralBasis| |parseString| |width| + |elaborateFile| |df2ef| |principalIdeal| |basisOfCommutingElements| + |palginfieldint| |showTheFTable| |univariate?| |rules| |double| + |littleEndian| |createPrimitiveElement| |lfinfieldint| |generic?| + |front| |inverse| |odd?| |qualifier| |nextPrime| |coshIfCan| |uniform| + |normal?| |rightUnit| |indicialEquation| |integerBound| |genus| + |fglmIfCan| |e01bhf| |call| |integralMatrix| |charthRoot| |zeroMatrix| + |signAround| |internalLastSubResultant| |coerceListOfPairs| + |minPoints3D| |irVar| |horizConcat| |subresultantSequence| |argscript| + |isImplies| |reciprocalPolynomial| |numberOfFractionalTerms| + |ratDenom| |sample| |checkPrecision| |mr| |bothWays| |cyclotomic| + |readByte!| |bitCoef| |realRoots| |toseSquareFreePart| |baseRDE| + |upDateBranches| |exportedOperators| |Is| |range| |laurentIfCan| + |iicot| |headReduced?| |mainMonomials| |lastSubResultant| + |skewSFunction| |extractIfCan| |prod| |coleman| |subst| |rem| + |numericIfCan| |setAdaptive3D| |bipolarCylindrical| |OMlistSymbols| + |doubleComplex?| |find| |shallowCopy| |tube| |po| |roughSubIdeal?| + |tryFunctionalDecomposition| |quo| |removeConstantTerm| |bernoulliB| + |internalSubPolSet?| |squareFreePart| |declare!| |varList| |axes| + |useEisensteinCriterion?| |stoseSquareFreePart| |cycleRagits| + |coHeight| |digamma| |open?| |unary?| |split| |equality| |lcm| + |leastMonomial| |s20adf| |closedCurve| |has?| |seriesToOutputForm| + |getProperties| |div| |delete| |elColumn2!| |makeTerm| |frst| |cAsin| + |iisin| |number?| |tRange| |invmod| UP2UTS |exquo| |e02bcf| + |stoseIntegralLastSubResultant| |iibinom| |bit?| |lyndon| |any| + |append| |status| |solveLinearPolynomialEquationByFractions| + |viewThetaDefault| |removeRoughlyRedundantFactorsInContents| + |viewPhiDefault| ~= |bfEntry| |leftGcd| |cAcot| |dmpToHdmp| + |factorOfDegree| |iiasin| |powmod| |intChoose| |gcd| |divideIfCan| + |useSingleFactorBound?| |symbol?| |objects| |#| |setprevious!| + |integers| |Si| |setMinPoints3D| |algebraicOf| |processTemplate| + |convergents| |showIntensityFunctions| |false| |eyeDistance| + |sumOfSquares| |jordanAdmissible?| |base| ~ |alternating| |compound?| + |halfExtendedResultant1| |create3Space| |univariateSolve| + |groebnerIdeal| |vedf2vef| |rootOfIrreduciblePoly| + |resetVariableOrder| |dominantTerm| |ravel| |octon| |newTypeLists| + |leftUnits| |getGoodPrime| |UpTriBddDenomInv| |segment| + |rootNormalize| |rightTraceMatrix| |divide| |basisOfNucleus| + |monomial?| |init| |f04axf| |supersub| |rotate!| |unmakeSUP| |reshape| + |rombergo| |maximumExponent| |findCycle| |addiag| |distdfact| + |maxRowIndex| |/\\| |useSingleFactorBound| |ScanArabic| |iicosh| + |monic?| |determinant| |OMgetBind| |fortranComplex| |stFunc2| + |realEigenvectors| |plot| |\\/| |s15adf| |generalInfiniteProduct| + |pointLists| |normalDenom| |clearTheFTable| |apply| |coerce| + |mapUnivariateIfCan| |PDESolve| |logIfCan| |absolutelyIrreducible?| + |quasiMonicPolynomials| |s17agf| |extractPoint| |setFieldInfo| + |getGraph| |empty| |first| |construct| |permutationGroup| + |commutative?| |tanAn| |pastel| |setStatus!| + |univariatePolynomialsGcds| |var2StepsDefault| |pushuconst| |redmat| + |contract| |rest| |perfectNthRoot| |build| |nullSpace| |reindex| + |makeSeries| |summation| |reducedContinuedFraction| |socf2socdf| + |plus| |cschIfCan| |parametric?| |update| |OMopenString| |palgRDE0| + |c05nbf| |comparison| |OMputSymbol| |rootSimp| |scalarTypeOf| + |OMgetObject| |csch2sinh| |asinIfCan| |cAcos| |s17dcf| |listLoops| + |exponentialOrder| |quadraticNorm| |matrixGcd| |argumentListOf| + |block| |shade| |spherical| |infix| |cAtan| |mathieu12| |HenselLift| + |setOrder| |changeVar| |concat!| |factorList| |monicCompleteDecompose| + |writable?| |times| |complexNumericIfCan| |integralBasisAtInfinity| + |quotedOperators| |expenseOfEvaluationIF| |initiallyReduce| |previous| + |delta| |permanent| |stoseInvertible?reg| |sayLength| + |squareFreePolynomial| |morphism| |typeForm| |unitNormalize| |overlap| + |intersect| |fractRadix| |autoReduced?| |repeating?| |fortranTypeOf| + |implies| |composite| |ramifiedAtInfinity?| |position| |makeSin| + |computeCycleEntry| |predicates| |bezoutMatrix| |internalInfRittWu?| + |fortranReal| |tubeRadiusDefault| |shallowExpand| |zeroSetSplit| + |indices| |datalist| |lift| |const| |recip| |reducedSystem| + |ScanFloatIgnoreSpacesIfCan| |leftReducedSystem| |addMatchRestricted| + |randomLC| |binomial| |box| |e01bgf| |degreeSubResultantEuclidean| + |LazardQuotient2| |monom| |reduce| |s18aef| |printStats!| |palgint| + |clearDenominator| F2FG |quasiAlgebraicSet| |redPol| |exactQuotient!| + |solve1| |c06eaf| |voidMode| |loadNativeModule| |cylindrical| + |linearlyDependentOverZ?| |rischDEsys| |geometric| |changeNameToObjf| + |d01anf| |d01bbf| |acschIfCan| |internalSubQuasiComponent?| |iiperm| + |primPartElseUnitCanonical| |cyclotomicFactorization| |OMgetInteger| + |extractProperty| |hconcat| |ode2| |e02ddf| |acothIfCan| + |isConnected?| |hex| |semiDiscriminantEuclidean| + |brillhartIrreducible?| |linearAssociatedLog| |OMread| + |leftExtendedGcd| |rightLcm| |subCase?| |factorsOfDegree| |order| + |lambda| |matrixConcat3D| |padicFraction| |iidsum| |maxint| |padecf| + |rank| |insertTop!| |clipParametric| |createLowComplexityNormalBasis| + |readInt16!| |semiSubResultantGcdEuclidean2| |boundOfCauchy| + |roughBase?| |f07fef| |OMconnInDevice| |e01bff| |log| + |algebraicDecompose| |inverseIntegralMatrix| |cothIfCan| |s17adf| + |abelianGroup| |setProperty| |screenResolution3D| |setsubMatrix!| + |linear?| |logpart| |setelt| |integral?| |setFormula!| |meshPar1Var| + |inGroundField?| |squareFree| |c06gcf| |zag| |nonSingularModel| + |vectorise| |mainValue| |tanh2coth| |iiexp| |node?| |getMatch| + |SFunction| |s17ajf| |createPrimitivePoly| + |removeIrreducibleRedundantFactors| |tubePoints| |imagI| + |binaryFunction| |kovacic| |removeRoughlyRedundantFactorsInPol| + |setValue!| |rectangularMatrix| |magnitude| |HermiteIntegrate| + |OMgetType| |kmax| |dihedralGroup| |readLine!| |fixedPoints| |augment| + |resetNew| |overbar| |radicalSolve| |iprint| |yCoord| |rootProduct| + |printHeader| |eigenvectors| |hasSolution?| |stronglyReduce| + |numberOfMonomials| |f01mcf| |approximants| |sizeMultiplication| + |upperCase?| |pmComplexintegrate| |exteriorDifferential| |cyclic?| + |lexGroebner| |byte| |lists| |powerAssociative?| + |multiplyCoefficients| |setButtonValue| |OMputAttr| |leftQuotient| + |strongGenerators| |gensym| |interpretString| + |irreducibleRepresentation| |perspective| |part?| |innerEigenvectors| + |useNagFunctions| |componentUpperBound| |infiniteProduct| |coth2trigh| + |erf| |flexible?| |genericLeftTraceForm| |setchildren!| |getStream| + |zero| |cycleElt| |prime?| |iiasech| |reverse| + |getSyntaxFormsFromFile| |evenlambert| |bezoutResultant| + |expandTrigProducts| |create| |aQuadratic| |rightRemainder| + |mightHaveRoots| |power!| |isTimes| |weakBiRank| |retractable?| + |toScale| |besselY| |li| |certainlySubVariety?| |dequeue| |d01akf| + |powers| |e01baf| |And| |powerSum| |integralRepresents| |character?| + |OMgetEndApp| |unknown| |clearTheIFTable| |dilog| |sparsityIF| + |validExponential| |eof?| |hitherPlane| |Or| |isAtom| |component| + |baseRDEsys| |contains?| |pushup| |var1Steps| |xn| |sin| |central?| + |mapExponents| |pseudoRemainder| |setMaxPoints3D| |Not| |schema| + |primlimintfrac| |screenResolution| |stosePrepareSubResAlgo| + |expenseOfEvaluation| |rename| |cos| |lfextlimint| |writeBytes!| + |remainder| |atanhIfCan| |startTableInvSet!| |int| |uniform01| |pol| + |removeSuperfluousCases| |complexSolve| |setelt!| |tan| + |totalDifferential| |Gamma| |f07fdf| |pleskenSplit| |leftRank| |sign| + |splitSquarefree| |numberOfComposites| |cot| |deepestInitial| + |compdegd| |c06ebf| |cCot| |ddFact| |eigenvector| |d01ajf| |read!| + |completeHermite| |sec| |region| |topFortranOutputStack| + |numberOfImproperPartitions| |leftDivide| |wholeRagits| |mapGen| + |f04jgf| |romberg| |hasoln| |csc| |quadratic| |createNormalElement| + |aromberg| |cPower| |generateIrredPoly| |univariatePolynomials| + |prologue| |asin| |removeCosSq| |test| |lowerPolynomial| |evaluate| + |shanksDiscLogAlgorithm| |root| |module| |remove| |operation| + |fortranCompilerName| |positiveRemainder| |constantIfCan| |acos| + |tablePow| |constantCoefficientRicDE| |viewPosDefault| |readBytes!| + |invertibleSet| |OMputEndAtp| |calcRanges| |pseudoDivide| + |unitsColorDefault| |atan| |oneDimensionalArray| |sn| |fortranLiteral| + |ScanFloatIgnoreSpaces| |parts| |currentScope| |f07adf| |last| + |createGenericMatrix| |standardBasisOfCyclicSubmodule| |arbitrary| + |bag| |acot| |anfactor| |normalElement| |assoc| |monomRDE| |decrease| + |separant| |pointColorPalette| |tanintegrate| |asec| |headAst| + |minimumExponent| |mainPrimitivePart| |condition| |tower| + |lineColorDefault| |ridHack1| |OMconnOutDevice| |isOpen?| |derivative| + |getlo| |acsc| |leftUnit| |ranges| |sincos| |pToHdmp| |byteBuffer| + |style| |mainVariable?| |prefix| |integral| |cdr| |sinh| + |genericRightTraceForm| |stoseLastSubResultant| |makingStats?| + |d01fcf| |trace2PowMod| |numerators| |e02adf| |cosh| |appendPoint| + |selectAndPolynomials| |root?| |minRowIndex| |d02kef| |d01asf| + |makeop| |elaborate| |reduceByQuasiMonic| |obj| |tanh| |minrank| |eq| + |primPartElseUnitCanonical!| |youngDiagram| |signatureAst| + |lSpaceBasis| |lflimitedint| |mainSquareFreePart| |antiAssociative?| + |repSq| |cache| |coth| |iicoth| |iter| |s18acf| |presub| + |sylvesterMatrix| |complexNumeric| |rightRank| |viewDeltaXDefault| + |expintegrate| |squareFreeFactors| |pToDmp| |isOr| |sech| |leftPower| + |nullary?| |polar| |recur| |relationsIdeal| |patternMatchTimes| + |disjunction| |allRootsOf| |factor1| |quasiRegular?| |csch| |interval| + |fractionFreeGauss!| |nativeModuleExtension| |purelyTranscendental?| + |primeFactor| |insertionSort!| |lllip| |unaryFunction| |f01rdf| + |asinh| |inverseLaplace| |consnewpol| |e01daf| |OMputEndApp| + |SturmHabichtSequence| |normalizeAtInfinity| |particularSolution| + |corrPoly| |difference| |expt| |pointSizeDefault| |acosh| + |scalarMatrix| |partition| |getMeasure| |simpleBounds?| |zeroVector| + |aspFilename| |c06fuf| |viewWriteAvailable| |safetyMargin| |refine| + |zeroSetSplitIntoTriangularSystems| |approxSqrt| |positiveSolve| + |coordinates| |OMreadStr| |enqueue!| |dot| |countable?| |LiePolyIfCan| + |droot| |exp| |imaginary| |exptMod| |symmetricTensors| |controlPanel| + |iflist2Result| |nextSubsetGray| |s17ahf| |removeRedundantFactors| + |e04naf| |e02bbf| |graphCurves| |nextColeman| |map| |rotatey| + |clipPointsDefault| |semiLastSubResultantEuclidean| + |numberOfOperations| |lazyIrreducibleFactors| |coefChoose| + |defineProperty| |pomopo!| |genericLeftMinimalPolynomial| + |constantLeft| |table| |generator| |cscIfCan| |iisec| |nthRoot| + |irForm| |limitedint| |nil| |computeCycleLength| |leftFactorIfCan| + |normalForm| |cyclicParents| |thetaCoord| |new| |yellow| + |structuralConstants| |abs| |expintfldpoly| |getBadValues| |heap| + |points| |compile| |derivationCoordinates| |satisfy?| |messagePrint| + |qfactor| |typeList| |inputBinaryFile| |antisymmetric?| + |lazyPseudoRemainder| |setAttributeButtonStep| |setleft!| |cCsc| + |integrate| |virtualDegree| |dimensions| |charClass| |hasHi| + |approximate| |rootsOf| |iiasec| |stop| |splitDenominator| + |viewSizeDefault| |convert| |rootBound| |setLength!| |s13aaf| + |numberOfHues| |makeCrit| |complex| |exponents| |intPatternMatch| + |resultantReduitEuclidean| |beauzamyBound| |cup| |outputFixed| + |identityMatrix| |leftTrace| |interpolate| + |stoseInternalLastSubResultant| |singleFactorBound| |linSolve| |crest| + |branchPoint?| |trailingCoefficient| |leftExactQuotient| + |partialNumerators| |unitCanonical| |failed| |invertIfCan| + |separateFactors| |orbits| |d03faf| |bombieriNorm| |f04adf| |column| + |exprHasLogarithmicWeights| |Vectorise| |UnVectorise| |wreath| |rk4f| + |e02ajf| |contractSolve| |numberOfPrimitivePoly| |evenInfiniteProduct| + |factors| |extendedint| |OMmakeConn| |viewDefaults| |transcendent?| + |leftMinimalPolynomial| |incr| |c06gsf| |hermite| |scale| + |basisOfCentroid| |df2fi| |factorial| |edf2efi| |palgRDE| |lintgcd| + |hi| |setProperties| |deepestTail| |sin2csc| |rspace| |inverseColeman| + |pseudoQuotient| |floor| |transcendentalDecompose| |iisqrt2| |left| + |OMclose| |bivariate?| |squareMatrix| |degreePartition| + |unrankImproperPartitions0| |setScreenResolution| |d03eef| + |currentCategoryFrame| |radicalEigenvectors| |right| |string?| + |figureUnits| |clearTheSymbolTable| |tanh2trigh| |multisect| + |trivialIdeal?| |ODESolve| |constant?| |green| |iisinh| |s17dgf| + |prem| |setnext!| |solve| |size?| |cap| |tanIfCan| |log2| + |extractTop!| |scanOneDimSubspaces| |neglist| |xCoord| |qelt| + |readLineIfCan!| |hostByteOrder| |RittWuCompare| |hostPlatform| + |commonDenominator| |qsetelt| |s14abf| |maxIndex| |generators| + |entry?| |laplace| |homogeneous?| |rotatez| |initial| |dn| + |GospersMethod| |iroot| |returnTypeOf| |atrapezoidal| |OMgetFloat| + |xRange| |lowerBound| |next| |factorPolynomial| |f02axf| + |OMputInteger| |writeByte!| |key| |chvar| |readIfCan!| |setCondition!| + |numberOfVariables| |yRange| |separate| |quasiRegular| |hyperelliptic| + |scaleRoots| |An| |c05adf| |d02cjf| |mainCharacterization| + |generalTwoFactor| |zRange| |low| |parabolicCylindrical| + |sumOfDivisors| |fixedDivisor| |divideExponents| |filename| |mkcomm| + |decompose| |isMult| |denominator| |map!| |lifting| |multMonom| + |totalDegree| |merge!| |shiftRoots| |qsetelt!| |pdf2ef| |resultant| + |cfirst| |c06frf| |diff| |leftScalarTimes!| |rightRecip| |poisson| + |rationalPoint?| |parse| |rdregime| |halfExtendedResultant2| |ref| + |unit| |cycleSplit!| |operators| |cyclicEqual?| |code| |parametersOf| + |check| |generate| |associative?| |arrayStack| |toseInvertible?| + |swap| |c02aff| |regime| |identitySquareMatrix| |polyRDE| + |usingTable?| |sPol| |alphabetic?| |antisymmetricTensors| + |prolateSpheroidal| |getZechTable| |parent| |leftRankPolynomial| + |content| |tableForDiscreteLogarithm| |incrementBy| |dAndcExp| + |enumerate| |outputForm| |rightOne| |cAsech| |radix| |changeName| + |irDef| |OMputBVar| |tryFunctionalDecomposition?| |partitions| + |c06gqf| |e02dcf| |d03edf| |acsch| |unknownEndian| |LiePoly| |imagk| + |returnType!| |resultantEuclidean| |ode1| |printInfo| |oddintegers| + |bracket| |cyclicSubmodule| |lfextendedint| |attributeData| + |modularGcdPrimitive| |e02ahf| |exponential1| |goodPoint| |float?| + |palglimint| |diagonalMatrix| |generalizedEigenvector| |mkAnswer| + |orbit| |startTable!| |mainExpression| + |inverseIntegralMatrixAtInfinity| |nil?| |copy!| |Lazard2| + |quotientByP| |epilogue| |resetBadValues| |options| |finiteBasis| + |meshPar2Var| |subResultantGcdEuclidean| |preprocess| |tail| + |iterationVar| |typeLists| |dom| |laplacian| |complexEigenvectors| + |normFactors| |totalfract| |localAbs| |trapezoidalo| |square?| + |primintegrate| |selectPDERoutines| |arg1| |binaryTree| |entry| |over| + |postfix| |cyclicCopy| |e02bdf| |s17akf| |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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T) ((-234 $) -2760 (|has| |#1| (-360)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) -2760 (|has| |#1| (-360)) (|has| |#1| (-238))) ((-237) -2760 (|has| |#1| (-360)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) -2760 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-294) |has| |#1| (-1223)) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) -2760 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-317) -2760 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) -2760 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-414) |has| |#1| (-360)) ((-379) -2760 (|has| |#1| (-379)) (|has| |#1| (-360))) ((-360) |has| |#1| (-360)) ((-381 |#1| #1#) . T) ((-421 |#1| #1#) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-423 |#1|) . T) ((-464) -2760 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1223)) ((-526 (-1197) |#1|) |has| |#1| (-526 (-1197) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2760 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -2760 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -2760 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -2760 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -2760 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -2760 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -2760 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-911 $ #3=(-1197)) -2760 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-917 (-1197)) |has| |#1| (-917 (-1197))) ((-919 #3#) -2760 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-901 (-390)) |has| |#1| (-901 (-390))) ((-901 (-576)) |has| |#1| (-901 (-576))) ((-899 |#1|) . T) ((-928) -12 (|has| |#1| (-317)) (|has| |#1| (-928))) ((-939) -2760 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1023) -12 (|has| |#1| (-1023)) (|has| |#1| (-1223))) ((-1059 (-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((-1059 (-576)) |has| |#1| (-1059 (-576))) ((-1059 |#1|) . T) ((-1072 #0#) -2760 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1072 |#1|) . T) ((-1072 $) . T) ((-1077 #0#) -2760 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1077 |#1|) . T) ((-1077 $) . T) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1173) |has| |#1| (-360)) ((-1223) |has| |#1| (-1223)) ((-1226) |has| |#1| (-1223)) ((-1238) . T) ((-1242) -2760 (|has| |#1| (-360)) (|has| |#1| (-374)) (-12 (|has| |#1| (-317)) (|has| |#1| (-928))))) +((-2738 (*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) (-4104 (*1 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) (-2272 (*1 *1 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) (-4177 (*1 *1 *2 *2) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) (-1860 (*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) (-1850 (*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) (-3475 (*1 *1 *1 *2) (|partial| -12 (-4 *1 (-167 *2)) (-4 *2 (-174)) (-4 *2 (-568)))) (-4143 (*1 *1 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)) (-4 *2 (-1081)))) (-1631 (*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)) (-4 *2 (-1223)))) (-2177 (*1 *2 *1) (-12 (-4 *1 (-167 *3)) (-4 *3 (-174)) (-4 *3 (-1081)) (-4 *3 (-1223)) (-5 *2 (-2 (|:| |r| *3) (|:| |phi| *3))))) (-2769 (*1 *2 *1) (-12 (-4 *1 (-167 *3)) (-4 *3 (-174)) (-4 *3 (-557)) (-5 *2 (-112)))) (-3025 (*1 *2 *1) (-12 (-4 *1 (-167 *3)) (-4 *3 (-174)) (-4 *3 (-557)) (-5 *2 (-419 (-576))))) (-2358 (*1 *2 *1) (|partial| -12 (-4 *1 (-167 *3)) (-4 *3 (-174)) (-4 *3 (-557)) (-5 *2 (-419 (-576)))))) +(-13 (-736 |t#1| (-1193 |t#1|)) (-423 |t#1|) (-232 |t#1|) (-349 |t#1|) (-412 |t#1|) (-899 |t#1|) (-388 |t#1|) (-174) (-10 -8 (-6 -4177) (-15 -4104 ($)) (-15 -2272 ($ $)) (-15 -4177 ($ |t#1| |t#1|)) (-15 -1860 (|t#1| $)) (-15 -1850 (|t#1| $)) (-15 -2738 (|t#1| $)) (IF (|has| |t#1| (-568)) (PROGN (-6 (-568)) (-15 -3475 ((-3 $ "failed") $ |t#1|))) |%noBranch|) (IF (|has| |t#1| (-317)) (-6 (-317)) |%noBranch|) (IF (|has| |t#1| (-6 -4463)) (-6 -4463) |%noBranch|) (IF (|has| |t#1| (-6 -4460)) (-6 -4460) |%noBranch|) (IF (|has| |t#1| (-374)) (-6 (-374)) |%noBranch|) (IF (|has| |t#1| (-626 (-548))) (-6 (-626 (-548))) |%noBranch|) (IF (|has| |t#1| (-148)) (-6 (-148)) |%noBranch|) (IF (|has| |t#1| (-146)) (-6 (-146)) |%noBranch|) (IF (|has| |t#1| (-1043)) (PROGN (-6 (-626 (-171 (-227)))) (-6 (-626 (-171 (-390))))) |%noBranch|) (IF (|has| |t#1| (-1081)) (-15 -4143 ($ $)) |%noBranch|) (IF (|has| |t#1| (-1223)) (PROGN (-6 (-1223)) (-15 -1631 (|t#1| $)) (IF (|has| |t#1| (-1023)) (-6 (-1023)) |%noBranch|) (IF (|has| |t#1| (-1081)) (-15 -2177 ((-2 (|:| |r| |t#1|) (|:| |phi| |t#1|)) $)) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (-557)) (PROGN (-15 -2769 ((-112) $)) (-15 -3025 ((-419 (-576)) $)) (-15 -2358 ((-3 (-419 (-576)) "failed") $))) |%noBranch|) (IF (|has| |t#1| (-928)) (IF (|has| |t#1| (-317)) (-6 (-928)) |%noBranch|) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1223)) ((-95) |has| |#1| (-1223)) ((-102) . T) ((-111 #0# #0#) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2759 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2759 (|has| |#1| (-1059 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-876)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1043)) ((-626 (-171 (-390))) |has| |#1| (-1043)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-907 (-390))) |has| |#1| (-626 (-907 (-390)))) ((-626 (-907 (-576))) |has| |#1| (-626 (-907 (-576)))) ((-626 #1=(-1193 |#1|)) . T) ((-234 $) -2759 (|has| |#1| (-360)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) -2759 (|has| |#1| (-360)) (|has| |#1| (-238))) ((-237) -2759 (|has| |#1| (-360)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-294) |has| |#1| (-1223)) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) -2759 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-317) -2759 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-414) |has| |#1| (-360)) ((-379) -2759 (|has| |#1| (-379)) (|has| |#1| (-360))) ((-360) |has| |#1| (-360)) ((-381 |#1| #1#) . T) ((-421 |#1| #1#) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-423 |#1|) . T) ((-464) -2759 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1223)) ((-526 (-1197) |#1|) |has| |#1| (-526 (-1197) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2759 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-911 $ #3=(-1197)) -2759 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-917 (-1197)) |has| |#1| (-917 (-1197))) ((-919 #3#) -2759 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-901 (-390)) |has| |#1| (-901 (-390))) ((-901 (-576)) |has| |#1| (-901 (-576))) ((-899 |#1|) . T) ((-928) -12 (|has| |#1| (-317)) (|has| |#1| (-928))) ((-939) -2759 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1023) -12 (|has| |#1| (-1023)) (|has| |#1| (-1223))) ((-1059 (-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((-1059 (-576)) |has| |#1| (-1059 (-576))) ((-1059 |#1|) . T) ((-1072 #0#) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1072 |#1|) . T) ((-1072 $) . T) ((-1077 #0#) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1077 |#1|) . T) ((-1077 $) . T) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1173) |has| |#1| (-360)) ((-1223) |has| |#1| (-1223)) ((-1226) |has| |#1| (-1223)) ((-1238) . 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T) ((-102) -2760 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2760 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2760 (|has| |#2| (-1070)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121))) ((-628 (-576)) -2760 (|has| |#2| (-1070)) (-12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121)))) ((-628 |#2|) |has| |#2| (-1121)) ((-625 (-876)) -2760 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-876))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1288 |#2|)) . T) ((-234 $) -2760 (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1070)))) ((-232 |#2|) |has| |#2| (-1070)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1070))) ((-237) -2760 (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1070)))) ((-272 |#2|) |has| |#2| (-1070)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1070)) ((-423 |#2|) |has| |#2| (-1121)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((-658 (-576)) -2760 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2760 (|has| |#2| (-1070)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1070)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070))) ((-660 |#2|) -2760 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1070)) ((-652 |#2|) -2760 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070))) ((-651 |#2|) |has| |#2| (-1070)) ((-729 |#2|) -2760 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1070)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-861) -2760 (|has| |#2| (-861)) (|has| |#2| (-805))) ((-864) -2760 (|has| |#2| (-861)) (|has| |#2| (-805))) ((-911 $ #3=(-1197)) -2760 (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) ((-917 (-1197)) -12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070))) ((-919 #3#) -2760 (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) ((-1059 #0#) -12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121))) ((-1059 (-576)) -12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121))) ((-1059 |#2|) |has| |#2| (-1121)) ((-1072 |#2|) -2760 (|has| |#2| (-1070)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1077 |#2|) -2760 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1070) |has| |#2| (-1070)) ((-1079) |has| |#2| (-1070)) ((-1133) |has| |#2| (-1070)) ((-1121) -2760 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1238) . T) ((-1295 |#2|) |has| |#2| (-374))) -((-1950 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-3686 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4117 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) -(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -1950 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3686 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4117 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1238) (-1238)) (T -244)) -((-4117 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1238)) (-4 *7 (-1238)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-3686 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1238)) (-4 *2 (-1238)) (-5 *1 (-244 *5 *6 *2)))) (-1950 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1238)) (-4 *5 (-1238)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) -(-10 -7 (-15 -1950 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3686 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4117 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) -((-3489 (((-112) $ $) NIL (|has| |#2| (-102)))) (-4308 (((-112) $) NIL (|has| |#2| (-23)))) (-2052 (($ (-940)) 62 (|has| |#2| (-1070)))) (-2047 (((-1293) $ (-576) (-576)) NIL (|has| $ (-6 -4466)))) (-2324 (($ $ $) 68 (|has| |#2| (-805)))) (-4367 (((-3 $ "failed") $ $) 53 (|has| |#2| (-132)))) (-1808 (((-112) $ (-783)) NIL)) (-2098 (((-783)) NIL (|has| |#2| (-379)))) (-3756 ((|#2| $ (-576) |#2|) NIL (|has| $ (-6 -4466)))) (-3886 (($) NIL T CONST)) (-1572 (((-3 (-576) "failed") $) NIL (-12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121)))) (((-3 (-419 (-576)) "failed") $) NIL (-12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121)))) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1121)))) (-2860 (((-576) $) NIL (-12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121)))) (((-419 (-576)) $) NIL (-12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121)))) ((|#2| $) 28 (|has| |#2| (-1121)))) (-2204 (((-701 (-576)) (-701 $)) NIL (-12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070)))) (((-2 (|:| -2590 (-701 (-576))) (|:| |vec| (-1288 (-576)))) (-701 $) (-1288 $)) NIL (-12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070)))) (((-2 (|:| -2590 (-701 |#2|)) (|:| |vec| (-1288 |#2|))) (-701 $) (-1288 $)) NIL (|has| |#2| (-1070))) (((-701 |#2|) (-701 $)) NIL (|has| |#2| (-1070)))) (-1561 (((-3 $ "failed") $) 58 (|has| |#2| (-1070)))) (-1836 (($) NIL (|has| |#2| (-379)))) (-4335 ((|#2| $ (-576) |#2|) NIL (|has| $ (-6 -4466)))) (-4274 ((|#2| $ (-576)) 56)) (-3966 (((-656 |#2|) $) 14 (|has| $ (-6 -4465)))) (-4193 (((-112) $) NIL (|has| |#2| (-1070)))) (-3870 (((-112) $ (-783)) NIL)) (-2924 (((-576) $) 19 (|has| (-576) (-861)))) (-3125 (($ $ $) NIL (|has| |#2| (-861)))) (-2014 (((-656 |#2|) $) NIL (|has| $ (-6 -4465)))) (-1612 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4465)) (|has| |#2| (-1121))))) (-2137 (((-576) $) NIL (|has| (-576) (-861)))) (-3133 (($ $ $) NIL (|has| |#2| (-861)))) (-4323 (($ (-1 |#2| |#2|) $) NIL (|has| $ (-6 -4466)))) (-4117 (($ (-1 |#2| |#2|) $) NIL)) (-4401 (((-940) $) NIL (|has| |#2| (-379)))) (-1330 (((-112) $ (-783)) NIL)) (-3913 (((-701 (-576)) (-1288 $)) NIL (-12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070)))) (((-2 (|:| -2590 (-701 (-576))) (|:| |vec| (-1288 (-576)))) (-1288 $) $) NIL (-12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070)))) (((-2 (|:| -2590 (-701 |#2|)) (|:| |vec| (-1288 |#2|))) (-1288 $) $) NIL (|has| |#2| (-1070))) (((-701 |#2|) (-1288 $)) NIL (|has| |#2| (-1070)))) (-3699 (((-1179) $) NIL (|has| |#2| (-1121)))) (-4234 (((-656 (-576)) $) NIL)) (-3354 (((-112) (-576) $) NIL)) (-3224 (($ (-940)) NIL (|has| |#2| (-379)))) (-1450 (((-1141) $) NIL (|has| |#2| (-1121)))) (-3581 ((|#2| $) NIL (|has| (-576) (-861)))) (-4046 (($ $ |#2|) NIL (|has| $ (-6 -4466)))) (-4320 (((-112) (-1 (-112) |#2|) $) 23 (|has| $ (-6 -4465)))) (-3284 (($ $ 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NIL (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070)))) (($ $ (-1197)) NIL (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1070))) (($ $ (-1 |#2| |#2|) (-783)) NIL (|has| |#2| (-1070)))) (-1460 (((-783) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4465))) (((-783) |#2| $) NIL (-12 (|has| $ (-6 -4465)) (|has| |#2| (-1121))))) (-1870 (($ $) NIL)) (-3570 (((-1288 |#2|) $) 9) (($ (-576)) NIL (-2760 (-12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121))) (|has| |#2| (-1070)))) (($ (-419 (-576))) NIL (-12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121)))) (($ |#2|) 12 (|has| |#2| (-1121))) (((-876) $) NIL (|has| |#2| (-625 (-876))))) (-3996 (((-783)) NIL (|has| |#2| (-1070)) CONST)) (-4055 (((-112) $ $) NIL (|has| |#2| (-102)))) (-3321 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4465)))) (-2721 (($) 36 (|has| |#2| (-23)) CONST)) (-2732 (($) 40 (|has| |#2| (-1070)) CONST)) (-2020 (($ $ (-783)) NIL (-12 (|has| |#2| (-237)) (|has| |#2| (-1070)))) (($ $) NIL (-12 (|has| |#2| (-237)) (|has| |#2| (-1070)))) (($ $ (-656 (-1197)) (-656 (-783))) NIL (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070)))) (($ $ (-1197) (-783)) NIL (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070)))) (($ $ (-656 (-1197))) NIL (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070)))) (($ $ (-1197)) NIL (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1070))) (($ $ (-1 |#2| |#2|) (-783)) NIL (|has| |#2| (-1070)))) (-2992 (((-112) $ $) NIL (|has| |#2| (-861)))) (-2964 (((-112) $ $) NIL (|has| |#2| (-861)))) (-2925 (((-112) $ $) 27 (|has| |#2| (-102)))) (-2978 (((-112) $ $) NIL (|has| |#2| (-861)))) (-2950 (((-112) $ $) 66 (|has| |#2| (-861)))) (-3057 (($ $ |#2|) NIL (|has| |#2| (-374)))) (-3044 (($ $ $) NIL (|has| |#2| (-21))) (($ $) NIL (|has| |#2| (-21)))) (-3030 (($ $ $) 34 (|has| |#2| (-25)))) (** (($ $ (-783)) NIL (|has| |#2| (-1070))) (($ $ (-940)) NIL (|has| |#2| (-1070)))) (* (($ $ $) 46 (|has| |#2| (-1070))) (($ $ |#2|) 44 (|has| |#2| (-738))) (($ |#2| $) 45 (|has| |#2| (-738))) (($ (-576) $) NIL (|has| |#2| (-21))) (($ (-783) $) NIL (|has| |#2| (-23))) (($ (-940) $) NIL (|has| |#2| (-25)))) (-3503 (((-783) $) NIL (|has| $ (-6 -4465))))) +((-1871 (*1 *1 *2) (-12 (-5 *2 (-1288 *4)) (-4 *4 (-1238)) (-4 *1 (-243 *3 *4)))) (-1545 (*1 *1 *2) (-12 (-5 *2 (-940)) (-4 *1 (-243 *3 *4)) (-4 *4 (-1070)) (-4 *4 (-1238)))) (-4099 (*1 *2 *1 *1) (-12 (-4 *1 (-243 *3 *2)) (-4 *2 (-1238)) (-4 *2 (-1070))))) +(-13 (-616 (-576) |t#2|) (-625 (-1288 |t#2|)) (-10 -8 (-6 -4464) (-15 -1871 ($ (-1288 |t#2|))) (IF (|has| |t#2| (-1121)) (-6 (-423 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1070)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-232 |t#2|)) (-6 (-388 |t#2|)) (-15 -1545 ($ (-940))) (-15 -4099 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-23)) (-6 (-23)) |%noBranch|) (IF (|has| |t#2| (-21)) (-6 (-21)) |%noBranch|) (IF (|has| |t#2| (-738)) (-6 (-652 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-379)) (-6 (-379)) |%noBranch|) (IF (|has| |t#2| (-174)) (-6 (-729 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4461)) (-6 -4461) |%noBranch|) (IF (|has| |t#2| (-861)) (-6 (-861)) |%noBranch|) (IF (|has| |t#2| (-805)) (-6 (-805)) |%noBranch|) (IF (|has| |t#2| (-374)) (-6 (-1295 |t#2|)) |%noBranch|))) +(((-21) -2759 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-23) -2759 (|has| |#2| (-1070)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -2759 (|has| |#2| (-1070)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2759 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2759 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2759 (|has| |#2| (-1070)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121))) ((-628 (-576)) -2759 (|has| |#2| (-1070)) (-12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121)))) ((-628 |#2|) |has| |#2| (-1121)) ((-625 (-876)) -2759 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-876))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1288 |#2|)) . T) ((-234 $) -2759 (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1070)))) ((-232 |#2|) |has| |#2| (-1070)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1070))) ((-237) -2759 (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1070)))) ((-272 |#2|) |has| |#2| (-1070)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1070)) ((-423 |#2|) |has| |#2| (-1121)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((-658 (-576)) -2759 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2759 (|has| |#2| (-1070)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1070)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070))) ((-660 |#2|) -2759 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1070)) ((-652 |#2|) -2759 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070))) ((-651 |#2|) |has| |#2| (-1070)) ((-729 |#2|) -2759 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1070)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-861) -2759 (|has| |#2| (-861)) (|has| |#2| (-805))) ((-864) -2759 (|has| |#2| (-861)) (|has| |#2| (-805))) ((-911 $ #3=(-1197)) -2759 (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) ((-917 (-1197)) -12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070))) ((-919 #3#) -2759 (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) ((-1059 #0#) -12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121))) ((-1059 (-576)) -12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121))) ((-1059 |#2|) |has| |#2| (-1121)) ((-1072 |#2|) -2759 (|has| |#2| (-1070)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1077 |#2|) -2759 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1070) |has| |#2| (-1070)) ((-1079) |has| |#2| (-1070)) ((-1133) |has| |#2| (-1070)) ((-1121) -2759 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1238) . T) ((-1295 |#2|) |has| |#2| (-374))) +((-3120 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-3685 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4116 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) +(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -3120 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3685 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4116 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1238) (-1238)) (T -244)) +((-4116 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1238)) (-4 *7 (-1238)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-3685 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1238)) (-4 *2 (-1238)) (-5 *1 (-244 *5 *6 *2)))) (-3120 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1238)) (-4 *5 (-1238)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2760 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2760 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) -2760 (|has| |#1| (-1059 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 |#2|) . T) ((-628 |#3|) . T) ((-628 $) -2760 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-625 (-876)) . 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T) ((-568) -2760 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-658 #0#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-576)))) ((-660 #1=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2760 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-651 #1#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2760 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-738) . T) ((-911 $ #2=(-1197)) -2760 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-911 $ |#3|) . T) ((-917 (-1197)) |has| |#1| (-917 (-1197))) ((-917 |#3|) . T) ((-919 #2#) -2760 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-919 |#3|) . T) ((-901 (-390)) -12 (|has| |#1| (-901 (-390))) (|has| |#3| (-901 (-390)))) ((-901 (-576)) -12 (|has| |#1| (-901 (-576))) (|has| |#3| (-901 (-576)))) ((-968 |#1| |#4| |#3|) . T) ((-928) |has| |#1| (-928)) ((-1059 (-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((-1059 (-576)) |has| |#1| (-1059 (-576))) ((-1059 |#1|) . T) ((-1059 |#2|) . T) ((-1059 |#3|) . T) ((-1072 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1072 |#1|) . T) ((-1072 $) -2760 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1077 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1077 |#1|) . T) ((-1077 $) -2760 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1238) . T) ((-1242) |has| |#1| (-928))) -((-3489 (((-112) $ $) 20 (|has| |#1| (-102)))) (-2576 ((|#1| $) 55)) (-1419 ((|#1| $) 45)) (-1808 (((-112) $ (-783)) 8)) (-3886 (($) 7 T CONST)) (-2496 (($ $) 61)) (-3990 (($ $) 49)) (-3659 ((|#1| |#1| $) 47)) (-3469 ((|#1| $) 46)) (-3966 (((-656 |#1|) $) 31 (|has| $ (-6 -4465)))) (-3870 (((-112) $ (-783)) 9)) (-2014 (((-656 |#1|) $) 30 (|has| $ (-6 -4465)))) (-1612 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1121)) (|has| $ (-6 -4465))))) (-4323 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4466)))) (-4117 (($ (-1 |#1| |#1|) $) 36)) (-1330 (((-112) $ (-783)) 10)) (-2437 (((-783) $) 62)) (-3699 (((-1179) $) 23 (|has| |#1| (-1121)))) (-1597 ((|#1| $) 40)) (-1567 ((|#1| |#1| $) 53)) (-1954 ((|#1| |#1| $) 52)) (-1901 (($ |#1| $) 41)) (-2327 (((-783) $) 56)) (-1450 (((-1141) $) 22 (|has| |#1| (-1121)))) (-3883 ((|#1| $) 63)) (-3844 ((|#1| $) 51)) (-2313 ((|#1| $) 50)) (-3449 ((|#1| $) 42)) (-4320 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4465)))) (-3284 (($ $ (-656 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (($ $ (-656 |#1|) (-656 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121))))) (-4040 (((-112) $ $) 14)) (-3206 ((|#1| |#1| $) 59)) (-3973 (((-112) $) 11)) (-4225 (($) 12)) (-3692 ((|#1| $) 60)) (-2997 (($) 58) (($ (-656 |#1|)) 57)) (-1888 (((-783) $) 44)) (-1460 (((-783) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4465))) (((-783) |#1| $) 29 (-12 (|has| |#1| (-1121)) (|has| $ (-6 -4465))))) (-1870 (($ $) 13)) (-3570 (((-876) $) 18 (|has| |#1| (-625 (-876))))) (-2322 ((|#1| $) 54)) (-4055 (((-112) $ $) 21 (|has| |#1| (-102)))) (-3943 (($ (-656 |#1|)) 43)) (-1741 ((|#1| $) 64)) (-3321 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4465)))) (-2925 (((-112) $ $) 19 (|has| |#1| (-102)))) (-3503 (((-783) $) 6 (|has| $ (-6 -4465))))) +((-2150 (*1 *2 *3) (-12 (-4 *4 (-1070)) (-4 *3 (-861)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-1 *1 (-783))) (-4 *1 (-260 *4 *3 *5 *6)))) (-3051 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-656 *4)))) (-3726 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1070)) (-4 *3 (-861)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-3726 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-783)))) (-2683 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1070)) (-4 *3 (-861)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-1857 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-656 (-783))))) (-2791 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-783)))) (-1857 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1070)) (-4 *3 (-861)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-656 (-783))))) (-2791 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1070)) (-4 *3 (-861)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-1970 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-112)))) (-2758 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *2 *5)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-805)) (-4 *2 (-275 *4)))) (-4286 (*1 *1 *1) (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1070)) (-4 *3 (-861)) (-4 *4 (-275 *3)) (-4 *5 (-805)))) (-3979 (*1 *1 *1) (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1070)) (-4 *3 (-861)) (-4 *4 (-275 *3)) (-4 *5 (-805)))) (-2150 (*1 *2 *1) (-12 (-4 *3 (-238)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-1 *1 (-783))) (-4 *1 (-260 *3 *4 *5 *6))))) +(-13 (-968 |t#1| |t#4| |t#3|) (-232 |t#1|) (-1059 |t#2|) (-10 -8 (-15 -2150 ((-1 $ (-783)) |t#2|)) (-15 -3051 ((-656 |t#2|) $)) (-15 -3726 ((-783) $ |t#2|)) (-15 -3726 ((-783) $)) (-15 -2683 ((-783) $ |t#2|)) (-15 -1857 ((-656 (-783)) $)) (-15 -2791 ((-783) $)) (-15 -1857 ((-656 (-783)) $ |t#2|)) (-15 -2791 ((-783) $ |t#2|)) (-15 -1970 ((-112) $)) (-15 -2758 (|t#3| $)) (-15 -4286 ($ $)) (-15 -3979 ($ $)) (IF (|has| |t#1| (-238)) (PROGN (-6 (-526 |t#2| |t#1|)) (-6 (-526 |t#2| $)) (-6 (-319 $)) (-15 -2150 ((-1 $ (-783)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) -2759 (|has| |#1| (-1059 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 |#2|) . T) ((-628 |#3|) . T) ((-628 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-625 (-876)) . T) ((-174) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| |#1| (-626 (-548))) (|has| |#3| (-626 (-548)))) ((-626 (-907 (-390))) -12 (|has| |#1| (-626 (-907 (-390)))) (|has| |#3| (-626 (-907 (-390))))) ((-626 (-907 (-576))) -12 (|has| |#1| (-626 (-907 (-576)))) (|has| |#3| (-626 (-907 (-576))))) ((-234 $) -2759 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2759 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-300) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-319 $) . T) ((-336 |#1| |#4|) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2759 (|has| |#1| (-928)) (|has| |#1| (-464))) ((-526 |#2| |#1|) |has| |#1| (-238)) ((-526 |#2| $) |has| |#1| (-238)) ((-526 |#3| |#1|) . T) ((-526 |#3| $) . T) ((-526 $ $) . T) ((-568) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-658 #0#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-576)))) ((-660 #1=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-651 #1#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-738) . T) ((-911 $ #2=(-1197)) -2759 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-911 $ |#3|) . T) ((-917 (-1197)) |has| |#1| (-917 (-1197))) ((-917 |#3|) . T) ((-919 #2#) -2759 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-919 |#3|) . T) ((-901 (-390)) -12 (|has| |#1| (-901 (-390))) (|has| |#3| (-901 (-390)))) ((-901 (-576)) -12 (|has| |#1| (-901 (-576))) (|has| |#3| (-901 (-576)))) ((-968 |#1| |#4| |#3|) . T) ((-928) |has| |#1| (-928)) ((-1059 (-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((-1059 (-576)) |has| |#1| (-1059 (-576))) ((-1059 |#1|) . T) ((-1059 |#2|) . T) ((-1059 |#3|) . T) ((-1072 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1072 |#1|) . T) ((-1072 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1077 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1077 |#1|) . T) ((-1077 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1238) . T) ((-1242) |has| |#1| (-928))) +((-3488 (((-112) $ $) 20 (|has| |#1| (-102)))) (-3118 ((|#1| $) 55)) (-1419 ((|#1| $) 45)) (-4264 (((-112) $ (-783)) 8)) (-3404 (($) 7 T CONST)) (-3542 (($ $) 61)) (-3092 (($ $) 49)) (-2944 ((|#1| |#1| $) 47)) (-1718 ((|#1| $) 46)) (-3965 (((-656 |#1|) $) 31 (|has| $ (-6 -4464)))) (-1368 (((-112) $ (-783)) 9)) (-2425 (((-656 |#1|) $) 30 (|has| $ (-6 -4464)))) (-2885 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1121)) (|has| $ (-6 -4464))))) (-4326 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4465)))) (-4116 (($ (-1 |#1| |#1|) $) 36)) (-2883 (((-112) $ (-783)) 10)) (-2435 (((-783) $) 62)) (-2046 (((-1179) $) 23 (|has| |#1| (-1121)))) (-2722 ((|#1| $) 40)) (-3734 ((|#1| |#1| $) 53)) (-3155 ((|#1| |#1| $) 52)) (-2597 (($ |#1| $) 41)) (-2327 (((-783) $) 56)) (-1450 (((-1141) $) 22 (|has| |#1| (-1121)))) (-3374 ((|#1| $) 63)) (-4268 ((|#1| $) 51)) (-2261 ((|#1| $) 50)) (-1541 ((|#1| $) 42)) (-3252 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4464)))) (-3282 (($ $ (-656 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121)))) (($ $ (-656 |#1|) (-656 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121))))) (-2252 (((-112) $ $) 14)) (-4098 ((|#1| |#1| $) 59)) (-2940 (((-112) $) 11)) (-3579 (($) 12)) (-3265 ((|#1| $) 60)) (-3852 (($) 58) (($ (-656 |#1|)) 57)) (-1887 (((-783) $) 44)) (-1460 (((-783) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4464))) (((-783) |#1| $) 29 (-12 (|has| |#1| (-1121)) (|has| $ (-6 -4464))))) (-1870 (($ $) 13)) (-3569 (((-876) $) 18 (|has| |#1| (-625 (-876))))) (-2364 ((|#1| $) 54)) (-2399 (((-112) $ $) 21 (|has| |#1| (-102)))) (-3972 (($ (-656 |#1|)) 43)) (-1675 ((|#1| $) 64)) (-2708 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4464)))) (-2924 (((-112) $ $) 19 (|has| |#1| (-102)))) (-3502 (((-783) $) 6 (|has| $ (-6 -4464))))) (((-261 |#1|) (-141) (-1238)) (T -261)) -((-2997 (*1 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238)))) (-2997 (*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1238)) (-4 *1 (-261 *3)))) (-2327 (*1 *2 *1) (-12 (-4 *1 (-261 *3)) (-4 *3 (-1238)) (-5 *2 (-783)))) (-2576 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238)))) (-2322 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238)))) (-1567 (*1 *2 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238)))) (-1954 (*1 *2 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238)))) (-3844 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238)))) (-2313 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238)))) (-3990 (*1 *1 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238))))) -(-13 (-1142 |t#1|) (-1016 |t#1|) (-10 -8 (-15 -2997 ($)) (-15 -2997 ($ (-656 |t#1|))) (-15 -2327 ((-783) $)) (-15 -2576 (|t#1| $)) (-15 -2322 (|t#1| $)) (-15 -1567 (|t#1| |t#1| $)) (-15 -1954 (|t#1| |t#1| $)) (-15 -3844 (|t#1| $)) (-15 -2313 (|t#1| $)) (-15 -3990 ($ $)))) -(((-34) . T) ((-107 |#1|) . T) ((-102) -2760 (|has| |#1| (-1121)) (|has| |#1| (-102))) ((-625 (-876)) -2760 (|has| |#1| (-1121)) (|has| |#1| (-625 (-876)))) ((-319 |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121))) ((-501 |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1121))) ((-1016 |#1|) . T) ((-1121) |has| |#1| (-1121)) ((-1142 |#1|) . T) ((-1238) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-102) . T) ((-111 #0# #0#) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2759 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2759 (|has| |#1| (-1059 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-625 (-876)) . T) ((-174) . T) ((-626 |#2|) . T) ((-234 $) -2759 (|has| |#1| (-360)) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (-12 (|has| |#1| (-238)) (|has| |#1| (-374)))) ((-232 |#1|) |has| |#1| (-374)) ((-238) -2759 (|has| |#1| (-360)) (-12 (|has| |#1| (-238)) (|has| |#1| (-374)))) ((-237) -2759 (|has| |#1| (-360)) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (-12 (|has| |#1| (-238)) (|has| |#1| (-374)))) ((-272 |#1|) |has| |#1| (-374)) ((-248) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-300) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-317) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-374) -2759 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-414) |has| |#1| (-360)) ((-379) -2759 (|has| |#1| (-379)) (|has| |#1| (-360))) ((-360) |has| |#1| (-360)) ((-381 |#1| |#2|) . T) ((-421 |#1| |#2|) . T) ((-388 |#1|) . T) ((-423 |#1|) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) . T) ((-628 (-576)) . T) ((-628 #1=(-1197)) |has| |#1| (-1059 (-1197))) ((-628 |#1|) . T) ((-628 $) . T) ((-625 (-876)) . T) ((-174) . T) ((-626 (-227)) |has| |#1| (-1043)) ((-626 (-390)) |has| |#1| (-1043)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-907 (-390))) |has| |#1| (-626 (-907 (-390)))) ((-626 (-907 (-576))) |has| |#1| (-626 (-907 (-576)))) ((-234 $) -2759 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2759 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) . T) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) . T) ((-317) . T) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-464) . 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2760 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2760 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2760 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2760 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2760 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1197)) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-1197)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2760 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-876)) . T) ((-174) -2760 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1043))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1043))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-907 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-907 (-390))))) ((-626 (-907 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-907 (-576))))) ((-234 $) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1133)) ((-300) -2760 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1197) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1197) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2760 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -2760 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -2760 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2760 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2760 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2760 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2760 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-803) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-806) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-832) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-860) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-861) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-861))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-864) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-861))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-911 $ #4=(-1197)) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-919 (-1197)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1197)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197))))) ((-917 (-1197)) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1197)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197))))) ((-919 #4#) -2760 (-12 (|has| |#1| (-374)) (|has| |#2| (-919 (-1197)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1197)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197))))) ((-901 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-901 (-390)))) ((-901 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-901 (-576)))) ((-899 |#2|) |has| |#1| (-374)) ((-928) -12 (|has| |#1| (-374)) (|has| |#2| (-928))) ((-994 |#1| #0# (-1103)) . 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T) ((-628 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-876)) . 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T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1133)) ((-300) -2759 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1197) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1197) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2759 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -2759 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -2759 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2759 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2759 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-803) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-806) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-832) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-860) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-861) -2759 (-12 (|has| |#1| (-374)) (|has| |#2| (-861))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-864) -2759 (-12 (|has| |#1| (-374)) (|has| |#2| (-861))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-911 $ #4=(-1197)) -2759 (-12 (|has| |#1| (-374)) (|has| |#2| (-919 (-1197)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1197)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197))))) ((-917 (-1197)) -2759 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1197)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197))))) ((-919 #4#) -2759 (-12 (|has| |#1| (-374)) (|has| |#2| (-919 (-1197)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1197)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-917 (-1197))))) ((-901 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-901 (-390)))) ((-901 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-901 (-576)))) ((-899 |#2|) |has| |#1| (-374)) ((-928) -12 (|has| |#1| (-374)) (|has| |#2| (-928))) ((-994 |#1| #0# (-1103)) . T) ((-939) |has| |#1| (-374)) ((-1013 |#2|) |has| |#1| (-374)) ((-1023) |has| |#1| (-38 (-419 (-576)))) ((-1043) -12 (|has| |#1| (-374)) (|has| |#2| (-1043))) ((-1059 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-576)))) ((-1059 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-576)))) ((-1059 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-1197)))) ((-1059 |#2|) . T) ((-1072 #1#) -2759 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1072 |#1|) . T) ((-1072 |#2|) |has| |#1| (-374)) ((-1072 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1077 #1#) -2759 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1077 |#1|) . T) ((-1077 |#2|) |has| |#1| (-374)) ((-1077 $) -2759 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1173) -12 (|has| |#1| (-374)) (|has| |#2| (-1173))) ((-1223) |has| |#1| (-38 (-419 (-576)))) ((-1226) |has| |#1| (-38 (-419 (-576)))) ((-1238) . T) ((-1242) |has| |#1| (-374)) ((-1248 |#1|) . T) ((-1266 |#1| #0#) . 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T) ((-1242) |has| |#1| (-928))) -((-1969 (((-656 (-1103)) $) 34)) (-2114 (($ $) 31)) (-1945 (($ |#2| |#3|) NIL) (($ $ (-1103) |#3|) 28) (($ $ (-656 (-1103)) (-656 |#3|)) 27)) (-2081 (($ $) 14)) (-2091 ((|#2| $) 12)) (-3634 ((|#3| $) 10))) -(((-1265 |#1| |#2| |#3|) (-10 -8 (-15 -1969 ((-656 (-1103)) |#1|)) (-15 -1945 (|#1| |#1| (-656 (-1103)) (-656 |#3|))) (-15 -1945 (|#1| |#1| (-1103) |#3|)) (-15 -2114 (|#1| |#1|)) (-15 -1945 (|#1| |#2| |#3|)) (-15 -3634 (|#3| |#1|)) (-15 -2081 (|#1| |#1|)) (-15 -2091 (|#2| |#1|))) (-1266 |#2| |#3|) (-1070) (-804)) (T -1265)) -NIL -(-10 -8 (-15 -1969 ((-656 (-1103)) |#1|)) (-15 -1945 (|#1| |#1| (-656 (-1103)) (-656 |#3|))) (-15 -1945 (|#1| |#1| (-1103) |#3|)) (-15 -2114 (|#1| |#1|)) (-15 -1945 (|#1| |#2| |#3|)) (-15 -3634 (|#3| |#1|)) (-15 -2081 (|#1| |#1|)) (-15 -2091 (|#2| |#1|))) -((-3489 (((-112) $ $) 7)) (-4308 (((-112) $) 17)) (-1969 (((-656 (-1103)) $) 86)) (-3055 (((-1197) $) 118)) (-2246 (((-2 (|:| -2778 $) (|:| -4452 $) (|:| |associate| $)) 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2759 (|has| |#1| (-1059 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1103)) . T) ((-628 |#1|) . T) ((-628 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-876)) . T) ((-174) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| (-1103) (-626 (-548))) (|has| |#1| (-626 (-548)))) ((-626 (-907 (-390))) -12 (|has| (-1103) (-626 (-907 (-390)))) (|has| |#1| (-626 (-907 (-390))))) ((-626 (-907 (-576))) -12 (|has| (-1103) (-626 (-907 (-576)))) (|has| |#1| (-626 (-907 (-576))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-272 |#1|) . T) ((-296 (-419 $) (-419 $)) |has| |#1| (-568)) ((-296 |#1| |#1|) . T) ((-296 $ $) . T) ((-300) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 $) . T) ((-336 |#1| #0#) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2759 (|has| |#1| (-928)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-568) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-658 #1#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-576)))) ((-660 #3=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-651 #3#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #1#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-738) . T) ((-911 $ #2#) . T) ((-911 $ #4=(-1197)) -2759 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-917 #2#) . T) ((-917 (-1197)) |has| |#1| (-917 (-1197))) ((-919 #2#) . T) ((-919 #4#) -2759 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-901 (-390)) -12 (|has| (-1103) (-901 (-390))) (|has| |#1| (-901 (-390)))) ((-901 (-576)) -12 (|has| (-1103) (-901 (-576))) (|has| |#1| (-901 (-576)))) ((-968 |#1| #0# #2#) . T) ((-928) |has| |#1| (-928)) ((-939) |has| |#1| (-374)) ((-1059 (-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((-1059 (-576)) |has| |#1| (-1059 (-576))) ((-1059 #2#) . T) ((-1059 |#1|) . T) ((-1072 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1072 |#1|) . T) ((-1072 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1077 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1077 |#1|) . T) ((-1077 $) -2759 (|has| |#1| (-928)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1173) |has| |#1| (-1173)) ((-1238) . T) ((-1242) |has| |#1| (-928))) +((-1969 (((-656 (-1103)) $) 34)) (-2114 (($ $) 31)) (-1944 (($ |#2| |#3|) NIL) (($ $ (-1103) |#3|) 28) (($ $ (-656 (-1103)) (-656 |#3|)) 27)) (-2081 (($ $) 14)) (-2091 ((|#2| $) 12)) (-2683 ((|#3| $) 10))) +(((-1265 |#1| |#2| |#3|) (-10 -8 (-15 -1969 ((-656 (-1103)) |#1|)) (-15 -1944 (|#1| |#1| (-656 (-1103)) (-656 |#3|))) (-15 -1944 (|#1| |#1| (-1103) |#3|)) (-15 -2114 (|#1| |#1|)) (-15 -1944 (|#1| |#2| |#3|)) (-15 -2683 (|#3| |#1|)) (-15 -2081 (|#1| |#1|)) (-15 -2091 (|#2| |#1|))) (-1266 |#2| |#3|) (-1070) (-804)) (T -1265)) +NIL +(-10 -8 (-15 -1969 ((-656 (-1103)) |#1|)) (-15 -1944 (|#1| |#1| (-656 (-1103)) (-656 |#3|))) (-15 -1944 (|#1| |#1| (-1103) |#3|)) (-15 -2114 (|#1| |#1|)) (-15 -1944 (|#1| |#2| |#3|)) (-15 -2683 (|#3| |#1|)) (-15 -2081 (|#1| |#1|)) (-15 -2091 (|#2| |#1|))) +((-3488 (((-112) $ $) 7)) (-3135 (((-112) $) 17)) (-1969 (((-656 (-1103)) $) 86)) (-3054 (((-1197) $) 118)) (-2798 (((-2 (|:| -4346 $) (|:| -4451 $) (|:| |associate| $)) 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3050672 3050858 "UPCDEN" 3051213 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1256 3050079 3050148 3050297 "UP2" 3050485 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1255 3048546 3049283 3049560 "UNISEG" 3049837 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1254 3047761 3047888 3048093 "UNISEG2" 3048389 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1253 3046821 3047001 3047227 "UNIFACT" 3047577 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1252 3029573 3046133 3046375 "ULS" 3046637 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1251 3017203 3029477 3029549 "ULSCONS" 3029554 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1250 2997924 3010284 3010346 "ULSCCAT" 3010984 NIL ULSCCAT (NIL T T) -9 NIL 3011273 NIL) (-1249 2996974 2997219 2997607 "ULSCCAT-" 2997612 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1248 2986038 2992521 2992564 "ULSCAT" 2993427 NIL ULSCAT (NIL T) -9 NIL 2994158 NIL) (-1247 2985468 2985547 2985726 "ULS2" 2985953 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1246 2984587 2985097 2985204 "UINT8" 2985315 T UINT8 (NIL) -8 NIL NIL 2985400) (-1245 2983705 2984215 2984322 "UINT64" 2984433 T UINT64 (NIL) -8 NIL NIL 2984518) (-1244 2982823 2983333 2983440 "UINT32" 2983551 T UINT32 (NIL) -8 NIL NIL 2983636) (-1243 2981941 2982451 2982558 "UINT16" 2982669 T UINT16 (NIL) -8 NIL NIL 2982754) (-1242 2980230 2981187 2981217 "UFD" 2981429 T UFD (NIL) -9 NIL 2981543 NIL) (-1241 2980024 2980070 2980165 "UFD-" 2980170 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1240 2979106 2979289 2979505 "UDVO" 2979830 T UDVO (NIL) -7 NIL NIL NIL) (-1239 2976922 2977331 2977802 "UDPO" 2978670 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1238 2976855 2976860 2976890 "TYPE" 2976895 T TYPE (NIL) -9 NIL NIL NIL) (-1237 2976615 2976810 2976841 "TYPEAST" 2976846 T TYPEAST (NIL) -8 NIL NIL NIL) (-1236 2975586 2975788 2976028 "TWOFACT" 2976409 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1235 2974609 2974995 2975230 "TUPLE" 2975386 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1234 2972300 2972819 2973358 "TUBETOOL" 2974092 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1233 2971149 2971354 2971595 "TUBE" 2972093 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1232 2965878 2970121 2970404 "TS" 2970901 NIL TS (NIL T) -8 NIL NIL NIL) (-1231 2954518 2958637 2958734 "TSETCAT" 2964003 NIL TSETCAT (NIL T T T T) -9 NIL 2965534 NIL) (-1230 2949250 2950850 2952741 "TSETCAT-" 2952746 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1229 2943889 2944736 2945665 "TRMANIP" 2948386 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1228 2943330 2943393 2943556 "TRIMAT" 2943821 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1227 2941196 2941433 2941790 "TRIGMNIP" 2943079 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1226 2940716 2940829 2940859 "TRIGCAT" 2941072 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1225 2940385 2940464 2940605 "TRIGCAT-" 2940610 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1224 2937233 2939243 2939524 "TREE" 2940139 NIL TREE (NIL T) -8 NIL NIL NIL) (-1223 2936507 2937035 2937065 "TRANFUN" 2937100 T TRANFUN (NIL) -9 NIL 2937166 NIL) (-1222 2935786 2935977 2936257 "TRANFUN-" 2936262 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1221 2935590 2935622 2935683 "TOPSP" 2935747 T TOPSP (NIL) -7 NIL NIL NIL) (-1220 2934938 2935053 2935207 "TOOLSIGN" 2935471 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1219 2933572 2934115 2934354 "TEXTFILE" 2934721 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1218 2931484 2932025 2932454 "TEX" 2933165 T TEX (NIL) -8 NIL NIL NIL) (-1217 2931265 2931296 2931368 "TEX1" 2931447 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1216 2930913 2930976 2931066 "TEMUTL" 2931197 T TEMUTL (NIL) -7 NIL NIL NIL) (-1215 2929067 2929347 2929672 "TBCMPPK" 2930636 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1214 2920776 2927153 2927209 "TBAGG" 2927609 NIL TBAGG (NIL T T) -9 NIL 2927820 NIL) (-1213 2915846 2917334 2919088 "TBAGG-" 2919093 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1212 2915230 2915337 2915482 "TANEXP" 2915735 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1211 2914741 2915005 2915095 "TALGOP" 2915175 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1210 2908137 2914598 2914691 "TABLE" 2914696 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1209 2907549 2907648 2907786 "TABLEAU" 2908034 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1208 2902157 2903377 2904625 "TABLBUMP" 2906335 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1207 2901379 2901526 2901707 "SYSTEM" 2901998 T SYSTEM (NIL) -8 NIL NIL NIL) (-1206 2897838 2898537 2899320 "SYSSOLP" 2900630 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1205 2897636 2897793 2897824 "SYSPTR" 2897829 T SYSPTR (NIL) -8 NIL NIL NIL) (-1204 2896672 2897177 2897296 "SYSNNI" 2897482 NIL SYSNNI (NIL NIL) -8 NIL NIL 2897567) (-1203 2895971 2896430 2896509 "SYSINT" 2896569 NIL SYSINT (NIL NIL) -8 NIL NIL 2896614) (-1202 2892303 2893249 2893959 "SYNTAX" 2895283 T SYNTAX (NIL) -8 NIL NIL NIL) (-1201 2889461 2890063 2890695 "SYMTAB" 2891693 T SYMTAB (NIL) -8 NIL NIL NIL) (-1200 2884710 2885612 2886595 "SYMS" 2888500 T SYMS (NIL) -8 NIL NIL NIL) (-1199 2881945 2884168 2884398 "SYMPOLY" 2884515 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1198 2881462 2881537 2881660 "SYMFUNC" 2881857 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1197 2877482 2878774 2879587 "SYMBOL" 2880671 T SYMBOL (NIL) -8 NIL NIL NIL) (-1196 2871021 2872710 2874430 "SWITCH" 2875784 T SWITCH (NIL) -8 NIL NIL NIL) (-1195 2864365 2869977 2870271 "SUTS" 2870785 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 2856541 2863747 2864011 "SUPXS" 2864159 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1193 2848024 2856159 2856285 "SUP" 2856450 NIL SUP (NIL T) -8 NIL NIL NIL) (-1192 2847183 2847310 2847527 "SUPFRACF" 2847892 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1191 2846804 2846863 2846976 "SUP2" 2847118 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1190 2845252 2845526 2845882 "SUMRF" 2846503 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1189 2844587 2844653 2844845 "SUMFS" 2845173 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1188 2827374 2843899 2844141 "SULS" 2844403 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1187 2826976 2827196 2827266 "SUCHTAST" 2827326 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1186 2826271 2826501 2826641 "SUCH" 2826884 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1185 2820138 2821177 2822136 "SUBSPACE" 2825359 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1184 2819568 2819658 2819822 "SUBRESP" 2820026 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1183 2812936 2814233 2815544 "STTF" 2818304 NIL STTF (NIL T) -7 NIL NIL NIL) (-1182 2807109 2808229 2809376 "STTFNC" 2811836 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1181 2798422 2800291 2802085 "STTAYLOR" 2805350 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1180 2791558 2798286 2798369 "STRTBL" 2798374 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1179 2786519 2791267 2791366 "STRING" 2791481 T STRING (NIL) -8 NIL NIL NIL) (-1178 2779275 2784138 2784749 "STREAM" 2785943 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1177 2778785 2778862 2779006 "STREAM3" 2779192 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1176 2777767 2777950 2778185 "STREAM2" 2778598 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1175 2777455 2777507 2777600 "STREAM1" 2777709 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1174 2776471 2776652 2776883 "STINPROD" 2777271 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1173 2776009 2776219 2776249 "STEP" 2776329 T STEP (NIL) -9 NIL 2776407 NIL) (-1172 2775196 2775498 2775646 "STEPAST" 2775883 T STEPAST (NIL) -8 NIL NIL NIL) (-1171 2768634 2775095 2775172 "STBL" 2775177 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1170 2763704 2767797 2767840 "STAGG" 2767993 NIL STAGG (NIL T) -9 NIL 2768082 NIL) (-1169 2761406 2762008 2762880 "STAGG-" 2762885 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1168 2759556 2761176 2761268 "STACK" 2761349 NIL STACK (NIL T) -8 NIL NIL NIL) (-1167 2752251 2757697 2758153 "SREGSET" 2759186 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1166 2744676 2746045 2747558 "SRDCMPK" 2750857 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1165 2737513 2742035 2742065 "SRAGG" 2743368 T SRAGG (NIL) -9 NIL 2743976 NIL) (-1164 2736530 2736785 2737164 "SRAGG-" 2737169 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1163 2730714 2735477 2735898 "SQMATRIX" 2736156 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1162 2724402 2727432 2728159 "SPLTREE" 2730059 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1161 2720365 2721058 2721704 "SPLNODE" 2723828 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1160 2719412 2719645 2719675 "SPFCAT" 2720119 T SPFCAT (NIL) -9 NIL NIL NIL) (-1159 2718149 2718359 2718623 "SPECOUT" 2719170 T SPECOUT (NIL) -7 NIL NIL NIL) (-1158 2709245 2711117 2711147 "SPADXPT" 2715823 T SPADXPT (NIL) -9 NIL 2717987 NIL) (-1157 2709006 2709046 2709115 "SPADPRSR" 2709198 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1156 2707055 2708961 2708992 "SPADAST" 2708997 T SPADAST (NIL) -8 NIL NIL NIL) (-1155 2698986 2700759 2700802 "SPACEC" 2705175 NIL SPACEC (NIL T) -9 NIL 2706991 NIL) (-1154 2697116 2698918 2698967 "SPACE3" 2698972 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1153 2695868 2696039 2696330 "SORTPAK" 2696921 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1152 2693960 2694263 2694675 "SOLVETRA" 2695532 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1151 2693010 2693232 2693493 "SOLVESER" 2693733 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1150 2688314 2689202 2690197 "SOLVERAD" 2692062 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1149 2684129 2684738 2685467 "SOLVEFOR" 2687681 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1148 2678399 2683478 2683575 "SNTSCAT" 2683580 NIL SNTSCAT (NIL T T T T) -9 NIL 2683650 NIL) (-1147 2672505 2676722 2677113 "SMTS" 2678089 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1146 2666914 2672393 2672470 "SMP" 2672475 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1145 2665073 2665374 2665772 "SMITH" 2666611 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1144 2657177 2661652 2661755 "SMATCAT" 2663106 NIL SMATCAT (NIL NIL T T T) -9 NIL 2663656 NIL) (-1143 2654117 2654940 2656118 "SMATCAT-" 2656123 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1142 2651758 2653325 2653368 "SKAGG" 2653629 NIL SKAGG (NIL T) -9 NIL 2653764 NIL) (-1141 2647948 2651231 2651415 "SINT" 2651567 T SINT (NIL) -8 NIL NIL 2651729) (-1140 2647720 2647758 2647824 "SIMPAN" 2647904 T SIMPAN (NIL) -7 NIL NIL NIL) (-1139 2646999 2647255 2647395 "SIG" 2647602 T SIG (NIL) -8 NIL NIL NIL) (-1138 2645837 2646058 2646333 "SIGNRF" 2646758 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1137 2644670 2644821 2645105 "SIGNEF" 2645666 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1136 2643976 2644253 2644377 "SIGAST" 2644568 T SIGAST (NIL) -8 NIL NIL NIL) (-1135 2641666 2642120 2642626 "SHP" 2643517 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1134 2635495 2641567 2641643 "SHDP" 2641648 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1133 2635054 2635246 2635276 "SGROUP" 2635369 T SGROUP (NIL) -9 NIL 2635431 NIL) (-1132 2634912 2634938 2635011 "SGROUP-" 2635016 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1131 2631703 2632401 2633124 "SGCF" 2634211 T SGCF (NIL) -7 NIL NIL NIL) (-1130 2626071 2631150 2631247 "SFRTCAT" 2631252 NIL SFRTCAT (NIL T T T T) -9 NIL 2631291 NIL) (-1129 2619492 2620510 2621646 "SFRGCD" 2625054 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1128 2612618 2613691 2614877 "SFQCMPK" 2618425 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1127 2612238 2612327 2612438 "SFORT" 2612559 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1126 2611356 2612078 2612199 "SEXOF" 2612204 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1125 2610463 2611237 2611305 "SEX" 2611310 T SEX (NIL) -8 NIL NIL NIL) (-1124 2606244 2606959 2607054 "SEXCAT" 2609676 NIL SEXCAT (NIL T T T T T) -9 NIL 2610236 NIL) (-1123 2603397 2606178 2606226 "SET" 2606231 NIL SET (NIL T) -8 NIL NIL NIL) (-1122 2601621 2602110 2602415 "SETMN" 2603138 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1121 2601187 2601339 2601369 "SETCAT" 2601486 T SETCAT (NIL) -9 NIL 2601571 NIL) (-1120 2600967 2601019 2601118 "SETCAT-" 2601123 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1119 2597328 2599428 2599471 "SETAGG" 2600341 NIL SETAGG (NIL T) -9 NIL 2600681 NIL) (-1118 2596786 2596902 2597139 "SETAGG-" 2597144 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1117 2596229 2596482 2596583 "SEQAST" 2596707 T SEQAST (NIL) -8 NIL NIL NIL) (-1116 2595428 2595722 2595783 "SEGXCAT" 2596069 NIL SEGXCAT (NIL T T) -9 NIL 2596189 NIL) (-1115 2594434 2595094 2595276 "SEG" 2595281 NIL SEG (NIL T) -8 NIL NIL NIL) (-1114 2593413 2593627 2593670 "SEGCAT" 2594192 NIL SEGCAT (NIL T) -9 NIL 2594413 NIL) (-1113 2592345 2592776 2592984 "SEGBIND" 2593240 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1112 2591966 2592025 2592138 "SEGBIND2" 2592280 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1111 2591539 2591767 2591844 "SEGAST" 2591911 T SEGAST (NIL) -8 NIL NIL NIL) (-1110 2590758 2590884 2591088 "SEG2" 2591383 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1109 2590129 2590693 2590740 "SDVAR" 2590745 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1108 2582380 2589899 2590029 "SDPOL" 2590034 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1107 2580973 2581239 2581558 "SCPKG" 2582095 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1106 2580137 2580309 2580501 "SCOPE" 2580803 T SCOPE (NIL) -8 NIL NIL NIL) (-1105 2579357 2579491 2579670 "SCACHE" 2579992 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1104 2578989 2579175 2579205 "SASTCAT" 2579210 T SASTCAT (NIL) -9 NIL 2579223 NIL) (-1103 2578476 2578824 2578900 "SAOS" 2578935 T SAOS (NIL) -8 NIL NIL NIL) (-1102 2578041 2578076 2578249 "SAERFFC" 2578435 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1101 2571704 2577938 2578018 "SAE" 2578023 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1100 2571297 2571332 2571491 "SAEFACT" 2571663 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1099 2569618 2569932 2570333 "RURPK" 2570963 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1098 2568255 2568561 2568866 "RULESET" 2569452 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1097 2565478 2566008 2566466 "RULE" 2567936 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1096 2565090 2565272 2565355 "RULECOLD" 2565430 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1095 2564880 2564908 2564979 "RTVALUE" 2565041 T RTVALUE (NIL) -8 NIL NIL NIL) (-1094 2564351 2564597 2564691 "RSTRCAST" 2564808 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1093 2559199 2559994 2560914 "RSETGCD" 2563550 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1092 2548429 2553508 2553605 "RSETCAT" 2557724 NIL RSETCAT (NIL T T T T) -9 NIL 2558821 NIL) (-1091 2546356 2546895 2547719 "RSETCAT-" 2547724 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1090 2538742 2540118 2541638 "RSDCMPK" 2544955 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1089 2536707 2537174 2537248 "RRCC" 2538334 NIL RRCC (NIL T T) -9 NIL 2538678 NIL) (-1088 2536058 2536232 2536511 "RRCC-" 2536516 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1087 2535501 2535754 2535855 "RPTAST" 2535979 T RPTAST (NIL) -8 NIL NIL NIL) (-1086 2508977 2518613 2518680 "RPOLCAT" 2529346 NIL RPOLCAT (NIL T T T) -9 NIL 2532506 NIL) (-1085 2500475 2502815 2505937 "RPOLCAT-" 2505942 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1084 2491412 2498686 2499168 "ROUTINE" 2500015 T ROUTINE (NIL) -8 NIL NIL NIL) (-1083 2488073 2491038 2491178 "ROMAN" 2491294 T ROMAN (NIL) -8 NIL NIL NIL) (-1082 2486317 2486933 2487193 "ROIRC" 2487878 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1081 2482521 2484806 2484836 "RNS" 2485140 T RNS (NIL) -9 NIL 2485414 NIL) (-1080 2481030 2481413 2481947 "RNS-" 2482022 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1079 2480419 2480827 2480857 "RNG" 2480862 T RNG (NIL) -9 NIL 2480883 NIL) (-1078 2479422 2479784 2479986 "RNGBIND" 2480270 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1077 2478807 2479195 2479238 "RMODULE" 2479243 NIL RMODULE (NIL T) -9 NIL 2479270 NIL) (-1076 2477643 2477737 2478073 "RMCAT2" 2478708 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1075 2474493 2476989 2477286 "RMATRIX" 2477405 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1074 2467320 2469580 2469695 "RMATCAT" 2473054 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2474036 NIL) (-1073 2466695 2466842 2467149 "RMATCAT-" 2467154 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1072 2466310 2466482 2466525 "RLINSET" 2466587 NIL RLINSET (NIL T) -9 NIL 2466631 NIL) (-1071 2465877 2465952 2466080 "RINTERP" 2466229 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1070 2464921 2465475 2465505 "RING" 2465561 T RING (NIL) -9 NIL 2465653 NIL) (-1069 2464713 2464757 2464854 "RING-" 2464859 NIL RING- (NIL T) -8 NIL NIL NIL) (-1068 2463554 2463791 2464049 "RIDIST" 2464477 T RIDIST (NIL) -7 NIL NIL NIL) (-1067 2454843 2463022 2463228 "RGCHAIN" 2463402 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1066 2454179 2454585 2454626 "RGBCSPC" 2454684 NIL RGBCSPC (NIL T) -9 NIL 2454736 NIL) (-1065 2453323 2453704 2453745 "RGBCMDL" 2453977 NIL RGBCMDL (NIL T) -9 NIL 2454091 NIL) (-1064 2450317 2450931 2451601 "RF" 2452687 NIL RF (NIL T) -7 NIL NIL NIL) (-1063 2449963 2450026 2450129 "RFFACTOR" 2450248 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1062 2449688 2449723 2449820 "RFFACT" 2449922 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1061 2447805 2448169 2448551 "RFDIST" 2449328 T RFDIST (NIL) -7 NIL NIL NIL) (-1060 2447258 2447350 2447513 "RETSOL" 2447707 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1059 2446894 2446974 2447017 "RETRACT" 2447150 NIL RETRACT (NIL T) -9 NIL 2447237 NIL) (-1058 2446743 2446768 2446855 "RETRACT-" 2446860 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1057 2446345 2446565 2446635 "RETAST" 2446695 T RETAST (NIL) -8 NIL NIL NIL) (-1056 2439089 2445998 2446125 "RESULT" 2446240 T RESULT (NIL) -8 NIL NIL NIL) (-1055 2437680 2438358 2438557 "RESRING" 2438992 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1054 2437316 2437365 2437463 "RESLATC" 2437617 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1053 2437021 2437056 2437163 "REPSQ" 2437275 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1052 2434443 2435023 2435625 "REP" 2436441 T REP (NIL) -7 NIL NIL NIL) (-1051 2434140 2434175 2434286 "REPDB" 2434402 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1050 2428040 2429429 2430652 "REP2" 2432952 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1049 2424417 2425098 2425906 "REP1" 2427267 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1048 2417113 2422558 2423014 "REGSET" 2424047 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1047 2415878 2416261 2416511 "REF" 2416898 NIL REF (NIL T) -8 NIL NIL NIL) (-1046 2415255 2415358 2415525 "REDORDER" 2415762 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1045 2411223 2414468 2414695 "RECLOS" 2415083 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1044 2410275 2410456 2410671 "REALSOLV" 2411030 T REALSOLV (NIL) -7 NIL NIL NIL) (-1043 2410121 2410162 2410192 "REAL" 2410197 T REAL (NIL) -9 NIL 2410232 NIL) (-1042 2406604 2407406 2408290 "REAL0Q" 2409286 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1041 2402205 2403193 2404254 "REAL0" 2405585 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1040 2401676 2401922 2402016 "RDUCEAST" 2402133 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1039 2401081 2401153 2401360 "RDIV" 2401598 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1038 2400149 2400323 2400536 "RDIST" 2400903 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1037 2398746 2399033 2399405 "RDETRS" 2399857 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1036 2396558 2397012 2397550 "RDETR" 2398288 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1035 2395183 2395461 2395858 "RDEEFS" 2396274 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1034 2393692 2393998 2394423 "RDEEF" 2394871 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1033 2387725 2390646 2390676 "RCFIELD" 2391971 T RCFIELD (NIL) -9 NIL 2392702 NIL) (-1032 2385789 2386293 2386989 "RCFIELD-" 2387064 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1031 2382033 2383862 2383905 "RCAGG" 2384989 NIL RCAGG (NIL T) -9 NIL 2385454 NIL) (-1030 2381661 2381755 2381918 "RCAGG-" 2381923 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1029 2380996 2381108 2381273 "RATRET" 2381545 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1028 2380549 2380616 2380737 "RATFACT" 2380924 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1027 2379857 2379977 2380129 "RANDSRC" 2380419 T RANDSRC (NIL) -7 NIL NIL NIL) (-1026 2379591 2379635 2379708 "RADUTIL" 2379806 T RADUTIL (NIL) -7 NIL NIL NIL) (-1025 2372419 2378422 2378733 "RADIX" 2379314 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1024 2362879 2372261 2372391 "RADFF" 2372396 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1023 2362526 2362601 2362631 "RADCAT" 2362791 T RADCAT (NIL) -9 NIL NIL NIL) (-1022 2362308 2362356 2362456 "RADCAT-" 2362461 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1021 2360409 2362078 2362170 "QUEUE" 2362251 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1020 2356670 2360342 2360390 "QUAT" 2360395 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1019 2356301 2356344 2356475 "QUATCT2" 2356621 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1018 2349099 2352724 2352766 "QUATCAT" 2353557 NIL QUATCAT (NIL T) -9 NIL 2354323 NIL) (-1017 2345238 2346275 2347665 "QUATCAT-" 2347761 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1016 2342678 2344286 2344329 "QUAGG" 2344710 NIL QUAGG (NIL T) -9 NIL 2344885 NIL) (-1015 2342280 2342500 2342570 "QQUTAST" 2342630 T QQUTAST (NIL) -8 NIL NIL NIL) (-1014 2341293 2341793 2341958 "QFORM" 2342161 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1013 2331625 2337140 2337182 "QFCAT" 2337850 NIL QFCAT (NIL T) -9 NIL 2338851 NIL) (-1012 2327192 2328393 2329987 "QFCAT-" 2330083 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1011 2326823 2326866 2326997 "QFCAT2" 2327143 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1010 2326278 2326388 2326520 "QEQUAT" 2326713 T QEQUAT (NIL) -8 NIL NIL NIL) (-1009 2319404 2320477 2321663 "QCMPACK" 2325211 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1008 2316942 2317390 2317820 "QALGSET" 2319059 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1007 2316177 2316353 2316589 "QALGSET2" 2316760 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1006 2314862 2315086 2315405 "PWFFINTB" 2315950 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1005 2313037 2313205 2313561 "PUSHVAR" 2314676 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1004 2308926 2309980 2310023 "PTRANFN" 2311934 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1003 2307317 2307608 2307932 "PTPACK" 2308637 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1002 2306946 2307003 2307114 "PTFUNC2" 2307254 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1001 2301341 2305735 2305778 "PTCAT" 2306078 NIL PTCAT (NIL T) -9 NIL 2306231 NIL) (-1000 2300996 2301031 2301157 "PSQFR" 2301300 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-999 2299591 2299889 2300223 "PSEUDLIN" 2300694 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-998 2286354 2288725 2291049 "PSETPK" 2297351 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-997 2279372 2282112 2282208 "PSETCAT" 2285229 NIL PSETCAT (NIL T T T T) -9 NIL 2286043 NIL) (-996 2277208 2277842 2278663 "PSETCAT-" 2278668 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-995 2276557 2276722 2276750 "PSCURVE" 2277018 T PSCURVE (NIL) -9 NIL 2277185 NIL) (-994 2272541 2274057 2274122 "PSCAT" 2274966 NIL PSCAT (NIL T T T) -9 NIL 2275206 NIL) (-993 2271604 2271820 2272220 "PSCAT-" 2272225 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-992 2269963 2270673 2270936 "PRTITION" 2271361 T PRTITION (NIL) -8 NIL NIL NIL) (-991 2269438 2269684 2269776 "PRTDAST" 2269891 T PRTDAST (NIL) -8 NIL NIL NIL) (-990 2258528 2260742 2262930 "PRS" 2267300 NIL PRS (NIL T T) -7 NIL NIL NIL) (-989 2256314 2257850 2257890 "PRQAGG" 2258073 NIL PRQAGG (NIL T) -9 NIL 2258175 NIL) (-988 2255650 2255955 2255983 "PROPLOG" 2256122 T PROPLOG (NIL) -9 NIL 2256237 NIL) (-987 2255254 2255311 2255434 "PROPFUN2" 2255573 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-986 2254569 2254690 2254862 "PROPFUN1" 2255115 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-985 2252750 2253316 2253613 "PROPFRML" 2254305 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-984 2252219 2252326 2252454 "PROPERTY" 2252642 T PROPERTY (NIL) -8 NIL NIL NIL) (-983 2246277 2250385 2251205 "PRODUCT" 2251445 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-982 2243555 2245735 2245969 "PR" 2246088 NIL PR (NIL T T) -8 NIL NIL NIL) (-981 2243351 2243383 2243442 "PRINT" 2243516 T PRINT (NIL) -7 NIL NIL NIL) (-980 2242691 2242808 2242960 "PRIMES" 2243231 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-979 2240756 2241157 2241623 "PRIMELT" 2242270 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-978 2240485 2240534 2240562 "PRIMCAT" 2240686 T PRIMCAT (NIL) -9 NIL NIL NIL) (-977 2236603 2240423 2240468 "PRIMARR" 2240473 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-976 2235610 2235788 2236016 "PRIMARR2" 2236421 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-975 2235253 2235309 2235420 "PREASSOC" 2235548 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-974 2234728 2234861 2234889 "PPCURVE" 2235094 T PPCURVE (NIL) -9 NIL 2235230 NIL) (-973 2234323 2234523 2234606 "PORTNUM" 2234665 T PORTNUM (NIL) -8 NIL NIL NIL) (-972 2231682 2232081 2232673 "POLYROOT" 2233904 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-971 2225588 2231286 2231446 "POLY" 2231555 NIL POLY (NIL T) -8 NIL NIL NIL) (-970 2224971 2225029 2225263 "POLYLIFT" 2225524 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-969 2221246 2221695 2222324 "POLYCATQ" 2224516 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-968 2207588 2212993 2213058 "POLYCAT" 2216572 NIL POLYCAT (NIL T T T) -9 NIL 2218450 NIL) (-967 2201037 2202899 2205283 "POLYCAT-" 2205288 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-966 2200624 2200692 2200812 "POLY2UP" 2200963 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-965 2200256 2200313 2200422 "POLY2" 2200561 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-964 2198941 2199180 2199456 "POLUTIL" 2200030 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-963 2197296 2197573 2197904 "POLTOPOL" 2198663 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-962 2192762 2197230 2197277 "POINT" 2197282 NIL POINT (NIL T) -8 NIL NIL NIL) (-961 2190949 2191306 2191681 "PNTHEORY" 2192407 T PNTHEORY (NIL) -7 NIL NIL NIL) (-960 2189407 2189704 2190103 "PMTOOLS" 2190647 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-959 2189000 2189078 2189195 "PMSYM" 2189323 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-958 2188508 2188577 2188752 "PMQFCAT" 2188925 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-957 2187863 2187973 2188129 "PMPRED" 2188385 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-956 2187256 2187342 2187504 "PMPREDFS" 2187764 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-955 2185920 2186128 2186506 "PMPLCAT" 2187018 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-954 2185452 2185531 2185683 "PMLSAGG" 2185835 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-953 2184925 2185001 2185183 "PMKERNEL" 2185370 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-952 2184542 2184617 2184730 "PMINS" 2184844 NIL PMINS (NIL T) -7 NIL NIL NIL) (-951 2183984 2184053 2184262 "PMFS" 2184467 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-950 2183212 2183330 2183535 "PMDOWN" 2183861 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-949 2182379 2182537 2182718 "PMASS" 2183051 T PMASS (NIL) -7 NIL NIL NIL) (-948 2181652 2181762 2181925 "PMASSFS" 2182266 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-947 2181307 2181375 2181469 "PLOTTOOL" 2181578 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-946 2175914 2177118 2178266 "PLOT" 2180179 T PLOT (NIL) -8 NIL NIL NIL) (-945 2171718 2172762 2173683 "PLOT3D" 2175013 T PLOT3D (NIL) -8 NIL NIL NIL) (-944 2170630 2170807 2171042 "PLOT1" 2171522 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-943 2146021 2150696 2155547 "PLEQN" 2165896 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-942 2145339 2145461 2145641 "PINTERP" 2145886 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-941 2145032 2145079 2145182 "PINTERPA" 2145286 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-940 2144248 2144796 2144883 "PI" 2144923 T PI (NIL) -8 NIL NIL 2144990) (-939 2142531 2143506 2143534 "PID" 2143716 T PID (NIL) -9 NIL 2143850 NIL) (-938 2142282 2142319 2142394 "PICOERCE" 2142488 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-937 2141602 2141741 2141917 "PGROEB" 2142138 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-936 2137189 2138003 2138908 "PGE" 2140717 T PGE (NIL) -7 NIL NIL NIL) (-935 2135312 2135559 2135925 "PGCD" 2136906 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-934 2134650 2134753 2134914 "PFRPAC" 2135196 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-933 2131290 2133198 2133551 "PFR" 2134329 NIL PFR (NIL T) -8 NIL NIL NIL) (-932 2129679 2129923 2130248 "PFOTOOLS" 2131037 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-931 2128212 2128451 2128802 "PFOQ" 2129436 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-930 2126713 2126925 2127281 "PFO" 2127996 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-929 2123266 2126602 2126671 "PF" 2126676 NIL PF (NIL NIL) -8 NIL NIL NIL) (-928 2120586 2121857 2121885 "PFECAT" 2122470 T PFECAT (NIL) -9 NIL 2122854 NIL) (-927 2120031 2120185 2120399 "PFECAT-" 2120404 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-926 2118634 2118886 2119187 "PFBRU" 2119780 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-925 2116500 2116852 2117284 "PFBR" 2118285 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-924 2112546 2114012 2114659 "PERM" 2115886 NIL PERM (NIL T) -8 NIL NIL NIL) (-923 2107780 2108753 2109623 "PERMGRP" 2111709 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-922 2105844 2106804 2106845 "PERMCAT" 2107245 NIL PERMCAT (NIL T) -9 NIL 2107543 NIL) (-921 2105497 2105538 2105662 "PERMAN" 2105797 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-920 2102988 2105162 2105284 "PENDTREE" 2105408 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-919 2101917 2102132 2102173 "PDSPC" 2102706 NIL PDSPC (NIL T) -9 NIL 2102951 NIL) (-918 2101020 2101238 2101600 "PDSPC-" 2101605 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-917 2099902 2100670 2100711 "PDRING" 2100716 NIL PDRING (NIL T) -9 NIL 2100744 NIL) (-916 2098789 2099407 2099461 "PDMOD" 2099466 NIL PDMOD (NIL T T) -9 NIL 2099570 NIL) (-915 2096004 2096782 2097450 "PDEPROB" 2098141 T PDEPROB (NIL) -8 NIL NIL NIL) (-914 2093549 2094053 2094608 "PDEPACK" 2095469 T PDEPACK (NIL) -7 NIL NIL NIL) (-913 2092461 2092651 2092902 "PDECOMP" 2093348 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-912 2090026 2090869 2090897 "PDECAT" 2091684 T PDECAT (NIL) -9 NIL 2092397 NIL) (-911 2089655 2089710 2089764 "PDDOM" 2089929 NIL PDDOM (NIL T T) -9 NIL 2090009 NIL) (-910 2089474 2089504 2089611 "PDDOM-" 2089616 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-909 2089225 2089258 2089348 "PCOMP" 2089435 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-908 2087403 2088026 2088323 "PBWLB" 2088954 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-907 2079876 2081476 2082814 "PATTERN" 2086086 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-906 2079508 2079565 2079674 "PATTERN2" 2079813 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-905 2077265 2077653 2078110 "PATTERN1" 2079097 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-904 2074633 2075214 2075695 "PATRES" 2076830 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-903 2074197 2074264 2074396 "PATRES2" 2074560 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-902 2072080 2072485 2072892 "PATMATCH" 2073864 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-901 2071576 2071785 2071826 "PATMAB" 2071933 NIL PATMAB (NIL T) -9 NIL 2072016 NIL) (-900 2070094 2070430 2070688 "PATLRES" 2071381 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-899 2069640 2069763 2069804 "PATAB" 2069809 NIL PATAB (NIL T) -9 NIL 2069981 NIL) (-898 2067822 2068217 2068640 "PARTPERM" 2069237 T PARTPERM (NIL) -7 NIL NIL NIL) (-897 2067443 2067506 2067608 "PARSURF" 2067753 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-896 2067075 2067132 2067241 "PARSU2" 2067380 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-895 2066839 2066879 2066946 "PARSER" 2067028 T PARSER (NIL) -7 NIL NIL NIL) (-894 2066460 2066523 2066625 "PARSCURV" 2066770 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-893 2066092 2066149 2066258 "PARSC2" 2066397 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-892 2065731 2065789 2065886 "PARPCURV" 2066028 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-891 2065363 2065420 2065529 "PARPC2" 2065668 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-890 2064424 2064736 2064918 "PARAMAST" 2065201 T PARAMAST (NIL) -8 NIL NIL NIL) (-889 2063944 2064030 2064149 "PAN2EXPR" 2064325 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-888 2062721 2063065 2063293 "PALETTE" 2063736 T PALETTE (NIL) -8 NIL NIL NIL) (-887 2061114 2061726 2062086 "PAIR" 2062407 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-886 2054706 2060371 2060566 "PADICRC" 2060968 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-885 2047622 2054050 2054235 "PADICRAT" 2054553 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-884 2045937 2047559 2047604 "PADIC" 2047609 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-883 2043033 2044597 2044637 "PADICCT" 2045218 NIL PADICCT (NIL NIL) -9 NIL 2045500 NIL) (-882 2041990 2042190 2042458 "PADEPAC" 2042820 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-881 2041202 2041335 2041541 "PADE" 2041852 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-880 2039589 2040410 2040690 "OWP" 2041006 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-879 2039082 2039295 2039392 "OVERSET" 2039512 T OVERSET (NIL) -8 NIL NIL NIL) (-878 2038128 2038687 2038859 "OVAR" 2038950 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-877 2037392 2037513 2037674 "OUT" 2037987 T OUT (NIL) -7 NIL NIL NIL) (-876 2026264 2028501 2030701 "OUTFORM" 2035212 T OUTFORM (NIL) -8 NIL NIL NIL) (-875 2025600 2025861 2025988 "OUTBFILE" 2026157 T OUTBFILE (NIL) -8 NIL NIL NIL) (-874 2024907 2025072 2025100 "OUTBCON" 2025418 T OUTBCON (NIL) -9 NIL 2025584 NIL) (-873 2024508 2024620 2024777 "OUTBCON-" 2024782 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-872 2023888 2024237 2024326 "OSI" 2024439 T OSI (NIL) -8 NIL NIL NIL) (-871 2023391 2023729 2023757 "OSGROUP" 2023762 T OSGROUP (NIL) -9 NIL 2023784 NIL) (-870 2022136 2022363 2022648 "ORTHPOL" 2023138 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-869 2019687 2021971 2022092 "OREUP" 2022097 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-868 2017090 2019378 2019505 "ORESUP" 2019629 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-867 2014618 2015118 2015679 "OREPCTO" 2016579 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-866 2008290 2010491 2010532 "OREPCAT" 2012880 NIL OREPCAT (NIL T) -9 NIL 2013984 NIL) (-865 2005437 2006219 2007277 "OREPCAT-" 2007282 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-864 2004684 2004907 2004935 "ORDTYPE" 2005244 T ORDTYPE (NIL) -9 NIL 2005407 NIL) (-863 2004027 2004201 2004456 "ORDTYPE-" 2004461 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-862 2003641 2003910 2003996 "ORDSTRCT" 2004001 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-861 2003211 2003509 2003537 "ORDSET" 2003542 T ORDSET (NIL) -9 NIL 2003564 NIL) (-860 2001749 2002540 2002568 "ORDRING" 2002770 T ORDRING (NIL) -9 NIL 2002895 NIL) (-859 2001394 2001488 2001632 "ORDRING-" 2001637 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 2000747 2001210 2001238 "ORDMON" 2001243 T ORDMON (NIL) -9 NIL 2001264 NIL) (-857 1999909 2000056 2000251 "ORDFUNS" 2000596 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1999220 1999639 1999667 "ORDFIN" 1999732 T ORDFIN (NIL) -9 NIL 1999806 NIL) (-855 1995779 1997806 1998215 "ORDCOMP" 1998844 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1995045 1995172 1995358 "ORDCOMP2" 1995639 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1991626 1992536 1993350 "OPTPROB" 1994251 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1988428 1989067 1989771 "OPTPACK" 1990942 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1986101 1986867 1986895 "OPTCAT" 1987714 T OPTCAT (NIL) -9 NIL 1988364 NIL) (-850 1985485 1985778 1985883 "OPSIG" 1986016 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1985253 1985292 1985358 "OPQUERY" 1985439 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1982384 1983564 1984068 "OP" 1984782 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1981744 1981970 1982011 "OPERCAT" 1982223 NIL OPERCAT (NIL T) -9 NIL 1982320 NIL) (-846 1981499 1981555 1981672 "OPERCAT-" 1981677 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1978312 1980296 1980665 "ONECOMP" 1981163 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1977617 1977732 1977906 "ONECOMP2" 1978184 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1977036 1977142 1977272 "OMSERVER" 1977507 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1973898 1976476 1976516 "OMSAGG" 1976577 NIL OMSAGG (NIL T) -9 NIL 1976641 NIL) (-841 1972521 1972784 1973066 "OMPKG" 1973636 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1971951 1972054 1972082 "OM" 1972381 T OM (NIL) -9 NIL NIL NIL) (-839 1970498 1971500 1971669 "OMLO" 1971832 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1969458 1969605 1969825 "OMEXPR" 1970324 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1968749 1969004 1969140 "OMERR" 1969342 T OMERR (NIL) -8 NIL NIL NIL) (-836 1967900 1968170 1968330 "OMERRK" 1968609 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1967351 1967577 1967685 "OMENC" 1967812 T OMENC (NIL) -8 NIL NIL NIL) (-834 1961246 1962431 1963602 "OMDEV" 1966200 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1960315 1960486 1960680 "OMCONN" 1961072 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1958809 1959785 1959813 "OINTDOM" 1959818 T OINTDOM (NIL) -9 NIL 1959839 NIL) (-831 1956147 1957497 1957834 "OFMONOID" 1958504 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1955519 1956084 1956129 "ODVAR" 1956134 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1952942 1955264 1955419 "ODR" 1955424 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1945247 1952718 1952844 "ODPOL" 1952849 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1939046 1945119 1945224 "ODP" 1945229 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1937812 1938027 1938302 "ODETOOLS" 1938820 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1934779 1935437 1936153 "ODESYS" 1937145 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1929661 1930569 1931594 "ODERTRIC" 1933854 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1929087 1929169 1929363 "ODERED" 1929573 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1925975 1926523 1927200 "ODERAT" 1928510 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1922934 1923399 1923996 "ODEPRRIC" 1925504 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1920877 1921473 1921959 "ODEPROB" 1922468 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1917397 1917882 1918529 "ODEPRIM" 1920356 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1916646 1916748 1917008 "ODEPAL" 1917289 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1912808 1913599 1914463 "ODEPACK" 1915802 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1911869 1911976 1912198 "ODEINT" 1912697 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1905970 1907395 1908842 "ODEIFTBL" 1910442 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1901368 1902154 1903106 "ODEEF" 1905129 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1900717 1900806 1901029 "ODECONST" 1901273 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1898828 1899489 1899517 "ODECAT" 1900122 T ODECAT (NIL) -9 NIL 1900653 NIL) (-811 1895683 1898533 1898655 "OCT" 1898738 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1895321 1895364 1895491 "OCTCT2" 1895634 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1889928 1892364 1892404 "OC" 1893501 NIL OC (NIL T) -9 NIL 1894359 NIL) (-808 1887155 1887903 1888893 "OC-" 1888987 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1886480 1886948 1886976 "OCAMON" 1886981 T OCAMON (NIL) -9 NIL 1887002 NIL) (-806 1885984 1886325 1886353 "OASGP" 1886358 T OASGP (NIL) -9 NIL 1886378 NIL) (-805 1885218 1885707 1885735 "OAMONS" 1885775 T OAMONS (NIL) -9 NIL 1885818 NIL) (-804 1884605 1885038 1885066 "OAMON" 1885071 T OAMON (NIL) -9 NIL 1885091 NIL) (-803 1883836 1884354 1884382 "OAGROUP" 1884387 T OAGROUP (NIL) -9 NIL 1884407 NIL) (-802 1883526 1883576 1883664 "NUMTUBE" 1883780 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1877099 1878617 1880153 "NUMQUAD" 1882010 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1872855 1873843 1874868 "NUMODE" 1876094 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1870196 1871076 1871104 "NUMINT" 1872027 T NUMINT (NIL) -9 NIL 1872791 NIL) (-798 1869144 1869341 1869559 "NUMFMT" 1869998 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1855503 1858448 1860980 "NUMERIC" 1866651 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1849873 1854952 1855047 "NTSCAT" 1855052 NIL NTSCAT (NIL T T T T) -9 NIL 1855091 NIL) (-795 1849067 1849232 1849425 "NTPOLFN" 1849712 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1836868 1845892 1846704 "NSUP" 1848288 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1836500 1836557 1836666 "NSUP2" 1836805 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1826450 1836274 1836407 "NSMP" 1836412 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1824882 1825183 1825540 "NREP" 1826138 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1823473 1823725 1824083 "NPCOEF" 1824625 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1822539 1822654 1822870 "NORMRETR" 1823354 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1820580 1820870 1821279 "NORMPK" 1822247 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1820265 1820293 1820417 "NORMMA" 1820546 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1820065 1820222 1820251 "NONE" 1820256 T NONE (NIL) -8 NIL NIL NIL) (-785 1819854 1819883 1819952 "NONE1" 1820029 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1819351 1819413 1819592 "NODE1" 1819786 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1817632 1818483 1818738 "NNI" 1819085 T NNI (NIL) -8 NIL NIL 1819320) (-782 1816052 1816365 1816729 "NLINSOL" 1817300 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1812293 1813288 1814187 "NIPROB" 1815173 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1811050 1811284 1811586 "NFINTBAS" 1812055 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1810224 1810700 1810741 "NETCLT" 1810913 NIL NETCLT (NIL T) -9 NIL 1810995 NIL) (-778 1808932 1809163 1809444 "NCODIV" 1809992 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1808694 1808731 1808806 "NCNTFRAC" 1808889 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1806874 1807238 1807658 "NCEP" 1808319 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1805711 1806484 1806512 "NASRING" 1806622 T NASRING (NIL) -9 NIL 1806702 NIL) (-774 1805506 1805550 1805644 "NASRING-" 1805649 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1804599 1805124 1805152 "NARNG" 1805269 T NARNG (NIL) -9 NIL 1805360 NIL) (-772 1804291 1804358 1804492 "NARNG-" 1804497 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1803170 1803377 1803612 "NAGSP" 1804076 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1794442 1796126 1797799 "NAGS" 1801517 T NAGS (NIL) -7 NIL NIL NIL) (-769 1792990 1793298 1793629 "NAGF07" 1794131 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1787528 1788819 1790126 "NAGF04" 1791703 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1780496 1782110 1783743 "NAGF02" 1785915 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1775720 1776820 1777937 "NAGF01" 1779399 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1769348 1770914 1772499 "NAGE04" 1774155 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1760517 1762638 1764768 "NAGE02" 1767238 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1756470 1757417 1758381 "NAGE01" 1759573 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1754265 1754799 1755357 "NAGD03" 1755932 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1746015 1747943 1749897 "NAGD02" 1752331 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1739826 1741251 1742691 "NAGD01" 1744595 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1736035 1736857 1737694 "NAGC06" 1739009 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1734500 1734832 1735188 "NAGC05" 1735699 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1733876 1733995 1734139 "NAGC02" 1734376 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1732821 1733404 1733444 "NAALG" 1733523 NIL NAALG (NIL T) -9 NIL 1733584 NIL) (-755 1732656 1732685 1732775 "NAALG-" 1732780 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1726606 1727714 1728901 "MULTSQFR" 1731552 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1725925 1726000 1726184 "MULTFACT" 1726518 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1718596 1722510 1722563 "MTSCAT" 1723633 NIL MTSCAT (NIL T T) -9 NIL 1724148 NIL) (-751 1718308 1718362 1718454 "MTHING" 1718536 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1718100 1718133 1718193 "MSYSCMD" 1718268 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1714182 1716855 1717175 "MSET" 1717813 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1711251 1713743 1713784 "MSETAGG" 1713789 NIL MSETAGG (NIL T) -9 NIL 1713823 NIL) (-747 1707093 1708630 1709375 "MRING" 1710551 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1706659 1706726 1706857 "MRF2" 1707020 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1706277 1706312 1706456 "MRATFAC" 1706618 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1703889 1704184 1704615 "MPRFF" 1705982 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1697910 1703743 1703840 "MPOLY" 1703845 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1697400 1697435 1697643 "MPCPF" 1697869 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1696914 1696957 1697141 "MPC3" 1697351 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1696109 1696190 1696411 "MPC2" 1696829 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1694410 1694747 1695137 "MONOTOOL" 1695769 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1693621 1693938 1693966 "MONOID" 1694185 T MONOID (NIL) -9 NIL 1694332 NIL) (-737 1693167 1693286 1693467 "MONOID-" 1693472 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1682757 1688987 1689046 "MONOGEN" 1689720 NIL MONOGEN (NIL T T) -9 NIL 1690176 NIL) (-735 1679975 1680710 1681710 "MONOGEN-" 1681829 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1678794 1679240 1679268 "MONADWU" 1679660 T MONADWU (NIL) -9 NIL 1679898 NIL) (-733 1678166 1678325 1678573 "MONADWU-" 1678578 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1677511 1677755 1677783 "MONAD" 1677990 T MONAD (NIL) -9 NIL 1678102 NIL) (-731 1677196 1677274 1677406 "MONAD-" 1677411 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1675485 1676109 1676388 "MOEBIUS" 1676949 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1674749 1675153 1675193 "MODULE" 1675198 NIL MODULE (NIL T) -9 NIL 1675237 NIL) (-728 1674317 1674413 1674603 "MODULE-" 1674608 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1671997 1672681 1673008 "MODRING" 1674141 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1668941 1670102 1670623 "MODOP" 1671526 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1667529 1668008 1668285 "MODMONOM" 1668804 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1657297 1665820 1666234 "MODMON" 1667166 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1654453 1656141 1656417 "MODFIELD" 1657172 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1653430 1653734 1653924 "MMLFORM" 1654283 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1652956 1652999 1653178 "MMAP" 1653381 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1651021 1651788 1651829 "MLO" 1652252 NIL MLO (NIL T) -9 NIL 1652494 NIL) (-719 1648387 1648903 1649505 "MLIFT" 1650502 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1647778 1647862 1648016 "MKUCFUNC" 1648298 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1647377 1647447 1647570 "MKRECORD" 1647701 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1646424 1646586 1646814 "MKFUNC" 1647188 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1645812 1645916 1646072 "MKFLCFN" 1646307 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1645089 1645191 1645376 "MKBCFUNC" 1645705 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1641678 1644643 1644779 "MINT" 1644973 T MINT (NIL) -8 NIL NIL NIL) (-712 1640490 1640733 1641010 "MHROWRED" 1641433 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1635870 1639025 1639430 "MFLOAT" 1640105 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1635227 1635303 1635474 "MFINFACT" 1635782 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1631542 1632390 1633274 "MESH" 1634363 T MESH (NIL) -7 NIL NIL NIL) (-708 1629932 1630244 1630597 "MDDFACT" 1631229 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1626702 1629063 1629104 "MDAGG" 1629359 NIL MDAGG (NIL T) -9 NIL 1629502 NIL) (-706 1615396 1625995 1626202 "MCMPLX" 1626515 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1614533 1614679 1614880 "MCDEN" 1615245 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1612423 1612693 1613073 "MCALCFN" 1614263 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1611348 1611588 1611821 "MAYBE" 1612229 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1608960 1609483 1610045 "MATSTOR" 1610819 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1604872 1608332 1608580 "MATRIX" 1608745 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1600638 1601345 1602081 "MATLIN" 1604229 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1590464 1593695 1593772 "MATCAT" 1598804 NIL MATCAT (NIL T T T) -9 NIL 1600276 NIL) (-698 1586657 1587727 1589140 "MATCAT-" 1589145 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1585251 1585404 1585737 "MATCAT2" 1586492 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1583363 1583687 1584071 "MAPPKG3" 1584926 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1582344 1582517 1582739 "MAPPKG2" 1583187 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1580843 1581127 1581454 "MAPPKG1" 1582050 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1579922 1580249 1580426 "MAPPAST" 1580686 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1579533 1579591 1579714 "MAPHACK3" 1579858 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1579125 1579186 1579300 "MAPHACK2" 1579465 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1578563 1578666 1578808 "MAPHACK1" 1579016 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1576642 1577263 1577567 "MAGMA" 1578291 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1576121 1576366 1576457 "MACROAST" 1576571 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1572542 1574360 1574821 "M3D" 1575693 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1566592 1570853 1570894 "LZSTAGG" 1571676 NIL LZSTAGG (NIL T) -9 NIL 1571971 NIL) (-685 1562550 1563723 1565180 "LZSTAGG-" 1565185 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1559637 1560441 1560928 "LWORD" 1562095 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1559213 1559441 1559516 "LSTAST" 1559582 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1552103 1558984 1559118 "LSQM" 1559123 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1551327 1551466 1551694 "LSPP" 1551958 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1549139 1549440 1549896 "LSMP" 1551016 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1545918 1546592 1547322 "LSMP1" 1548441 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1539720 1545008 1545049 "LSAGG" 1545111 NIL LSAGG (NIL T) -9 NIL 1545189 NIL) (-677 1536415 1537339 1538552 "LSAGG-" 1538557 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1534014 1535559 1535808 "LPOLY" 1536210 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1533596 1533681 1533804 "LPEFRAC" 1533923 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1531917 1532690 1532943 "LO" 1533428 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1531529 1531667 1531695 "LOGIC" 1531806 T LOGIC (NIL) -9 NIL 1531887 NIL) (-672 1531391 1531414 1531485 "LOGIC-" 1531490 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1530584 1530724 1530917 "LODOOPS" 1531247 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1528007 1530500 1530566 "LODO" 1530571 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1526545 1526780 1527133 "LODOF" 1527754 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1522749 1525180 1525221 "LODOCAT" 1525659 NIL LODOCAT (NIL T) -9 NIL 1525870 NIL) (-667 1522482 1522540 1522667 "LODOCAT-" 1522672 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1519802 1522323 1522441 "LODO2" 1522446 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1517237 1519739 1519784 "LODO1" 1519789 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1516118 1516283 1516588 "LODEEF" 1517060 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1511396 1514284 1514325 "LNAGG" 1515187 NIL LNAGG (NIL T) -9 NIL 1515622 NIL) (-662 1510543 1510757 1511099 "LNAGG-" 1511104 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1506679 1507468 1508107 "LMOPS" 1509958 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1506068 1506456 1506497 "LMODULE" 1506502 NIL LMODULE (NIL T) -9 NIL 1506528 NIL) (-659 1503269 1505713 1505836 "LMDICT" 1505978 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1502887 1503059 1503100 "LLINSET" 1503161 NIL LLINSET (NIL T) -9 NIL 1503205 NIL) (-657 1502586 1502795 1502855 "LITERAL" 1502860 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1495752 1501520 1501824 "LIST" 1502315 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1495277 1495351 1495490 "LIST3" 1495672 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1494284 1494462 1494690 "LIST2" 1495095 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1492418 1492730 1493129 "LIST2MAP" 1493931 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1492049 1492237 1492278 "LINSET" 1492283 NIL LINSET (NIL T) -9 NIL 1492317 NIL) (-651 1490462 1491076 1491117 "LINEXP" 1491607 NIL LINEXP (NIL T) -9 NIL 1491880 NIL) (-650 1489039 1489299 1489610 "LINDEP" 1490214 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485806 1486525 1487302 "LIMITRF" 1488294 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1484109 1484405 1484814 "LIMITPS" 1485501 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1478537 1483620 1483848 "LIE" 1483930 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1477471 1477940 1477980 "LIECAT" 1478120 NIL LIECAT (NIL T) -9 NIL 1478271 NIL) (-645 1477312 1477339 1477427 "LIECAT-" 1477432 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469905 1476852 1477008 "LIB" 1477176 T LIB (NIL) -8 NIL NIL NIL) (-643 1465540 1466423 1467358 "LGROBP" 1469022 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1463538 1463812 1464162 "LF" 1465261 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1462378 1463070 1463098 "LFCAT" 1463305 T LFCAT (NIL) -9 NIL 1463444 NIL) (-640 1459280 1459910 1460598 "LEXTRIPK" 1461742 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1456024 1456850 1457353 "LEXP" 1458860 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1455500 1455745 1455837 "LETAST" 1455952 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453898 1454211 1454612 "LEADCDET" 1455182 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1453088 1453162 1453391 "LAZM3PK" 1453819 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1448005 1451165 1451703 "LAUPOL" 1452600 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1447584 1447628 1447789 "LAPLACE" 1447955 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1445523 1446685 1446936 "LA" 1447417 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1444503 1445087 1445128 "LALG" 1445190 NIL LALG (NIL T) -9 NIL 1445249 NIL) (-631 1444217 1444276 1444412 "LALG-" 1444417 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1444052 1444076 1444117 "KVTFROM" 1444179 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442975 1443419 1443604 "KTVLOGIC" 1443887 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442810 1442834 1442875 "KRCFROM" 1442937 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441714 1441901 1442200 "KOVACIC" 1442610 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1441549 1441573 1441614 "KONVERT" 1441676 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1441384 1441408 1441449 "KOERCE" 1441511 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1439215 1439977 1440354 "KERNEL" 1441040 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438711 1438792 1438924 "KERNEL2" 1439129 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1432422 1437188 1437242 "KDAGG" 1437619 NIL KDAGG (NIL T T) -9 NIL 1437825 NIL) (-621 1431951 1432075 1432280 "KDAGG-" 1432285 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1425099 1431612 1431767 "KAFILE" 1431829 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1419527 1424610 1424838 "JORDAN" 1424920 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418906 1419176 1419297 "JOINAST" 1419426 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418752 1418811 1418866 "JAVACODE" 1418871 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414979 1416929 1416983 "IXAGG" 1417912 NIL IXAGG (NIL T T) -9 NIL 1418371 NIL) (-615 1413898 1414204 1414623 "IXAGG-" 1414628 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1409431 1413820 1413879 "IVECTOR" 1413884 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1408197 1408434 1408700 "ITUPLE" 1409198 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406699 1406876 1407171 "ITRIGMNP" 1408019 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1405444 1405648 1405931 "ITFUN3" 1406475 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1405076 1405133 1405242 "ITFUN2" 1405381 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1404235 1404556 1404730 "ITFORM" 1404922 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1402196 1403255 1403533 "ITAYLOR" 1403990 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1391141 1396333 1397496 "ISUPS" 1401066 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1390245 1390385 1390621 "ISUMP" 1390988 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385623 1390190 1390231 "ISTRING" 1390236 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1385099 1385344 1385436 "ISAST" 1385551 T ISAST (NIL) -8 NIL NIL NIL) (-603 1384308 1384390 1384606 "IRURPK" 1385013 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1383244 1383445 1383685 "IRSN" 1384088 T IRSN (NIL) -7 NIL NIL NIL) (-601 1381315 1381670 1382099 "IRRF2F" 1382882 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1381062 1381100 1381176 "IRREDFFX" 1381271 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379677 1379936 1380235 "IROOT" 1380795 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1376281 1377361 1378053 "IR" 1379017 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1375486 1375774 1375925 "IRFORM" 1376150 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1373099 1373594 1374160 "IR2" 1374964 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1372199 1372312 1372526 "IR2F" 1372982 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371990 1372024 1372084 "IPRNTPK" 1372159 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1368571 1371879 1371948 "IPF" 1371953 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366898 1368496 1368553 "IPADIC" 1368558 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1366210 1366458 1366588 "IP4ADDR" 1366788 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365584 1365839 1365971 "IOMODE" 1366098 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364657 1365181 1365308 "IOBFILE" 1365477 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1364145 1364561 1364589 "IOBCON" 1364594 T IOBCON (NIL) -9 NIL 1364615 NIL) (-587 1363656 1363714 1363897 "INVLAPLA" 1364081 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1353304 1355658 1358044 "INTTR" 1361320 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349639 1350381 1351246 "INTTOOLS" 1352489 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1349225 1349316 1349433 "INTSLPE" 1349542 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1347178 1349148 1349207 "INTRVL" 1349212 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344780 1345292 1345867 "INTRF" 1346663 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1344191 1344288 1344430 "INTRET" 1344678 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1342188 1342577 1343047 "INTRAT" 1343799 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1339451 1340034 1340653 "INTPM" 1341673 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1336196 1336795 1337533 "INTPAF" 1338837 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1331375 1332337 1333388 "INTPACK" 1335165 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1328187 1331172 1331281 "INT" 1331286 T INT (NIL) -8 NIL NIL NIL) (-575 1327439 1327591 1327799 "INTHERTR" 1328029 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326878 1326958 1327146 "INTHERAL" 1327353 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324724 1325167 1325624 "INTHEORY" 1326441 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1316130 1317751 1319523 "INTG0" 1323076 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296703 1301493 1306303 "INTFTBL" 1311340 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295952 1296090 1296263 "INTFACT" 1296562 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1293379 1293825 1294382 "INTEF" 1295506 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291732 1292471 1292499 "INTDOM" 1292800 T INTDOM (NIL) -9 NIL 1293007 NIL) (-567 1291101 1291275 1291517 "INTDOM-" 1291522 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1287461 1289390 1289444 "INTCAT" 1290243 NIL INTCAT (NIL T) -9 NIL 1290564 NIL) (-565 1286933 1287036 1287164 "INTBIT" 1287353 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285632 1285786 1286093 "INTALG" 1286778 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1285115 1285205 1285362 "INTAF" 1285536 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1278464 1284925 1285065 "INTABL" 1285070 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277797 1278263 1278328 "INT8" 1278362 T INT8 (NIL) -8 NIL NIL 1278407) (-560 1277129 1277595 1277660 "INT64" 1277694 T INT64 (NIL) -8 NIL NIL 1277739) (-559 1276461 1276927 1276992 "INT32" 1277026 T INT32 (NIL) -8 NIL NIL 1277071) (-558 1275793 1276259 1276324 "INT16" 1276358 T INT16 (NIL) -8 NIL NIL 1276403) (-557 1270488 1273341 1273369 "INS" 1274303 T INS (NIL) -9 NIL 1274968 NIL) (-556 1267728 1268499 1269473 "INS-" 1269546 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1266503 1266730 1267028 "INPSIGN" 1267481 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265621 1265738 1265935 "INPRODPF" 1266383 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264515 1264632 1264869 "INPRODFF" 1265501 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263515 1263667 1263927 "INNMFACT" 1264351 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262712 1262809 1262997 "INMODGCD" 1263414 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1261220 1261465 1261789 "INFSP" 1262457 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1260404 1260521 1260704 "INFPROD0" 1261100 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1257259 1258469 1258984 "INFORM" 1259897 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256869 1256929 1257027 "INFORM1" 1257194 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1256392 1256481 1256595 "INFINITY" 1256775 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255568 1256112 1256213 "INETCLTS" 1256311 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1254184 1254434 1254755 "INEP" 1255316 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1253389 1254081 1254146 "INDE" 1254151 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252953 1253021 1253138 "INCRMAPS" 1253316 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251771 1252222 1252428 "INBFILE" 1252767 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1247070 1248007 1248951 "INBFF" 1250859 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245978 1246247 1246275 "INBCON" 1246788 T INBCON (NIL) -9 NIL 1247054 NIL) (-538 1245230 1245453 1245729 "INBCON-" 1245734 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244709 1244954 1245045 "INAST" 1245159 T INAST (NIL) -8 NIL NIL NIL) (-536 1244136 1244388 1244494 "IMPTAST" 1244623 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240537 1243980 1244084 "IMATRIX" 1244089 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1239245 1239368 1239684 "IMATQF" 1240393 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1237465 1237692 1238029 "IMATLIN" 1239001 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1232046 1237389 1237447 "ILIST" 1237452 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229954 1231906 1232019 "IIARRAY2" 1232024 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1225352 1229865 1229929 "IFF" 1229934 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224699 1224969 1225085 "IFAST" 1225256 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219697 1223991 1224179 "IFARRAY" 1224556 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218877 1219601 1219674 "IFAMON" 1219679 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1218461 1218526 1218580 "IEVALAB" 1218787 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1218136 1218204 1218364 "IEVALAB-" 1218369 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217472 1217837 1217955 "IDPO" 1218063 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216680 1217361 1217436 "IDPOAMS" 1217441 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215945 1216569 1216644 "IDPOAM" 1216649 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214802 1215119 1215172 "IDPC" 1215690 NIL IDPC (NIL T T) -9 NIL 1215881 NIL) (-520 1213990 1214495 1214617 "IDPAM" 1214723 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213324 1213882 1213955 "IDPAG" 1213960 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212969 1213160 1213235 "IDENT" 1213269 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209224 1210072 1210967 "IDECOMP" 1212126 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202061 1203147 1204194 "IDEAL" 1208260 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201221 1201333 1201533 "ICDEN" 1201945 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200292 1200701 1200848 "ICARD" 1201094 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198352 1198665 1199070 "IBPTOOLS" 1199969 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193959 1197972 1198085 "IBITS" 1198271 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190682 1191258 1191953 "IBATOOL" 1193376 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188461 1188923 1189456 "IBACHIN" 1190217 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186293 1188307 1188410 "IARRAY2" 1188415 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182402 1186219 1186276 "IARRAY1" 1186281 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176262 1180814 1181295 "IAN" 1181941 T IAN (NIL) -8 NIL NIL NIL) (-506 1175773 1175830 1176003 "IALGFACT" 1176199 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175301 1175414 1175442 "HYPCAT" 1175649 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174839 1174956 1175142 "HYPCAT-" 1175147 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174434 1174634 1174717 "HOSTNAME" 1174776 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174279 1174316 1174357 "HOMOTOP" 1174362 NIL HOMOTOP (NIL T) -9 NIL 1174395 NIL) (-501 1170836 1172211 1172252 "HOAGG" 1173233 NIL HOAGG (NIL T) -9 NIL 1173962 NIL) (-500 1169430 1169829 1170355 "HOAGG-" 1170360 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163146 1169023 1169173 "HEXADEC" 1169300 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161894 1162116 1162379 "HEUGCD" 1162923 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160970 1161731 1161861 "HELLFDIV" 1161866 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159152 1160747 1160835 "HEAP" 1160914 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158415 1158704 1158838 "HEADAST" 1159038 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152258 1158330 1158392 "HDP" 1158397 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145970 1151893 1152045 "HDMP" 1152159 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145294 1145434 1145598 "HB" 1145826 T HB (NIL) -7 NIL NIL NIL) (-491 1138686 1145140 1145244 "HASHTBL" 1145249 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138162 1138407 1138499 "HASAST" 1138614 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135940 1137784 1137966 "HACKPI" 1138000 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131608 1135793 1135906 "GTSET" 1135911 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125029 1131486 1131584 "GSTBL" 1131589 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117416 1124194 1124450 "GSERIES" 1124829 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116543 1116960 1116988 "GROUP" 1117191 T GROUP (NIL) -9 NIL 1117325 NIL) (-484 1115909 1116068 1116319 "GROUP-" 1116324 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114276 1114597 1114984 "GROEBSOL" 1115586 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113176 1113464 1113515 "GRMOD" 1114044 NIL GRMOD (NIL T T) -9 NIL 1114212 NIL) (-481 1112944 1112980 1113108 "GRMOD-" 1113113 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108234 1109298 1110298 "GRIMAGE" 1111964 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106700 1106961 1107285 "GRDEF" 1107930 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106144 1106260 1106401 "GRAY" 1106579 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105317 1105723 1105774 "GRALG" 1105927 NIL GRALG (NIL T T) -9 NIL 1106020 NIL) (-476 1104978 1105051 1105214 "GRALG-" 1105219 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101755 1104563 1104741 "GPOLSET" 1104885 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101109 1101166 1101424 "GOSPER" 1101692 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096841 1097547 1098073 "GMODPOL" 1100808 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095846 1096030 1096268 "GHENSEL" 1096653 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090002 1090845 1091865 "GENUPS" 1094930 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089699 1089750 1089839 "GENUFACT" 1089945 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089111 1089188 1089353 "GENPGCD" 1089617 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088585 1088620 1088833 "GENMFACT" 1089070 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087151 1087408 1087715 "GENEEZ" 1088328 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081023 1086762 1086924 "GDMP" 1087074 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070366 1074794 1075900 "GCNAALG" 1080006 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068679 1069541 1069569 "GCDDOM" 1069824 T GCDDOM (NIL) -9 NIL 1069981 NIL) (-463 1068149 1068276 1068491 "GCDDOM-" 1068496 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066821 1067006 1067310 "GB" 1067928 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1055437 1057767 1060159 "GBINTERN" 1064512 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053274 1053566 1053987 "GBF" 1055112 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052055 1052220 1052487 "GBEUCLID" 1053090 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1051404 1051529 1051678 "GAUSSFAC" 1051926 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049771 1050073 1050387 "GALUTIL" 1051123 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048079 1048353 1048677 "GALPOLYU" 1049498 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1045444 1045734 1046141 "GALFACTU" 1047776 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037250 1038749 1040357 "GALFACT" 1043876 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034638 1035296 1035324 "FVFUN" 1036480 T FVFUN (NIL) -9 NIL 1037200 NIL) (-452 1033904 1034086 1034114 "FVC" 1034405 T FVC (NIL) -9 NIL 1034588 NIL) (-451 1033547 1033729 1033797 "FUNDESC" 1033856 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033162 1033344 1033425 "FUNCTION" 1033499 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030906 1031484 1031950 "FT" 1032716 T FT (NIL) -8 NIL NIL NIL) (-448 1029697 1030207 1030410 "FTEM" 1030723 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027988 1028277 1028674 "FSUPFACT" 1029388 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1026385 1026674 1027006 "FST" 1027676 T FST (NIL) -8 NIL NIL NIL) (-445 1025584 1025690 1025878 "FSRED" 1026267 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024283 1024539 1024886 "FSPRMELT" 1025299 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021589 1022027 1022513 "FSPECF" 1023846 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002654 1011363 1011404 "FS" 1015288 NIL FS (NIL T) -9 NIL 1017577 NIL) (-441 991297 994290 998347 "FS-" 998647 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990825 990879 991049 "FSINT" 991238 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989117 989818 990121 "FSERIES" 990604 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988159 988275 988499 "FSCINT" 988997 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 984367 987103 987144 "FSAGG" 987514 NIL FSAGG (NIL T) -9 NIL 987773 NIL) (-436 982129 982730 983526 "FSAGG-" 983621 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981171 981314 981541 "FSAGG2" 981982 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978849 979129 979677 "FS2UPS" 980889 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 978483 978526 978655 "FS2" 978800 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977361 977532 977834 "FS2EXPXP" 978308 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976787 976902 977054 "FRUTIL" 977241 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968200 972282 973640 "FR" 975461 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963214 965889 965929 "FRNAALG" 967249 NIL FRNAALG (NIL T) -9 NIL 967847 NIL) (-428 958887 959963 961238 "FRNAALG-" 961988 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958525 958568 958695 "FRNAAF2" 958838 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956900 957374 957670 "FRMOD" 958337 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954643 955275 955593 "FRIDEAL" 956691 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953834 953921 954212 "FRIDEAL2" 954550 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952967 953381 953422 "FRETRCT" 953427 NIL FRETRCT (NIL T) -9 NIL 953603 NIL) (-422 952079 952310 952661 "FRETRCT-" 952666 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949153 950363 950422 "FRAMALG" 951304 NIL FRAMALG (NIL T T) -9 NIL 951596 NIL) (-420 947287 947742 948372 "FRAMALG-" 948595 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940930 946760 947037 "FRAC" 947042 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940566 940623 940730 "FRAC2" 940867 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940202 940259 940366 "FR2" 940503 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934687 937581 937609 "FPS" 938728 T FPS (NIL) -9 NIL 939285 NIL) (-415 934136 934245 934409 "FPS-" 934555 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 931424 933093 933121 "FPC" 933346 T FPC (NIL) -9 NIL 933488 NIL) (-413 931217 931257 931354 "FPC-" 931359 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930007 930705 930746 "FPATMAB" 930751 NIL FPATMAB (NIL T) -9 NIL 930903 NIL) (-411 928246 928749 929096 "FPARFRAC" 929723 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923640 924138 924820 "FORTRAN" 927678 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 921356 921856 922395 "FORT" 923121 T FORT (NIL) -7 NIL NIL NIL) (-408 919032 919594 919622 "FORTFN" 920682 T FORTFN (NIL) -9 NIL 921306 NIL) (-407 918796 918846 918874 "FORTCAT" 918933 T FORTCAT (NIL) -9 NIL 918995 NIL) (-406 916902 917412 917802 "FORMULA" 918426 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916690 916720 916789 "FORMULA1" 916866 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916213 916265 916438 "FORDER" 916632 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 915309 915473 915666 "FOP" 916040 T FOP (NIL) -7 NIL NIL NIL) (-402 913890 914589 914763 "FNLA" 915191 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912605 913020 913048 "FNCAT" 913508 T FNCAT (NIL) -9 NIL 913768 NIL) (-400 912144 912564 912592 "FNAME" 912597 T FNAME (NIL) -8 NIL NIL NIL) (-399 910680 911643 911671 "FMTC" 911676 T FMTC (NIL) -9 NIL 911712 NIL) (-398 909426 910616 910662 "FMONOID" 910667 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906213 907381 907422 "FMONCAT" 908639 NIL FMONCAT (NIL T) -9 NIL 909244 NIL) (-396 905363 905955 906104 "FM" 906109 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902787 903433 903461 "FMFUN" 904605 T FMFUN (NIL) -9 NIL 905313 NIL) (-394 902056 902237 902265 "FMC" 902555 T FMC (NIL) -9 NIL 902737 NIL) (-393 899121 899981 900035 "FMCAT" 901230 NIL FMCAT (NIL T T) -9 NIL 901725 NIL) (-392 897987 898887 898987 "FM1" 899066 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895761 896177 896671 "FLOATRP" 897538 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 889339 893490 894111 "FLOAT" 895160 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886777 887277 887855 "FLOATCP" 888806 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 885425 886369 886410 "FLINEXP" 886415 NIL FLINEXP (NIL T) -9 NIL 886508 NIL) (-387 884579 884814 885142 "FLINEXP-" 885147 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883655 883799 884023 "FLASORT" 884431 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880757 881625 881677 "FLALG" 882904 NIL FLALG (NIL T T) -9 NIL 883371 NIL) (-384 874417 878166 878207 "FLAGG" 879469 NIL FLAGG (NIL T) -9 NIL 880121 NIL) (-383 873143 873482 873972 "FLAGG-" 873977 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872185 872328 872555 "FLAGG2" 872996 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869022 870030 870089 "FINRALG" 871217 NIL FINRALG (NIL T T) -9 NIL 871725 NIL) (-380 868182 868411 868750 "FINRALG-" 868755 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867548 867787 867815 "FINITE" 868011 T FINITE (NIL) -9 NIL 868118 NIL) (-378 859891 862078 862118 "FINAALG" 865785 NIL FINAALG (NIL T) -9 NIL 867238 NIL) (-377 855223 856273 857417 "FINAALG-" 858796 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854591 854978 855081 "FILE" 855153 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853235 853573 853627 "FILECAT" 854311 NIL FILECAT (NIL T T) -9 NIL 854527 NIL) (-374 850937 852465 852493 "FIELD" 852533 T FIELD (NIL) -9 NIL 852613 NIL) (-373 849557 849942 850453 "FIELD-" 850458 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847407 848192 848539 "FGROUP" 849243 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846497 846661 846881 "FGLMICPK" 847239 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842329 846422 846479 "FFX" 846484 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841930 841991 842126 "FFSLPE" 842262 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837920 838702 839498 "FFPOLY" 841166 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837424 837460 837669 "FFPOLY2" 837878 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833270 837343 837406 "FFP" 837411 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828668 833181 833245 "FF" 833250 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823794 828011 828201 "FFNBX" 828522 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818722 822929 823187 "FFNBP" 823648 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813355 818006 818217 "FFNB" 818555 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812187 812385 812700 "FFINTBAS" 813152 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808213 810434 810462 "FFIELDC" 811082 T FFIELDC (NIL) -9 NIL 811458 NIL) (-359 806875 807246 807743 "FFIELDC-" 807748 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806444 806490 806614 "FFHOM" 806817 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804139 804626 805143 "FFF" 805959 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799757 803881 803982 "FFCGX" 804082 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795379 799489 799596 "FFCGP" 799700 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790562 795106 795214 "FFCG" 795315 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770091 780294 780380 "FFCAT" 785545 NIL FFCAT (NIL T T T) -9 NIL 786996 NIL) (-352 765288 766336 767650 "FFCAT-" 768880 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764699 764742 764977 "FFCAT2" 765239 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754022 757671 758891 "FEXPR" 763551 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752984 753419 753460 "FEVALAB" 753544 NIL FEVALAB (NIL T) -9 NIL 753805 NIL) (-348 752143 752353 752691 "FEVALAB-" 752696 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750709 751526 751729 "FDIV" 752042 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747715 748456 748571 "FDIVCAT" 750139 NIL FDIVCAT (NIL T T T T) -9 NIL 750576 NIL) (-345 747477 747504 747674 "FDIVCAT-" 747679 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746697 746784 747061 "FDIV2" 747384 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745671 745992 746194 "FCTRDATA" 746515 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744357 744616 744905 "FCPAK1" 745402 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743456 743857 743998 "FCOMP" 744248 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727161 730606 734144 "FC" 739938 T FC (NIL) -8 NIL NIL NIL) (-339 719454 723482 723522 "FAXF" 725324 NIL FAXF (NIL T) -9 NIL 726016 NIL) (-338 716731 717388 718213 "FAXF-" 718678 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711786 716107 716283 "FARRAY" 716588 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706666 708733 708786 "FAMR" 709809 NIL FAMR (NIL T T) -9 NIL 710269 NIL) (-335 705556 705858 706293 "FAMR-" 706298 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704725 705478 705531 "FAMONOID" 705536 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702497 703207 703260 "FAMONC" 704201 NIL FAMONC (NIL T T) -9 NIL 704587 NIL) (-332 701161 702251 702388 "FAGROUP" 702393 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698956 699275 699678 "FACUTIL" 700842 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698055 698240 698462 "FACTFUNC" 698766 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690477 697358 697557 "EXPUPXS" 697911 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687960 688500 689086 "EXPRTUBE" 689911 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684231 684823 685553 "EXPRODE" 687299 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669715 682880 683309 "EXPR" 683835 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664269 664856 665662 "EXPR2UPS" 669013 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663901 663958 664067 "EXPR2" 664206 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654898 663052 663343 "EXPEXPAN" 663737 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654698 654855 654884 "EXIT" 654889 T EXIT (NIL) -8 NIL NIL NIL) (-321 654178 654422 654513 "EXITAST" 654627 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653805 653867 653980 "EVALCYC" 654110 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653346 653464 653505 "EVALAB" 653675 NIL EVALAB (NIL T) -9 NIL 653779 NIL) (-318 652827 652949 653170 "EVALAB-" 653175 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650181 651483 651511 "EUCDOM" 652066 T EUCDOM (NIL) -9 NIL 652416 NIL) (-316 648586 649028 649618 "EUCDOM-" 649623 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636125 638884 641634 "ESTOOLS" 645856 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635757 635814 635923 "ESTOOLS2" 636062 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635508 635550 635630 "ESTOOLS1" 635709 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629531 631139 631167 "ES" 633935 T ES (NIL) -9 NIL 635345 NIL) (-311 624478 625765 627582 "ES-" 627746 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620852 621613 622393 "ESCONT" 623718 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620597 620629 620711 "ESCONT1" 620814 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620272 620322 620422 "ES2" 620541 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619902 619960 620069 "ES1" 620208 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619118 619247 619423 "ERROR" 619746 T ERROR (NIL) -7 NIL NIL NIL) (-305 612516 618977 619068 "EQTBL" 619073 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605019 607830 609279 "EQ" 611100 NIL -2037 (NIL T) -8 NIL NIL NIL) (-303 604651 604708 604817 "EQ2" 604956 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599942 600989 602082 "EP" 603590 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598542 598833 599139 "ENV" 599656 T ENV (NIL) -8 NIL NIL NIL) (-300 597622 598176 598204 "ENTIRER" 598209 T ENTIRER (NIL) -9 NIL 598255 NIL) (-299 594316 595804 596165 "EMR" 597430 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593446 593631 593685 "ELTAGG" 594065 NIL ELTAGG (NIL T T) -9 NIL 594276 NIL) (-297 593165 593227 593368 "ELTAGG-" 593373 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592929 592958 593012 "ELTAB" 593096 NIL ELTAB (NIL T T) -9 NIL 593148 NIL) (-295 592055 592201 592400 "ELFUTS" 592780 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591797 591853 591881 "ELEMFUN" 591986 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591667 591688 591756 "ELEMFUN-" 591761 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586456 589709 589750 "ELAGG" 590690 NIL ELAGG (NIL T) -9 NIL 591153 NIL) (-291 584741 585175 585838 "ELAGG-" 585843 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584053 584190 584346 "ELABOR" 584605 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582714 582993 583287 "ELABEXPR" 583779 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575548 577351 578180 "EFUPXS" 581989 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568996 570797 571608 "EFULS" 574823 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566481 566839 567311 "EFSTRUC" 568628 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556272 557838 559386 "EF" 564996 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555346 555757 555906 "EAB" 556143 T EAB (NIL) -8 NIL NIL NIL) (-283 554528 555305 555333 "E04UCFA" 555338 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553710 554487 554515 "E04NAFA" 554520 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552892 553669 553697 "E04MBFA" 553702 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552074 552851 552879 "E04JAFA" 552884 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551258 552033 552061 "E04GCFA" 552066 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550442 551217 551245 "E04FDFA" 551250 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549624 550401 550429 "E04DGFA" 550434 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543797 545149 546513 "E04AGNT" 548280 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542555 543098 543138 "DVARCAT" 543479 NIL DVARCAT (NIL T) -9 NIL 543642 NIL) (-274 541759 541971 542285 "DVARCAT-" 542290 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534620 541558 541687 "DSMP" 541692 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533043 533762 533803 "DSEXT" 534166 NIL DSEXT (NIL T) -9 NIL 534460 NIL) (-271 531328 531756 532422 "DSEXT-" 532427 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526109 527273 528341 "DROPT" 530280 T DROPT (NIL) -8 NIL NIL NIL) (-269 525774 525833 525931 "DROPT1" 526044 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520889 522015 523152 "DROPT0" 524657 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519234 519559 519945 "DRAWPT" 520523 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513821 514744 515823 "DRAW" 518208 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513454 513507 513625 "DRAWHACK" 513762 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512185 512454 512745 "DRAWCX" 513183 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511700 511769 511920 "DRAWCURV" 512111 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502168 504130 506245 "DRAWCFUN" 509605 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498907 500833 500874 "DQAGG" 501503 NIL DQAGG (NIL T) -9 NIL 501777 NIL) (-260 486372 493118 493201 "DPOLCAT" 495053 NIL DPOLCAT (NIL T T T T) -9 NIL 495598 NIL) (-259 481209 482557 484515 "DPOLCAT-" 484520 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474556 481070 481168 "DPMO" 481173 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467806 474336 474503 "DPMM" 474508 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467376 467590 467679 "DOMTMPLT" 467737 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466809 467178 467258 "DOMCTOR" 467316 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466021 466289 466440 "DOMAIN" 466678 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459733 465656 465808 "DMP" 465922 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457678 458800 458841 "DMEXT" 458846 NIL DMEXT (NIL T) -9 NIL 459022 NIL) (-251 457278 457334 457478 "DLP" 457616 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451103 456605 456795 "DLIST" 457120 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447875 449928 449969 "DLAGG" 450519 NIL DLAGG (NIL T) -9 NIL 450749 NIL) (-248 446537 447201 447229 "DIVRING" 447321 T DIVRING (NIL) -9 NIL 447404 NIL) (-247 445774 445964 446264 "DIVRING-" 446269 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443876 444233 444639 "DISPLAY" 445388 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437739 443790 443853 "DIRPROD" 443858 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436587 436790 437055 "DIRPROD2" 437532 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425262 431298 431351 "DIRPCAT" 431609 NIL DIRPCAT (NIL NIL T) -9 NIL 432484 NIL) (-242 422588 423230 424111 "DIRPCAT-" 424448 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421875 422035 422221 "DIOSP" 422422 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418505 420759 420800 "DIOPS" 421234 NIL DIOPS (NIL T) -9 NIL 421463 NIL) (-239 418054 418168 418359 "DIOPS-" 418364 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 417105 417733 417761 "DIFRING" 417766 T DIFRING (NIL) -9 NIL 417788 NIL) (-237 416777 416851 416879 "DIFFSPC" 416998 T DIFFSPC (NIL) -9 NIL 417073 NIL) (-236 416422 416500 416652 "DIFFSPC-" 416657 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415478 415956 415997 "DIFFMOD" 416002 NIL DIFFMOD (NIL T) -9 NIL 416100 NIL) (-234 415186 415231 415272 "DIFFDOM" 415393 NIL DIFFDOM (NIL T) -9 NIL 415461 NIL) (-233 415039 415063 415147 "DIFFDOM-" 415152 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412971 414243 414284 "DIFEXT" 414289 NIL DIFEXT (NIL T) -9 NIL 414442 NIL) (-231 410221 412475 412516 "DIAGG" 412521 NIL DIAGG (NIL T) -9 NIL 412541 NIL) (-230 409605 409762 410014 "DIAGG-" 410019 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404977 408564 408841 "DHMATRIX" 409374 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400589 401498 402508 "DFSFUN" 403987 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395667 399520 399832 "DFLOAT" 400297 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393930 394211 394600 "DFINTTLS" 395375 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390959 391951 392351 "DERHAM" 393596 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388763 390734 390823 "DEQUEUE" 390903 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 388017 388150 388333 "DEGRED" 388625 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384447 385192 386038 "DEFINTRF" 387245 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 382002 382471 383063 "DEFINTEF" 383966 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381352 381622 381737 "DEFAST" 381907 T DEFAST (NIL) -8 NIL NIL NIL) (-219 375068 380945 381095 "DECIMAL" 381222 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372580 373038 373544 "DDFACT" 374612 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372176 372219 372370 "DBLRESP" 372531 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 370044 370406 370767 "DBASE" 371942 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369286 369524 369670 "DATAARY" 369943 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368392 369245 369273 "D03FAFA" 369278 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367499 368351 368379 "D03EEFA" 368384 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365449 365915 366404 "D03AGNT" 367030 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364738 365408 365436 "D02EJFA" 365441 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364027 364697 364725 "D02CJFA" 364730 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363316 363986 364014 "D02BHFA" 364019 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362605 363275 363303 "D02BBFA" 363308 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355802 357391 358997 "D02AGNT" 361019 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353570 354093 354639 "D01WGTS" 355276 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352637 353529 353557 "D01TRNS" 353562 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351705 352596 352624 "D01GBFA" 352629 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350773 351664 351692 "D01FCFA" 351697 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349841 350732 350760 "D01ASFA" 350765 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348909 349800 349828 "D01AQFA" 349833 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347977 348868 348896 "D01APFA" 348901 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347045 347936 347964 "D01ANFA" 347969 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346113 347004 347032 "D01AMFA" 347037 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345181 346072 346100 "D01ALFA" 346105 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344249 345140 345168 "D01AKFA" 345173 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343317 344208 344236 "D01AJFA" 344241 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336612 338165 339726 "D01AGNT" 341776 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335949 336077 336229 "CYCLOTOM" 336480 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332682 333397 334124 "CYCLES" 335242 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331994 332128 332299 "CVMP" 332543 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329835 330093 330462 "CTRIGMNP" 331722 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329271 329629 329702 "CTOR" 329782 T CTOR (NIL) -8 NIL NIL NIL) (-188 328780 329002 329103 "CTORKIND" 329190 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328057 328373 328401 "CTORCAT" 328583 T CTORCAT (NIL) -9 NIL 328696 NIL) (-186 327655 327766 327925 "CTORCAT-" 327930 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327117 327329 327437 "CTORCALL" 327579 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326491 326590 326743 "CSTTOOLS" 327014 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322290 322947 323705 "CRFP" 325803 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321765 322011 322103 "CRCEAST" 322218 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320812 320997 321225 "CRAPACK" 321569 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320196 320297 320501 "CPMATCH" 320688 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319921 319949 320055 "CPIMA" 320162 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316269 316941 317660 "COORDSYS" 319256 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315681 315802 315944 "CONTOUR" 316147 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311572 313684 314176 "CONTFRAC" 315221 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311452 311473 311501 "CONDUIT" 311538 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310526 311080 311108 "COMRING" 311113 T COMRING (NIL) -9 NIL 311165 NIL) (-173 309580 309884 310068 "COMPPROP" 310362 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309241 309276 309404 "COMPLPAT" 309539 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298544 309050 309159 "COMPLEX" 309164 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298180 298237 298344 "COMPLEX2" 298481 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297519 297640 297800 "COMPILER" 298040 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297237 297272 297370 "COMPFACT" 297478 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279516 290941 290981 "COMPCAT" 291985 NIL COMPCAT (NIL T) -9 NIL 293333 NIL) (-166 269028 271955 275582 "COMPCAT-" 275938 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268757 268785 268888 "COMMUPC" 268994 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268551 268585 268644 "COMMONOP" 268718 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 268107 268302 268389 "COMM" 268484 T COMM (NIL) -8 NIL NIL NIL) (-162 267683 267911 267986 "COMMAAST" 268052 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266932 267126 267154 "COMBOPC" 267492 T COMBOPC (NIL) -9 NIL 267667 NIL) (-160 265828 266038 266280 "COMBINAT" 266722 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 262285 262859 263486 "COMBF" 265250 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 261043 261401 261636 "COLOR" 262070 T COLOR (NIL) -8 NIL NIL NIL) (-157 260519 260764 260856 "COLONAST" 260971 T COLONAST (NIL) -8 NIL NIL NIL) (-156 260159 260206 260331 "CMPLXRT" 260466 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259607 259859 259958 "CLLCTAST" 260080 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 255109 256137 257217 "CLIP" 258547 T CLIP (NIL) -7 NIL NIL NIL) (-153 253450 254210 254450 "CLIF" 254936 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249600 251568 251609 "CLAGG" 252538 NIL CLAGG (NIL T) -9 NIL 253074 NIL) (-151 248022 248479 249062 "CLAGG-" 249067 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247566 247651 247791 "CINTSLPE" 247931 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 245067 245538 246086 "CHVAR" 247094 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 244227 244781 244809 "CHARZ" 244814 T CHARZ (NIL) -9 NIL 244829 NIL) (-147 243981 244021 244099 "CHARPOL" 244181 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 243025 243612 243640 "CHARNZ" 243687 T CHARNZ (NIL) -9 NIL 243743 NIL) (-145 240931 241679 242032 "CHAR" 242692 T CHAR (NIL) -8 NIL NIL NIL) (-144 240657 240718 240746 "CFCAT" 240857 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239898 240009 240192 "CDEN" 240541 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235863 239051 239331 "CCLASS" 239638 T CCLASS (NIL) -8 NIL NIL NIL) (-141 235114 235271 235448 "CATEGORY" 235706 T -10 (NIL) -8 NIL NIL NIL) (-140 234687 235033 235081 "CATCTOR" 235086 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 234138 234390 234488 "CATAST" 234609 T CATAST (NIL) -8 NIL NIL NIL) (-138 233614 233859 233951 "CASEAST" 234066 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228752 229771 230515 "CARTEN" 232926 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227860 228008 228229 "CARTEN2" 228599 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 226176 227010 227267 "CARD" 227623 T CARD (NIL) -8 NIL NIL NIL) (-134 225752 225980 226055 "CAPSLAST" 226121 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 225242 225450 225478 "CACHSET" 225610 T CACHSET (NIL) -9 NIL 225688 NIL) (-132 224698 225020 225048 "CABMON" 225098 T CABMON (NIL) -9 NIL 225154 NIL) (-131 224171 224402 224512 "BYTEORD" 224608 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 223148 223700 223842 "BYTE" 224005 T BYTE (NIL) -8 NIL NIL 224127) (-129 218501 222653 222825 "BYTEBUF" 222996 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 216013 218193 218300 "BTREE" 218427 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213465 215661 215783 "BTOURN" 215923 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210810 212907 212948 "BTCAT" 213016 NIL BTCAT (NIL T) -9 NIL 213093 NIL) (-125 210477 210557 210706 "BTCAT-" 210711 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205842 209723 209751 "BTAGG" 209865 T BTAGG (NIL) -9 NIL 209975 NIL) (-123 205332 205457 205663 "BTAGG-" 205668 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 202330 204610 204825 "BSTREE" 205149 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201468 201594 201778 "BRILL" 202186 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 198095 200166 200207 "BRAGG" 200856 NIL BRAGG (NIL T) -9 NIL 201114 NIL) (-119 196624 197030 197585 "BRAGG-" 197590 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189540 195968 196153 "BPADICRT" 196471 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187855 189477 189522 "BPADIC" 189527 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187553 187583 187697 "BOUNDZRO" 187819 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182781 183979 184891 "BOP" 186661 T BOP (NIL) -8 NIL NIL NIL) (-114 180562 180966 181441 "BOP1" 182339 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 180263 180324 180352 "BOOLE" 180463 T BOOLE (NIL) -9 NIL 180545 NIL) (-112 179088 179837 179986 "BOOLEAN" 180134 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 178353 178757 178811 "BMODULE" 178816 NIL BMODULE (NIL T T) -9 NIL 178881 NIL) (-110 174154 178151 178224 "BITS" 178300 T BITS (NIL) -8 NIL NIL NIL) (-109 173575 173694 173834 "BINDING" 174034 T BINDING (NIL) -8 NIL NIL NIL) (-108 167294 173170 173319 "BINARY" 173446 T BINARY (NIL) -8 NIL NIL NIL) (-107 165049 166521 166562 "BGAGG" 166822 NIL BGAGG (NIL T) -9 NIL 166959 NIL) (-106 164880 164912 165003 "BGAGG-" 165008 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163951 164264 164469 "BFUNCT" 164695 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162641 162819 163107 "BEZOUT" 163775 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 159113 161493 161823 "BBTREE" 162344 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158714 158792 158820 "BASTYPE" 158997 T BASTYPE (NIL) -9 NIL 159096 NIL) (-101 158390 158471 158606 "BASTYPE-" 158611 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157824 157900 158052 "BALFACT" 158301 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156680 157239 157425 "AUTOMOR" 157669 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156406 156411 156437 "ATTREG" 156442 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154658 155103 155455 "ATTRBUT" 156072 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154266 154486 154552 "ATTRAST" 154610 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153802 153915 153941 "ATRIG" 154142 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153611 153652 153739 "ATRIG-" 153744 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153242 153428 153454 "ASTCAT" 153459 T ASTCAT (NIL) -9 NIL 153489 NIL) (-92 152969 153028 153147 "ASTCAT-" 153152 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151121 152745 152833 "ASTACK" 152912 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149626 149923 150288 "ASSOCEQ" 150803 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148658 149285 149409 "ASP9" 149533 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148421 148606 148645 "ASP8" 148650 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147289 148026 148168 "ASP80" 148310 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146187 146924 147056 "ASP7" 147188 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145141 145864 145982 "ASP78" 146100 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144110 144821 144938 "ASP77" 145055 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 143022 143748 143879 "ASP74" 144010 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141922 142657 142789 "ASP73" 142921 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 141026 141748 141848 "ASP6" 141853 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139973 140703 140821 "ASP55" 140939 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138922 139647 139766 "ASP50" 139885 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 138010 138623 138733 "ASP4" 138843 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 137098 137711 137821 "ASP49" 137931 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135882 136637 136805 "ASP42" 136987 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134659 135415 135585 "ASP41" 135769 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133609 134336 134454 "ASP35" 134572 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133374 133557 133596 "ASP34" 133601 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133111 133178 133254 "ASP33" 133329 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 132005 132746 132878 "ASP31" 133010 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131770 131953 131992 "ASP30" 131997 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131505 131574 131650 "ASP29" 131725 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131270 131453 131492 "ASP28" 131497 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 131035 131218 131257 "ASP27" 131262 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130119 130733 130844 "ASP24" 130955 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129196 129921 130033 "ASP20" 130038 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128284 128897 129007 "ASP1" 129117 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127227 127958 128077 "ASP19" 128196 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126964 127031 127107 "ASP12" 127182 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125816 126563 126707 "ASP10" 126851 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123670 125660 125751 "ARRAY2" 125756 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119438 123318 123432 "ARRAY1" 123587 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118470 118643 118864 "ARRAY12" 119261 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112757 114672 114747 "ARR2CAT" 117377 NIL ARR2CAT (NIL T T T) -9 NIL 118135 NIL) (-56 110191 110935 111889 "ARR2CAT-" 111894 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109508 109818 109943 "ARITY" 110084 T ARITY (NIL) -8 NIL NIL NIL) (-54 108284 108436 108735 "APPRULE" 109344 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107935 107983 108102 "APPLYORE" 108230 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107289 107528 107648 "ANY" 107833 T ANY (NIL) -8 NIL NIL NIL) (-51 106567 106690 106847 "ANY1" 107163 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104097 105004 105331 "ANTISYM" 106291 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103589 103804 103900 "ANON" 104019 T ANON (NIL) -8 NIL NIL NIL) (-48 97589 102128 102582 "AN" 103153 T AN (NIL) -8 NIL NIL NIL) (-47 93473 94861 94912 "AMR" 95660 NIL AMR (NIL T T) -9 NIL 96260 NIL) (-46 92585 92806 93169 "AMR-" 93174 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 77030 92502 92563 "ALIST" 92568 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73835 76624 76793 "ALGSC" 76948 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70391 70945 71552 "ALGPKG" 73275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69668 69769 69953 "ALGMFACT" 70277 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65703 66282 66876 "ALGMANIP" 69252 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55914 65329 65479 "ALGFF" 65636 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55110 55241 55420 "ALGFACT" 55772 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54037 54637 54675 "ALGEBRA" 54680 NIL ALGEBRA (NIL T) -9 NIL 54721 NIL) (-37 53755 53814 53946 "ALGEBRA-" 53951 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35692 51592 51644 "ALAGG" 51780 NIL ALAGG (NIL T T) -9 NIL 51941 NIL) (-35 35228 35341 35367 "AHYP" 35568 T AHYP (NIL) -9 NIL NIL NIL) (-34 34159 34407 34433 "AGG" 34932 T AGG (NIL) -9 NIL 35211 NIL) (-33 33593 33755 33969 "AGG-" 33974 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31399 31822 32227 "AF" 33235 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30879 31124 31214 "ADDAST" 31327 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30147 30406 30562 "ACPLOT" 30741 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18770 27079 27117 "ACFS" 27724 NIL ACFS (NIL T) -9 NIL 27963 NIL) (-28 16797 17287 18049 "ACFS-" 18054 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12901 14830 14856 "ACF" 15735 T ACF (NIL) -9 NIL 16148 NIL) (-26 11605 11939 12432 "ACF-" 12437 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11163 11358 11384 "ABELSG" 11476 T ABELSG (NIL) -9 NIL 11541 NIL) (-24 11030 11055 11121 "ABELSG-" 11126 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10359 10646 10672 "ABELMON" 10842 T ABELMON (NIL) -9 NIL 10954 NIL) (-22 10023 10107 10245 "ABELMON-" 10250 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9357 9729 9755 "ABELGRP" 9827 T ABELGRP (NIL) -9 NIL 9902 NIL) (-20 8820 8949 9165 "ABELGRP-" 9170 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8082 8121 "A1AGG" 8126 NIL A1AGG (NIL T) -9 NIL 8166 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3262593 3262598 3262603 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3262578 3262583 3262588 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3262563 3262568 3262573 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3262548 3262553 3262558 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1317 3261691 3262423 3262500 "ZMOD" 3262505 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1316 3260745 3260909 3261132 "ZLINDEP" 3261523 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1315 3250045 3251813 3253785 "ZDSOLVE" 3258875 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1314 3249291 3249432 3249621 "YSTREAM" 3249891 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1313 3248719 3248965 3249078 "YDIAGRAM" 3249200 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1312 3246493 3248020 3248224 "XRPOLY" 3248562 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1311 3243046 3244364 3244939 "XPR" 3245965 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1310 3240767 3242377 3242581 "XPOLY" 3242877 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1309 3238406 3239774 3239829 "XPOLYC" 3240117 NIL XPOLYC (NIL T T) -9 NIL 3240230 NIL) (-1308 3234782 3236923 3237311 "XPBWPOLY" 3238064 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1307 3230463 3232758 3232800 "XF" 3233421 NIL XF (NIL T) -9 NIL 3233821 NIL) (-1306 3230084 3230172 3230341 "XF-" 3230346 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1305 3225266 3226555 3226610 "XFALG" 3228782 NIL XFALG (NIL T T) -9 NIL 3229571 NIL) (-1304 3224399 3224503 3224708 "XEXPPKG" 3225158 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1303 3222508 3224249 3224345 "XDPOLY" 3224350 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1302 3221301 3221901 3221944 "XALG" 3221949 NIL XALG (NIL T) -9 NIL 3222060 NIL) (-1301 3214743 3219278 3219772 "WUTSET" 3220893 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1300 3212999 3213795 3214118 "WP" 3214554 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1299 3212601 3212821 3212891 "WHILEAST" 3212951 T WHILEAST (NIL) -8 NIL NIL NIL) (-1298 3212073 3212318 3212412 "WHEREAST" 3212529 T WHEREAST (NIL) -8 NIL NIL NIL) (-1297 3210959 3211157 3211452 "WFFINTBS" 3211870 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1296 3208863 3209290 3209752 "WEIER" 3210531 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1295 3207895 3208345 3208387 "VSPACE" 3208523 NIL VSPACE (NIL T) -9 NIL 3208597 NIL) (-1294 3207733 3207760 3207851 "VSPACE-" 3207856 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1293 3207542 3207584 3207652 "VOID" 3207687 T VOID (NIL) -8 NIL NIL NIL) (-1292 3205678 3206037 3206443 "VIEW" 3207158 T VIEW (NIL) -7 NIL NIL NIL) (-1291 3202102 3202741 3203478 "VIEWDEF" 3204963 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1290 3191406 3193650 3195823 "VIEW3D" 3199951 T VIEW3D (NIL) -8 NIL NIL NIL) (-1289 3183657 3185317 3186896 "VIEW2D" 3189849 T VIEW2D (NIL) -8 NIL NIL NIL) (-1288 3179013 3183427 3183519 "VECTOR" 3183600 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1287 3177590 3177849 3178167 "VECTOR2" 3178743 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1286 3170988 3175294 3175337 "VECTCAT" 3176332 NIL VECTCAT (NIL T) -9 NIL 3176919 NIL) (-1285 3170002 3170256 3170646 "VECTCAT-" 3170651 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1284 3169456 3169653 3169773 "VARIABLE" 3169917 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1283 3169389 3169394 3169424 "UTYPE" 3169429 T UTYPE (NIL) -9 NIL NIL NIL) (-1282 3168219 3168373 3168635 "UTSODETL" 3169215 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1281 3165659 3166119 3166643 "UTSODE" 3167760 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1280 3157607 3163420 3163900 "UTS" 3165237 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3148171 3153541 3153584 "UTSCAT" 3154696 NIL UTSCAT (NIL T) -9 NIL 3155454 NIL) (-1278 3145519 3146241 3147230 "UTSCAT-" 3147235 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1277 3145146 3145189 3145322 "UTS2" 3145470 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1276 3139347 3141956 3141999 "URAGG" 3144069 NIL URAGG (NIL T) -9 NIL 3144792 NIL) (-1275 3136286 3137149 3138272 "URAGG-" 3138277 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1274 3131995 3134921 3135386 "UPXSSING" 3135950 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1273 3124171 3131377 3131641 "UPXS" 3131789 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1272 3117244 3124075 3124147 "UPXSCONS" 3124152 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1271 3106651 3113447 3113509 "UPXSCCA" 3114083 NIL UPXSCCA (NIL T T) -9 NIL 3114316 NIL) (-1270 3106289 3106374 3106548 "UPXSCCA-" 3106553 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1269 3095548 3102117 3102160 "UPXSCAT" 3102808 NIL UPXSCAT (NIL T) -9 NIL 3103417 NIL) (-1268 3094978 3095057 3095236 "UPXS2" 3095463 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1267 3093632 3093885 3094236 "UPSQFREE" 3094721 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1266 3086840 3089900 3089955 "UPSCAT" 3091035 NIL UPSCAT (NIL T T) -9 NIL 3091800 NIL) (-1265 3086044 3086251 3086578 "UPSCAT-" 3086583 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1264 3071126 3079171 3079214 "UPOLYC" 3081315 NIL UPOLYC (NIL T) -9 NIL 3082536 NIL) (-1263 3062454 3064880 3068027 "UPOLYC-" 3068032 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1262 3062081 3062124 3062257 "UPOLYC2" 3062405 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1261 3053616 3061764 3061893 "UP" 3062000 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1260 3052955 3053062 3053226 "UPMP" 3053505 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1259 3052508 3052589 3052728 "UPDIVP" 3052868 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1258 3051076 3051325 3051641 "UPDECOMP" 3052257 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1257 3050307 3050419 3050605 "UPCDEN" 3050960 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1256 3049826 3049895 3050044 "UP2" 3050232 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1255 3048293 3049030 3049307 "UNISEG" 3049584 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1254 3047508 3047635 3047840 "UNISEG2" 3048136 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1253 3046568 3046748 3046974 "UNIFACT" 3047324 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1252 3029320 3045880 3046122 "ULS" 3046384 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1251 3016950 3029224 3029296 "ULSCONS" 3029301 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1250 2997671 3010031 3010093 "ULSCCAT" 3010731 NIL ULSCCAT (NIL T T) -9 NIL 3011020 NIL) (-1249 2996721 2996966 2997354 "ULSCCAT-" 2997359 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1248 2985785 2992268 2992311 "ULSCAT" 2993174 NIL ULSCAT (NIL T) -9 NIL 2993905 NIL) (-1247 2985215 2985294 2985473 "ULS2" 2985700 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1246 2984334 2984844 2984951 "UINT8" 2985062 T UINT8 (NIL) -8 NIL NIL 2985147) (-1245 2983452 2983962 2984069 "UINT64" 2984180 T UINT64 (NIL) -8 NIL NIL 2984265) (-1244 2982570 2983080 2983187 "UINT32" 2983298 T UINT32 (NIL) -8 NIL NIL 2983383) (-1243 2981688 2982198 2982305 "UINT16" 2982416 T UINT16 (NIL) -8 NIL NIL 2982501) (-1242 2979977 2980934 2980964 "UFD" 2981176 T UFD (NIL) -9 NIL 2981290 NIL) (-1241 2979771 2979817 2979912 "UFD-" 2979917 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1240 2978853 2979036 2979252 "UDVO" 2979577 T UDVO (NIL) -7 NIL NIL NIL) (-1239 2976669 2977078 2977549 "UDPO" 2978417 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1238 2976602 2976607 2976637 "TYPE" 2976642 T TYPE (NIL) -9 NIL NIL NIL) (-1237 2976362 2976557 2976588 "TYPEAST" 2976593 T TYPEAST (NIL) -8 NIL NIL NIL) (-1236 2975333 2975535 2975775 "TWOFACT" 2976156 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1235 2974356 2974742 2974977 "TUPLE" 2975133 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1234 2972047 2972566 2973105 "TUBETOOL" 2973839 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1233 2970896 2971101 2971342 "TUBE" 2971840 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1232 2965625 2969868 2970151 "TS" 2970648 NIL TS (NIL T) -8 NIL NIL NIL) (-1231 2954265 2958384 2958481 "TSETCAT" 2963750 NIL TSETCAT (NIL T T T T) -9 NIL 2965281 NIL) (-1230 2948997 2950597 2952488 "TSETCAT-" 2952493 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1229 2943636 2944483 2945412 "TRMANIP" 2948133 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1228 2943077 2943140 2943303 "TRIMAT" 2943568 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1227 2940943 2941180 2941537 "TRIGMNIP" 2942826 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1226 2940463 2940576 2940606 "TRIGCAT" 2940819 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1225 2940132 2940211 2940352 "TRIGCAT-" 2940357 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1224 2936980 2938990 2939271 "TREE" 2939886 NIL TREE (NIL T) -8 NIL NIL NIL) (-1223 2936254 2936782 2936812 "TRANFUN" 2936847 T TRANFUN (NIL) -9 NIL 2936913 NIL) (-1222 2935533 2935724 2936004 "TRANFUN-" 2936009 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1221 2935337 2935369 2935430 "TOPSP" 2935494 T TOPSP (NIL) -7 NIL NIL NIL) (-1220 2934685 2934800 2934954 "TOOLSIGN" 2935218 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1219 2933319 2933862 2934101 "TEXTFILE" 2934468 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1218 2931231 2931772 2932201 "TEX" 2932912 T TEX (NIL) -8 NIL NIL NIL) (-1217 2931012 2931043 2931115 "TEX1" 2931194 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1216 2930660 2930723 2930813 "TEMUTL" 2930944 T TEMUTL (NIL) -7 NIL NIL NIL) (-1215 2928814 2929094 2929419 "TBCMPPK" 2930383 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1214 2920523 2926900 2926956 "TBAGG" 2927356 NIL TBAGG (NIL T T) -9 NIL 2927567 NIL) (-1213 2915593 2917081 2918835 "TBAGG-" 2918840 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1212 2914977 2915084 2915229 "TANEXP" 2915482 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1211 2914488 2914752 2914842 "TALGOP" 2914922 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1210 2907884 2914345 2914438 "TABLE" 2914443 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1209 2907296 2907395 2907533 "TABLEAU" 2907781 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1208 2901904 2903124 2904372 "TABLBUMP" 2906082 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1207 2901126 2901273 2901454 "SYSTEM" 2901745 T SYSTEM (NIL) -8 NIL NIL NIL) (-1206 2897585 2898284 2899067 "SYSSOLP" 2900377 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1205 2897383 2897540 2897571 "SYSPTR" 2897576 T SYSPTR (NIL) -8 NIL NIL NIL) (-1204 2896419 2896924 2897043 "SYSNNI" 2897229 NIL SYSNNI (NIL NIL) -8 NIL NIL 2897314) (-1203 2895718 2896177 2896256 "SYSINT" 2896316 NIL SYSINT (NIL NIL) -8 NIL NIL 2896361) (-1202 2892050 2892996 2893706 "SYNTAX" 2895030 T SYNTAX (NIL) -8 NIL NIL NIL) (-1201 2889208 2889810 2890442 "SYMTAB" 2891440 T SYMTAB (NIL) -8 NIL NIL NIL) (-1200 2884457 2885359 2886342 "SYMS" 2888247 T SYMS (NIL) -8 NIL NIL NIL) (-1199 2881692 2883915 2884145 "SYMPOLY" 2884262 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1198 2881209 2881284 2881407 "SYMFUNC" 2881604 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1197 2877229 2878521 2879334 "SYMBOL" 2880418 T SYMBOL (NIL) -8 NIL NIL NIL) (-1196 2870768 2872457 2874177 "SWITCH" 2875531 T SWITCH (NIL) -8 NIL NIL NIL) (-1195 2864112 2869724 2870018 "SUTS" 2870532 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 2856288 2863494 2863758 "SUPXS" 2863906 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1193 2847771 2855906 2856032 "SUP" 2856197 NIL SUP (NIL T) -8 NIL NIL NIL) (-1192 2846930 2847057 2847274 "SUPFRACF" 2847639 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1191 2846551 2846610 2846723 "SUP2" 2846865 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1190 2844999 2845273 2845629 "SUMRF" 2846250 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1189 2844334 2844400 2844592 "SUMFS" 2844920 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1188 2827121 2843646 2843888 "SULS" 2844150 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1187 2826723 2826943 2827013 "SUCHTAST" 2827073 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1186 2826018 2826248 2826388 "SUCH" 2826631 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1185 2819885 2820924 2821883 "SUBSPACE" 2825106 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1184 2819315 2819405 2819569 "SUBRESP" 2819773 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1183 2812683 2813980 2815291 "STTF" 2818051 NIL STTF (NIL T) -7 NIL NIL NIL) (-1182 2806856 2807976 2809123 "STTFNC" 2811583 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1181 2798169 2800038 2801832 "STTAYLOR" 2805097 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1180 2791305 2798033 2798116 "STRTBL" 2798121 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1179 2786266 2791014 2791113 "STRING" 2791228 T STRING (NIL) -8 NIL NIL NIL) (-1178 2779022 2783885 2784496 "STREAM" 2785690 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1177 2778532 2778609 2778753 "STREAM3" 2778939 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1176 2777514 2777697 2777932 "STREAM2" 2778345 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1175 2777202 2777254 2777347 "STREAM1" 2777456 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1174 2776218 2776399 2776630 "STINPROD" 2777018 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1173 2775756 2775966 2775996 "STEP" 2776076 T STEP (NIL) -9 NIL 2776154 NIL) (-1172 2774943 2775245 2775393 "STEPAST" 2775630 T STEPAST (NIL) -8 NIL NIL NIL) (-1171 2768381 2774842 2774919 "STBL" 2774924 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1170 2763451 2767544 2767587 "STAGG" 2767740 NIL STAGG (NIL T) -9 NIL 2767829 NIL) (-1169 2761153 2761755 2762627 "STAGG-" 2762632 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1168 2759303 2760923 2761015 "STACK" 2761096 NIL STACK (NIL T) -8 NIL NIL NIL) (-1167 2751998 2757444 2757900 "SREGSET" 2758933 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1166 2744423 2745792 2747305 "SRDCMPK" 2750604 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1165 2737260 2741782 2741812 "SRAGG" 2743115 T SRAGG (NIL) -9 NIL 2743723 NIL) (-1164 2736277 2736532 2736911 "SRAGG-" 2736916 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1163 2730461 2735224 2735645 "SQMATRIX" 2735903 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1162 2724149 2727179 2727906 "SPLTREE" 2729806 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1161 2720112 2720805 2721451 "SPLNODE" 2723575 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1160 2719159 2719392 2719422 "SPFCAT" 2719866 T SPFCAT (NIL) -9 NIL NIL NIL) (-1159 2717896 2718106 2718370 "SPECOUT" 2718917 T SPECOUT (NIL) -7 NIL NIL NIL) (-1158 2708992 2710864 2710894 "SPADXPT" 2715570 T SPADXPT (NIL) -9 NIL 2717734 NIL) (-1157 2708753 2708793 2708862 "SPADPRSR" 2708945 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1156 2706802 2708708 2708739 "SPADAST" 2708744 T SPADAST (NIL) -8 NIL NIL NIL) (-1155 2698733 2700506 2700549 "SPACEC" 2704922 NIL SPACEC (NIL T) -9 NIL 2706738 NIL) (-1154 2696863 2698665 2698714 "SPACE3" 2698719 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1153 2695615 2695786 2696077 "SORTPAK" 2696668 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1152 2693707 2694010 2694422 "SOLVETRA" 2695279 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1151 2692757 2692979 2693240 "SOLVESER" 2693480 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1150 2688061 2688949 2689944 "SOLVERAD" 2691809 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1149 2683876 2684485 2685214 "SOLVEFOR" 2687428 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1148 2678146 2683225 2683322 "SNTSCAT" 2683327 NIL SNTSCAT (NIL T T T T) -9 NIL 2683397 NIL) (-1147 2672252 2676469 2676860 "SMTS" 2677836 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1146 2666661 2672140 2672217 "SMP" 2672222 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1145 2664820 2665121 2665519 "SMITH" 2666358 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1144 2656924 2661399 2661502 "SMATCAT" 2662853 NIL SMATCAT (NIL NIL T T T) -9 NIL 2663403 NIL) (-1143 2653864 2654687 2655865 "SMATCAT-" 2655870 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1142 2651505 2653072 2653115 "SKAGG" 2653376 NIL SKAGG (NIL T) -9 NIL 2653511 NIL) (-1141 2647695 2650978 2651162 "SINT" 2651314 T SINT (NIL) -8 NIL NIL 2651476) (-1140 2647467 2647505 2647571 "SIMPAN" 2647651 T SIMPAN (NIL) -7 NIL NIL NIL) (-1139 2646746 2647002 2647142 "SIG" 2647349 T SIG (NIL) -8 NIL NIL NIL) (-1138 2645584 2645805 2646080 "SIGNRF" 2646505 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1137 2644417 2644568 2644852 "SIGNEF" 2645413 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1136 2643723 2644000 2644124 "SIGAST" 2644315 T SIGAST (NIL) -8 NIL NIL NIL) (-1135 2641413 2641867 2642373 "SHP" 2643264 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1134 2635242 2641314 2641390 "SHDP" 2641395 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1133 2634801 2634993 2635023 "SGROUP" 2635116 T SGROUP (NIL) -9 NIL 2635178 NIL) (-1132 2634659 2634685 2634758 "SGROUP-" 2634763 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1131 2631450 2632148 2632871 "SGCF" 2633958 T SGCF (NIL) -7 NIL NIL NIL) (-1130 2625818 2630897 2630994 "SFRTCAT" 2630999 NIL SFRTCAT (NIL T T T T) -9 NIL 2631038 NIL) (-1129 2619239 2620257 2621393 "SFRGCD" 2624801 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1128 2612365 2613438 2614624 "SFQCMPK" 2618172 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1127 2611985 2612074 2612185 "SFORT" 2612306 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1126 2611103 2611825 2611946 "SEXOF" 2611951 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1125 2610210 2610984 2611052 "SEX" 2611057 T SEX (NIL) -8 NIL NIL NIL) (-1124 2605991 2606706 2606801 "SEXCAT" 2609423 NIL SEXCAT (NIL T T T T T) -9 NIL 2609983 NIL) (-1123 2603144 2605925 2605973 "SET" 2605978 NIL SET (NIL T) -8 NIL NIL NIL) (-1122 2601368 2601857 2602162 "SETMN" 2602885 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1121 2600934 2601086 2601116 "SETCAT" 2601233 T SETCAT (NIL) -9 NIL 2601318 NIL) (-1120 2600714 2600766 2600865 "SETCAT-" 2600870 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1119 2597075 2599175 2599218 "SETAGG" 2600088 NIL SETAGG (NIL T) -9 NIL 2600428 NIL) (-1118 2596533 2596649 2596886 "SETAGG-" 2596891 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1117 2595976 2596229 2596330 "SEQAST" 2596454 T SEQAST (NIL) -8 NIL NIL NIL) (-1116 2595175 2595469 2595530 "SEGXCAT" 2595816 NIL SEGXCAT (NIL T T) -9 NIL 2595936 NIL) (-1115 2594181 2594841 2595023 "SEG" 2595028 NIL SEG (NIL T) -8 NIL NIL NIL) (-1114 2593160 2593374 2593417 "SEGCAT" 2593939 NIL SEGCAT (NIL T) -9 NIL 2594160 NIL) (-1113 2592092 2592523 2592731 "SEGBIND" 2592987 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1112 2591713 2591772 2591885 "SEGBIND2" 2592027 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1111 2591286 2591514 2591591 "SEGAST" 2591658 T SEGAST (NIL) -8 NIL NIL NIL) (-1110 2590505 2590631 2590835 "SEG2" 2591130 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1109 2589876 2590440 2590487 "SDVAR" 2590492 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1108 2582127 2589646 2589776 "SDPOL" 2589781 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1107 2580720 2580986 2581305 "SCPKG" 2581842 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1106 2579884 2580056 2580248 "SCOPE" 2580550 T SCOPE (NIL) -8 NIL NIL NIL) (-1105 2579104 2579238 2579417 "SCACHE" 2579739 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1104 2578736 2578922 2578952 "SASTCAT" 2578957 T SASTCAT (NIL) -9 NIL 2578970 NIL) (-1103 2578223 2578571 2578647 "SAOS" 2578682 T SAOS (NIL) -8 NIL NIL NIL) (-1102 2577788 2577823 2577996 "SAERFFC" 2578182 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1101 2571451 2577685 2577765 "SAE" 2577770 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1100 2571044 2571079 2571238 "SAEFACT" 2571410 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1099 2569365 2569679 2570080 "RURPK" 2570710 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1098 2568002 2568308 2568613 "RULESET" 2569199 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1097 2565225 2565755 2566213 "RULE" 2567683 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1096 2564837 2565019 2565102 "RULECOLD" 2565177 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1095 2564627 2564655 2564726 "RTVALUE" 2564788 T RTVALUE (NIL) -8 NIL NIL NIL) (-1094 2564098 2564344 2564438 "RSTRCAST" 2564555 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1093 2558946 2559741 2560661 "RSETGCD" 2563297 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1092 2548176 2553255 2553352 "RSETCAT" 2557471 NIL RSETCAT (NIL T T T T) -9 NIL 2558568 NIL) (-1091 2546103 2546642 2547466 "RSETCAT-" 2547471 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1090 2538489 2539865 2541385 "RSDCMPK" 2544702 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1089 2536454 2536921 2536995 "RRCC" 2538081 NIL RRCC (NIL T T) -9 NIL 2538425 NIL) (-1088 2535805 2535979 2536258 "RRCC-" 2536263 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1087 2535248 2535501 2535602 "RPTAST" 2535726 T RPTAST (NIL) -8 NIL NIL NIL) (-1086 2508724 2518360 2518427 "RPOLCAT" 2529093 NIL RPOLCAT (NIL T T T) -9 NIL 2532253 NIL) (-1085 2500222 2502562 2505684 "RPOLCAT-" 2505689 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1084 2491159 2498433 2498915 "ROUTINE" 2499762 T ROUTINE (NIL) -8 NIL NIL NIL) (-1083 2487820 2490785 2490925 "ROMAN" 2491041 T ROMAN (NIL) -8 NIL NIL NIL) (-1082 2486064 2486680 2486940 "ROIRC" 2487625 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1081 2482268 2484553 2484583 "RNS" 2484887 T RNS (NIL) -9 NIL 2485161 NIL) (-1080 2480777 2481160 2481694 "RNS-" 2481769 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1079 2480166 2480574 2480604 "RNG" 2480609 T RNG (NIL) -9 NIL 2480630 NIL) (-1078 2479169 2479531 2479733 "RNGBIND" 2480017 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1077 2478554 2478942 2478985 "RMODULE" 2478990 NIL RMODULE (NIL T) -9 NIL 2479017 NIL) (-1076 2477390 2477484 2477820 "RMCAT2" 2478455 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1075 2474240 2476736 2477033 "RMATRIX" 2477152 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1074 2467067 2469327 2469442 "RMATCAT" 2472801 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2473783 NIL) (-1073 2466442 2466589 2466896 "RMATCAT-" 2466901 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1072 2466057 2466229 2466272 "RLINSET" 2466334 NIL RLINSET (NIL T) -9 NIL 2466378 NIL) (-1071 2465624 2465699 2465827 "RINTERP" 2465976 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1070 2464668 2465222 2465252 "RING" 2465308 T RING (NIL) -9 NIL 2465400 NIL) (-1069 2464460 2464504 2464601 "RING-" 2464606 NIL RING- (NIL T) -8 NIL NIL NIL) (-1068 2463301 2463538 2463796 "RIDIST" 2464224 T RIDIST (NIL) -7 NIL NIL NIL) (-1067 2454590 2462769 2462975 "RGCHAIN" 2463149 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1066 2453926 2454332 2454373 "RGBCSPC" 2454431 NIL RGBCSPC (NIL T) -9 NIL 2454483 NIL) (-1065 2453070 2453451 2453492 "RGBCMDL" 2453724 NIL RGBCMDL (NIL T) -9 NIL 2453838 NIL) (-1064 2450064 2450678 2451348 "RF" 2452434 NIL RF (NIL T) -7 NIL NIL NIL) (-1063 2449710 2449773 2449876 "RFFACTOR" 2449995 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1062 2449435 2449470 2449567 "RFFACT" 2449669 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1061 2447552 2447916 2448298 "RFDIST" 2449075 T RFDIST (NIL) -7 NIL NIL NIL) (-1060 2447005 2447097 2447260 "RETSOL" 2447454 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1059 2446641 2446721 2446764 "RETRACT" 2446897 NIL RETRACT (NIL T) -9 NIL 2446984 NIL) (-1058 2446490 2446515 2446602 "RETRACT-" 2446607 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1057 2446092 2446312 2446382 "RETAST" 2446442 T RETAST (NIL) -8 NIL NIL NIL) (-1056 2438836 2445745 2445872 "RESULT" 2445987 T RESULT (NIL) -8 NIL NIL NIL) (-1055 2437427 2438105 2438304 "RESRING" 2438739 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1054 2437063 2437112 2437210 "RESLATC" 2437364 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1053 2436768 2436803 2436910 "REPSQ" 2437022 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1052 2434190 2434770 2435372 "REP" 2436188 T REP (NIL) -7 NIL NIL NIL) (-1051 2433887 2433922 2434033 "REPDB" 2434149 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1050 2427787 2429176 2430399 "REP2" 2432699 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1049 2424164 2424845 2425653 "REP1" 2427014 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1048 2416860 2422305 2422761 "REGSET" 2423794 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1047 2415625 2416008 2416258 "REF" 2416645 NIL REF (NIL T) -8 NIL NIL NIL) (-1046 2415002 2415105 2415272 "REDORDER" 2415509 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1045 2410970 2414215 2414442 "RECLOS" 2414830 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1044 2410022 2410203 2410418 "REALSOLV" 2410777 T REALSOLV (NIL) -7 NIL NIL NIL) (-1043 2409868 2409909 2409939 "REAL" 2409944 T REAL (NIL) -9 NIL 2409979 NIL) (-1042 2406351 2407153 2408037 "REAL0Q" 2409033 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1041 2401952 2402940 2404001 "REAL0" 2405332 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1040 2401423 2401669 2401763 "RDUCEAST" 2401880 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1039 2400828 2400900 2401107 "RDIV" 2401345 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1038 2399896 2400070 2400283 "RDIST" 2400650 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1037 2398493 2398780 2399152 "RDETRS" 2399604 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1036 2396305 2396759 2397297 "RDETR" 2398035 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1035 2394930 2395208 2395605 "RDEEFS" 2396021 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1034 2393439 2393745 2394170 "RDEEF" 2394618 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1033 2387472 2390393 2390423 "RCFIELD" 2391718 T RCFIELD (NIL) -9 NIL 2392449 NIL) (-1032 2385536 2386040 2386736 "RCFIELD-" 2386811 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1031 2381780 2383609 2383652 "RCAGG" 2384736 NIL RCAGG (NIL T) -9 NIL 2385201 NIL) (-1030 2381408 2381502 2381665 "RCAGG-" 2381670 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1029 2380743 2380855 2381020 "RATRET" 2381292 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1028 2380296 2380363 2380484 "RATFACT" 2380671 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1027 2379604 2379724 2379876 "RANDSRC" 2380166 T RANDSRC (NIL) -7 NIL NIL NIL) (-1026 2379338 2379382 2379455 "RADUTIL" 2379553 T RADUTIL (NIL) -7 NIL NIL NIL) (-1025 2372166 2378169 2378480 "RADIX" 2379061 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1024 2362626 2372008 2372138 "RADFF" 2372143 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1023 2362273 2362348 2362378 "RADCAT" 2362538 T RADCAT (NIL) -9 NIL NIL NIL) (-1022 2362055 2362103 2362203 "RADCAT-" 2362208 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1021 2360156 2361825 2361917 "QUEUE" 2361998 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1020 2356417 2360089 2360137 "QUAT" 2360142 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1019 2356048 2356091 2356222 "QUATCT2" 2356368 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1018 2348846 2352471 2352513 "QUATCAT" 2353304 NIL QUATCAT (NIL T) -9 NIL 2354070 NIL) (-1017 2344985 2346022 2347412 "QUATCAT-" 2347508 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1016 2342425 2344033 2344076 "QUAGG" 2344457 NIL QUAGG (NIL T) -9 NIL 2344632 NIL) (-1015 2342027 2342247 2342317 "QQUTAST" 2342377 T QQUTAST (NIL) -8 NIL NIL NIL) (-1014 2341040 2341540 2341705 "QFORM" 2341908 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1013 2331372 2336887 2336929 "QFCAT" 2337597 NIL QFCAT (NIL T) -9 NIL 2338598 NIL) (-1012 2326939 2328140 2329734 "QFCAT-" 2329830 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1011 2326570 2326613 2326744 "QFCAT2" 2326890 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1010 2326025 2326135 2326267 "QEQUAT" 2326460 T QEQUAT (NIL) -8 NIL NIL NIL) (-1009 2319151 2320224 2321410 "QCMPACK" 2324958 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1008 2316689 2317137 2317567 "QALGSET" 2318806 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1007 2315924 2316100 2316336 "QALGSET2" 2316507 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1006 2314609 2314833 2315152 "PWFFINTB" 2315697 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1005 2312784 2312952 2313308 "PUSHVAR" 2314423 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1004 2308673 2309727 2309770 "PTRANFN" 2311681 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1003 2307064 2307355 2307679 "PTPACK" 2308384 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1002 2306693 2306750 2306861 "PTFUNC2" 2307001 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1001 2301088 2305482 2305525 "PTCAT" 2305825 NIL PTCAT (NIL T) -9 NIL 2305978 NIL) (-1000 2300743 2300778 2300904 "PSQFR" 2301047 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-999 2299338 2299636 2299970 "PSEUDLIN" 2300441 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-998 2286101 2288472 2290796 "PSETPK" 2297098 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-997 2279119 2281859 2281955 "PSETCAT" 2284976 NIL PSETCAT (NIL T T T T) -9 NIL 2285790 NIL) (-996 2276955 2277589 2278410 "PSETCAT-" 2278415 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-995 2276304 2276469 2276497 "PSCURVE" 2276765 T PSCURVE (NIL) -9 NIL 2276932 NIL) (-994 2272288 2273804 2273869 "PSCAT" 2274713 NIL PSCAT (NIL T T T) -9 NIL 2274953 NIL) (-993 2271351 2271567 2271967 "PSCAT-" 2271972 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-992 2269710 2270420 2270683 "PRTITION" 2271108 T PRTITION (NIL) -8 NIL NIL NIL) (-991 2269185 2269431 2269523 "PRTDAST" 2269638 T PRTDAST (NIL) -8 NIL NIL NIL) (-990 2258275 2260489 2262677 "PRS" 2267047 NIL PRS (NIL T T) -7 NIL NIL NIL) (-989 2256061 2257597 2257637 "PRQAGG" 2257820 NIL PRQAGG (NIL T) -9 NIL 2257922 NIL) (-988 2255397 2255702 2255730 "PROPLOG" 2255869 T PROPLOG (NIL) -9 NIL 2255984 NIL) (-987 2255001 2255058 2255181 "PROPFUN2" 2255320 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-986 2254316 2254437 2254609 "PROPFUN1" 2254862 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-985 2252497 2253063 2253360 "PROPFRML" 2254052 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-984 2251966 2252073 2252201 "PROPERTY" 2252389 T PROPERTY (NIL) -8 NIL NIL NIL) (-983 2246024 2250132 2250952 "PRODUCT" 2251192 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-982 2243302 2245482 2245716 "PR" 2245835 NIL PR (NIL T T) -8 NIL NIL NIL) (-981 2243098 2243130 2243189 "PRINT" 2243263 T PRINT (NIL) -7 NIL NIL NIL) (-980 2242438 2242555 2242707 "PRIMES" 2242978 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-979 2240503 2240904 2241370 "PRIMELT" 2242017 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-978 2240232 2240281 2240309 "PRIMCAT" 2240433 T PRIMCAT (NIL) -9 NIL NIL NIL) (-977 2236350 2240170 2240215 "PRIMARR" 2240220 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-976 2235357 2235535 2235763 "PRIMARR2" 2236168 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-975 2235000 2235056 2235167 "PREASSOC" 2235295 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-974 2234475 2234608 2234636 "PPCURVE" 2234841 T PPCURVE (NIL) -9 NIL 2234977 NIL) (-973 2234070 2234270 2234353 "PORTNUM" 2234412 T PORTNUM (NIL) -8 NIL NIL NIL) (-972 2231429 2231828 2232420 "POLYROOT" 2233651 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-971 2225335 2231033 2231193 "POLY" 2231302 NIL POLY (NIL T) -8 NIL NIL NIL) (-970 2224718 2224776 2225010 "POLYLIFT" 2225271 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-969 2220993 2221442 2222071 "POLYCATQ" 2224263 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-968 2207335 2212740 2212805 "POLYCAT" 2216319 NIL POLYCAT (NIL T T T) -9 NIL 2218197 NIL) (-967 2200784 2202646 2205030 "POLYCAT-" 2205035 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-966 2200371 2200439 2200559 "POLY2UP" 2200710 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-965 2200003 2200060 2200169 "POLY2" 2200308 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-964 2198688 2198927 2199203 "POLUTIL" 2199777 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-963 2197043 2197320 2197651 "POLTOPOL" 2198410 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-962 2192509 2196977 2197024 "POINT" 2197029 NIL POINT (NIL T) -8 NIL NIL NIL) (-961 2190696 2191053 2191428 "PNTHEORY" 2192154 T PNTHEORY (NIL) -7 NIL NIL NIL) (-960 2189154 2189451 2189850 "PMTOOLS" 2190394 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-959 2188747 2188825 2188942 "PMSYM" 2189070 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-958 2188255 2188324 2188499 "PMQFCAT" 2188672 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-957 2187610 2187720 2187876 "PMPRED" 2188132 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-956 2187003 2187089 2187251 "PMPREDFS" 2187511 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-955 2185667 2185875 2186253 "PMPLCAT" 2186765 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-954 2185199 2185278 2185430 "PMLSAGG" 2185582 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-953 2184672 2184748 2184930 "PMKERNEL" 2185117 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-952 2184289 2184364 2184477 "PMINS" 2184591 NIL PMINS (NIL T) -7 NIL NIL NIL) (-951 2183731 2183800 2184009 "PMFS" 2184214 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-950 2182959 2183077 2183282 "PMDOWN" 2183608 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-949 2182126 2182284 2182465 "PMASS" 2182798 T PMASS (NIL) -7 NIL NIL NIL) (-948 2181399 2181509 2181672 "PMASSFS" 2182013 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-947 2181054 2181122 2181216 "PLOTTOOL" 2181325 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-946 2175661 2176865 2178013 "PLOT" 2179926 T PLOT (NIL) -8 NIL NIL NIL) (-945 2171465 2172509 2173430 "PLOT3D" 2174760 T PLOT3D (NIL) -8 NIL NIL NIL) (-944 2170377 2170554 2170789 "PLOT1" 2171269 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-943 2145768 2150443 2155294 "PLEQN" 2165643 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-942 2145086 2145208 2145388 "PINTERP" 2145633 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-941 2144779 2144826 2144929 "PINTERPA" 2145033 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-940 2143995 2144543 2144630 "PI" 2144670 T PI (NIL) -8 NIL NIL 2144737) (-939 2142278 2143253 2143281 "PID" 2143463 T PID (NIL) -9 NIL 2143597 NIL) (-938 2142029 2142066 2142141 "PICOERCE" 2142235 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-937 2141349 2141488 2141664 "PGROEB" 2141885 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-936 2136936 2137750 2138655 "PGE" 2140464 T PGE (NIL) -7 NIL NIL NIL) (-935 2135059 2135306 2135672 "PGCD" 2136653 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-934 2134397 2134500 2134661 "PFRPAC" 2134943 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-933 2131037 2132945 2133298 "PFR" 2134076 NIL PFR (NIL T) -8 NIL NIL NIL) (-932 2129426 2129670 2129995 "PFOTOOLS" 2130784 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-931 2127959 2128198 2128549 "PFOQ" 2129183 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-930 2126460 2126672 2127028 "PFO" 2127743 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-929 2123013 2126349 2126418 "PF" 2126423 NIL PF (NIL NIL) -8 NIL NIL NIL) (-928 2120333 2121604 2121632 "PFECAT" 2122217 T PFECAT (NIL) -9 NIL 2122601 NIL) (-927 2119778 2119932 2120146 "PFECAT-" 2120151 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-926 2118381 2118633 2118934 "PFBRU" 2119527 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-925 2116247 2116599 2117031 "PFBR" 2118032 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-924 2112293 2113759 2114406 "PERM" 2115633 NIL PERM (NIL T) -8 NIL NIL NIL) (-923 2107527 2108500 2109370 "PERMGRP" 2111456 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-922 2105591 2106551 2106592 "PERMCAT" 2106992 NIL PERMCAT (NIL T) -9 NIL 2107290 NIL) (-921 2105244 2105285 2105409 "PERMAN" 2105544 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-920 2102735 2104909 2105031 "PENDTREE" 2105155 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-919 2101664 2101879 2101920 "PDSPC" 2102453 NIL PDSPC (NIL T) -9 NIL 2102698 NIL) (-918 2100767 2100985 2101347 "PDSPC-" 2101352 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-917 2099649 2100417 2100458 "PDRING" 2100463 NIL PDRING (NIL T) -9 NIL 2100491 NIL) (-916 2098536 2099154 2099208 "PDMOD" 2099213 NIL PDMOD (NIL T T) -9 NIL 2099317 NIL) (-915 2095751 2096529 2097197 "PDEPROB" 2097888 T PDEPROB (NIL) -8 NIL NIL NIL) (-914 2093296 2093800 2094355 "PDEPACK" 2095216 T PDEPACK (NIL) -7 NIL NIL NIL) (-913 2092208 2092398 2092649 "PDECOMP" 2093095 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-912 2089773 2090616 2090644 "PDECAT" 2091431 T PDECAT (NIL) -9 NIL 2092144 NIL) (-911 2089402 2089457 2089511 "PDDOM" 2089676 NIL PDDOM (NIL T T) -9 NIL 2089756 NIL) (-910 2089221 2089251 2089358 "PDDOM-" 2089363 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-909 2088972 2089005 2089095 "PCOMP" 2089182 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-908 2087150 2087773 2088070 "PBWLB" 2088701 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-907 2079623 2081223 2082561 "PATTERN" 2085833 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-906 2079255 2079312 2079421 "PATTERN2" 2079560 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-905 2077012 2077400 2077857 "PATTERN1" 2078844 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-904 2074380 2074961 2075442 "PATRES" 2076577 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-903 2073944 2074011 2074143 "PATRES2" 2074307 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-902 2071827 2072232 2072639 "PATMATCH" 2073611 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-901 2071323 2071532 2071573 "PATMAB" 2071680 NIL PATMAB (NIL T) -9 NIL 2071763 NIL) (-900 2069841 2070177 2070435 "PATLRES" 2071128 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-899 2069387 2069510 2069551 "PATAB" 2069556 NIL PATAB (NIL T) -9 NIL 2069728 NIL) (-898 2067569 2067964 2068387 "PARTPERM" 2068984 T PARTPERM (NIL) -7 NIL NIL NIL) (-897 2067190 2067253 2067355 "PARSURF" 2067500 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-896 2066822 2066879 2066988 "PARSU2" 2067127 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-895 2066586 2066626 2066693 "PARSER" 2066775 T PARSER (NIL) -7 NIL NIL NIL) (-894 2066207 2066270 2066372 "PARSCURV" 2066517 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-893 2065839 2065896 2066005 "PARSC2" 2066144 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-892 2065478 2065536 2065633 "PARPCURV" 2065775 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-891 2065110 2065167 2065276 "PARPC2" 2065415 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-890 2064171 2064483 2064665 "PARAMAST" 2064948 T PARAMAST (NIL) -8 NIL NIL NIL) (-889 2063691 2063777 2063896 "PAN2EXPR" 2064072 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-888 2062468 2062812 2063040 "PALETTE" 2063483 T PALETTE (NIL) -8 NIL NIL NIL) (-887 2060861 2061473 2061833 "PAIR" 2062154 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-886 2054453 2060118 2060313 "PADICRC" 2060715 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-885 2047369 2053797 2053982 "PADICRAT" 2054300 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-884 2045684 2047306 2047351 "PADIC" 2047356 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-883 2042780 2044344 2044384 "PADICCT" 2044965 NIL PADICCT (NIL NIL) -9 NIL 2045247 NIL) (-882 2041737 2041937 2042205 "PADEPAC" 2042567 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-881 2040949 2041082 2041288 "PADE" 2041599 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-880 2039336 2040157 2040437 "OWP" 2040753 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-879 2038829 2039042 2039139 "OVERSET" 2039259 T OVERSET (NIL) -8 NIL NIL NIL) (-878 2037875 2038434 2038606 "OVAR" 2038697 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-877 2037139 2037260 2037421 "OUT" 2037734 T OUT (NIL) -7 NIL NIL NIL) (-876 2026011 2028248 2030448 "OUTFORM" 2034959 T OUTFORM (NIL) -8 NIL NIL NIL) (-875 2025347 2025608 2025735 "OUTBFILE" 2025904 T OUTBFILE (NIL) -8 NIL NIL NIL) (-874 2024654 2024819 2024847 "OUTBCON" 2025165 T OUTBCON (NIL) -9 NIL 2025331 NIL) (-873 2024255 2024367 2024524 "OUTBCON-" 2024529 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-872 2023635 2023984 2024073 "OSI" 2024186 T OSI (NIL) -8 NIL NIL NIL) (-871 2023138 2023476 2023504 "OSGROUP" 2023509 T OSGROUP (NIL) -9 NIL 2023531 NIL) (-870 2021883 2022110 2022395 "ORTHPOL" 2022885 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-869 2019434 2021718 2021839 "OREUP" 2021844 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-868 2016837 2019125 2019252 "ORESUP" 2019376 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-867 2014365 2014865 2015426 "OREPCTO" 2016326 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-866 2008037 2010238 2010279 "OREPCAT" 2012627 NIL OREPCAT (NIL T) -9 NIL 2013731 NIL) (-865 2005184 2005966 2007024 "OREPCAT-" 2007029 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-864 2004431 2004654 2004682 "ORDTYPE" 2004991 T ORDTYPE (NIL) -9 NIL 2005154 NIL) (-863 2003774 2003948 2004203 "ORDTYPE-" 2004208 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-862 2003387 2003657 2003743 "ORDSTRCT" 2003748 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-861 2002957 2003255 2003283 "ORDSET" 2003288 T ORDSET (NIL) -9 NIL 2003310 NIL) (-860 2001495 2002286 2002314 "ORDRING" 2002516 T ORDRING (NIL) -9 NIL 2002641 NIL) (-859 2001140 2001234 2001378 "ORDRING-" 2001383 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 2000493 2000956 2000984 "ORDMON" 2000989 T ORDMON (NIL) -9 NIL 2001010 NIL) (-857 1999655 1999802 1999997 "ORDFUNS" 2000342 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1998966 1999385 1999413 "ORDFIN" 1999478 T ORDFIN (NIL) -9 NIL 1999552 NIL) (-855 1995525 1997552 1997961 "ORDCOMP" 1998590 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1994791 1994918 1995104 "ORDCOMP2" 1995385 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1991372 1992282 1993096 "OPTPROB" 1993997 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1988174 1988813 1989517 "OPTPACK" 1990688 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1985847 1986613 1986641 "OPTCAT" 1987460 T OPTCAT (NIL) -9 NIL 1988110 NIL) (-850 1985231 1985524 1985629 "OPSIG" 1985762 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1984999 1985038 1985104 "OPQUERY" 1985185 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1982130 1983310 1983814 "OP" 1984528 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1981490 1981716 1981757 "OPERCAT" 1981969 NIL OPERCAT (NIL T) -9 NIL 1982066 NIL) (-846 1981245 1981301 1981418 "OPERCAT-" 1981423 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1978058 1980042 1980411 "ONECOMP" 1980909 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1977363 1977478 1977652 "ONECOMP2" 1977930 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1976782 1976888 1977018 "OMSERVER" 1977253 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1973644 1976222 1976262 "OMSAGG" 1976323 NIL OMSAGG (NIL T) -9 NIL 1976387 NIL) (-841 1972267 1972530 1972812 "OMPKG" 1973382 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1971697 1971800 1971828 "OM" 1972127 T OM (NIL) -9 NIL NIL NIL) (-839 1970244 1971246 1971415 "OMLO" 1971578 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1969204 1969351 1969571 "OMEXPR" 1970070 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1968495 1968750 1968886 "OMERR" 1969088 T OMERR (NIL) -8 NIL NIL NIL) (-836 1967646 1967916 1968076 "OMERRK" 1968355 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1967097 1967323 1967431 "OMENC" 1967558 T OMENC (NIL) -8 NIL NIL NIL) (-834 1960992 1962177 1963348 "OMDEV" 1965946 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1960061 1960232 1960426 "OMCONN" 1960818 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1958555 1959531 1959559 "OINTDOM" 1959564 T OINTDOM (NIL) -9 NIL 1959585 NIL) (-831 1955893 1957243 1957580 "OFMONOID" 1958250 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1955265 1955830 1955875 "ODVAR" 1955880 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1952688 1955010 1955165 "ODR" 1955170 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1944993 1952464 1952590 "ODPOL" 1952595 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1938792 1944865 1944970 "ODP" 1944975 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1937558 1937773 1938048 "ODETOOLS" 1938566 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1934525 1935183 1935899 "ODESYS" 1936891 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1929407 1930315 1931340 "ODERTRIC" 1933600 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1928833 1928915 1929109 "ODERED" 1929319 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1925721 1926269 1926946 "ODERAT" 1928256 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1922680 1923145 1923742 "ODEPRRIC" 1925250 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1920623 1921219 1921705 "ODEPROB" 1922214 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1917143 1917628 1918275 "ODEPRIM" 1920102 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1916392 1916494 1916754 "ODEPAL" 1917035 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1912554 1913345 1914209 "ODEPACK" 1915548 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1911615 1911722 1911944 "ODEINT" 1912443 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1905716 1907141 1908588 "ODEIFTBL" 1910188 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1901114 1901900 1902852 "ODEEF" 1904875 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1900463 1900552 1900775 "ODECONST" 1901019 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1898574 1899235 1899263 "ODECAT" 1899868 T ODECAT (NIL) -9 NIL 1900399 NIL) (-811 1895429 1898279 1898401 "OCT" 1898484 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1895067 1895110 1895237 "OCTCT2" 1895380 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1889674 1892110 1892150 "OC" 1893247 NIL OC (NIL T) -9 NIL 1894105 NIL) (-808 1886901 1887649 1888639 "OC-" 1888733 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1886226 1886694 1886722 "OCAMON" 1886727 T OCAMON (NIL) -9 NIL 1886748 NIL) (-806 1885730 1886071 1886099 "OASGP" 1886104 T OASGP (NIL) -9 NIL 1886124 NIL) (-805 1884964 1885453 1885481 "OAMONS" 1885521 T OAMONS (NIL) -9 NIL 1885564 NIL) (-804 1884351 1884784 1884812 "OAMON" 1884817 T OAMON (NIL) -9 NIL 1884837 NIL) (-803 1883582 1884100 1884128 "OAGROUP" 1884133 T OAGROUP (NIL) -9 NIL 1884153 NIL) (-802 1883272 1883322 1883410 "NUMTUBE" 1883526 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1876845 1878363 1879899 "NUMQUAD" 1881756 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1872601 1873589 1874614 "NUMODE" 1875840 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1869942 1870822 1870850 "NUMINT" 1871773 T NUMINT (NIL) -9 NIL 1872537 NIL) (-798 1868890 1869087 1869305 "NUMFMT" 1869744 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1855249 1858194 1860726 "NUMERIC" 1866397 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1849619 1854698 1854793 "NTSCAT" 1854798 NIL NTSCAT (NIL T T T T) -9 NIL 1854837 NIL) (-795 1848813 1848978 1849171 "NTPOLFN" 1849458 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1836614 1845638 1846450 "NSUP" 1848034 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1836246 1836303 1836412 "NSUP2" 1836551 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1826196 1836020 1836153 "NSMP" 1836158 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1824628 1824929 1825286 "NREP" 1825884 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1823219 1823471 1823829 "NPCOEF" 1824371 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1822285 1822400 1822616 "NORMRETR" 1823100 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1820326 1820616 1821025 "NORMPK" 1821993 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1820011 1820039 1820163 "NORMMA" 1820292 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1819811 1819968 1819997 "NONE" 1820002 T NONE (NIL) -8 NIL NIL NIL) (-785 1819600 1819629 1819698 "NONE1" 1819775 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1819097 1819159 1819338 "NODE1" 1819532 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1817378 1818229 1818484 "NNI" 1818831 T NNI (NIL) -8 NIL NIL 1819066) (-782 1815798 1816111 1816475 "NLINSOL" 1817046 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1812039 1813034 1813933 "NIPROB" 1814919 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1810796 1811030 1811332 "NFINTBAS" 1811801 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1809970 1810446 1810487 "NETCLT" 1810659 NIL NETCLT (NIL T) -9 NIL 1810741 NIL) (-778 1808678 1808909 1809190 "NCODIV" 1809738 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1808440 1808477 1808552 "NCNTFRAC" 1808635 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1806620 1806984 1807404 "NCEP" 1808065 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1805457 1806230 1806258 "NASRING" 1806368 T NASRING (NIL) -9 NIL 1806448 NIL) (-774 1805252 1805296 1805390 "NASRING-" 1805395 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1804345 1804870 1804898 "NARNG" 1805015 T NARNG (NIL) -9 NIL 1805106 NIL) (-772 1804037 1804104 1804238 "NARNG-" 1804243 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1802916 1803123 1803358 "NAGSP" 1803822 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1794188 1795872 1797545 "NAGS" 1801263 T NAGS (NIL) -7 NIL NIL NIL) (-769 1792736 1793044 1793375 "NAGF07" 1793877 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1787274 1788565 1789872 "NAGF04" 1791449 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1780242 1781856 1783489 "NAGF02" 1785661 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1775466 1776566 1777683 "NAGF01" 1779145 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1769094 1770660 1772245 "NAGE04" 1773901 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1760263 1762384 1764514 "NAGE02" 1766984 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1756216 1757163 1758127 "NAGE01" 1759319 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1754011 1754545 1755103 "NAGD03" 1755678 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1745761 1747689 1749643 "NAGD02" 1752077 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1739572 1740997 1742437 "NAGD01" 1744341 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1735781 1736603 1737440 "NAGC06" 1738755 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1734246 1734578 1734934 "NAGC05" 1735445 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1733622 1733741 1733885 "NAGC02" 1734122 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1732567 1733150 1733190 "NAALG" 1733269 NIL NAALG (NIL T) -9 NIL 1733330 NIL) (-755 1732402 1732431 1732521 "NAALG-" 1732526 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1726352 1727460 1728647 "MULTSQFR" 1731298 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1725671 1725746 1725930 "MULTFACT" 1726264 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1718342 1722256 1722309 "MTSCAT" 1723379 NIL MTSCAT (NIL T T) -9 NIL 1723894 NIL) (-751 1718054 1718108 1718200 "MTHING" 1718282 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1717846 1717879 1717939 "MSYSCMD" 1718014 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1713928 1716601 1716921 "MSET" 1717559 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1710997 1713489 1713530 "MSETAGG" 1713535 NIL MSETAGG (NIL T) -9 NIL 1713569 NIL) (-747 1706839 1708376 1709121 "MRING" 1710297 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1706405 1706472 1706603 "MRF2" 1706766 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1706023 1706058 1706202 "MRATFAC" 1706364 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1703635 1703930 1704361 "MPRFF" 1705728 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1697656 1703489 1703586 "MPOLY" 1703591 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1697146 1697181 1697389 "MPCPF" 1697615 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1696660 1696703 1696887 "MPC3" 1697097 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695855 1695936 1696157 "MPC2" 1696575 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1694156 1694493 1694883 "MONOTOOL" 1695515 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1693367 1693684 1693712 "MONOID" 1693931 T MONOID (NIL) -9 NIL 1694078 NIL) (-737 1692913 1693032 1693213 "MONOID-" 1693218 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1682503 1688733 1688792 "MONOGEN" 1689466 NIL MONOGEN (NIL T T) -9 NIL 1689922 NIL) (-735 1679721 1680456 1681456 "MONOGEN-" 1681575 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1678540 1678986 1679014 "MONADWU" 1679406 T MONADWU (NIL) -9 NIL 1679644 NIL) (-733 1677912 1678071 1678319 "MONADWU-" 1678324 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1677257 1677501 1677529 "MONAD" 1677736 T MONAD (NIL) -9 NIL 1677848 NIL) (-731 1676942 1677020 1677152 "MONAD-" 1677157 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1675231 1675855 1676134 "MOEBIUS" 1676695 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1674495 1674899 1674939 "MODULE" 1674944 NIL MODULE (NIL T) -9 NIL 1674983 NIL) (-728 1674063 1674159 1674349 "MODULE-" 1674354 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1671743 1672427 1672754 "MODRING" 1673887 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1668687 1669848 1670369 "MODOP" 1671272 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1667275 1667754 1668031 "MODMONOM" 1668550 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1657043 1665566 1665980 "MODMON" 1666912 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1654199 1655887 1656163 "MODFIELD" 1656918 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1653176 1653480 1653670 "MMLFORM" 1654029 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1652702 1652745 1652924 "MMAP" 1653127 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1650767 1651534 1651575 "MLO" 1651998 NIL MLO (NIL T) -9 NIL 1652240 NIL) (-719 1648133 1648649 1649251 "MLIFT" 1650248 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1647524 1647608 1647762 "MKUCFUNC" 1648044 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1647123 1647193 1647316 "MKRECORD" 1647447 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1646170 1646332 1646560 "MKFUNC" 1646934 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1645558 1645662 1645818 "MKFLCFN" 1646053 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1644835 1644937 1645122 "MKBCFUNC" 1645451 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1641424 1644389 1644525 "MINT" 1644719 T MINT (NIL) -8 NIL NIL NIL) (-712 1640236 1640479 1640756 "MHROWRED" 1641179 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1635616 1638771 1639176 "MFLOAT" 1639851 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1634973 1635049 1635220 "MFINFACT" 1635528 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1631288 1632136 1633020 "MESH" 1634109 T MESH (NIL) -7 NIL NIL NIL) (-708 1629678 1629990 1630343 "MDDFACT" 1630975 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1626448 1628809 1628850 "MDAGG" 1629105 NIL MDAGG (NIL T) -9 NIL 1629248 NIL) (-706 1615142 1625741 1625948 "MCMPLX" 1626261 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1614279 1614425 1614626 "MCDEN" 1614991 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1612169 1612439 1612819 "MCALCFN" 1614009 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1611094 1611334 1611567 "MAYBE" 1611975 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1608706 1609229 1609791 "MATSTOR" 1610565 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1604618 1608078 1608326 "MATRIX" 1608491 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1600384 1601091 1601827 "MATLIN" 1603975 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1590210 1593441 1593518 "MATCAT" 1598550 NIL MATCAT (NIL T T T) -9 NIL 1600022 NIL) (-698 1586403 1587473 1588886 "MATCAT-" 1588891 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1584997 1585150 1585483 "MATCAT2" 1586238 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1583109 1583433 1583817 "MAPPKG3" 1584672 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1582090 1582263 1582485 "MAPPKG2" 1582933 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1580589 1580873 1581200 "MAPPKG1" 1581796 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1579668 1579995 1580172 "MAPPAST" 1580432 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1579279 1579337 1579460 "MAPHACK3" 1579604 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1578871 1578932 1579046 "MAPHACK2" 1579211 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1578309 1578412 1578554 "MAPHACK1" 1578762 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1576388 1577009 1577313 "MAGMA" 1578037 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1575867 1576112 1576203 "MACROAST" 1576317 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1572288 1574106 1574567 "M3D" 1575439 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1566338 1570599 1570640 "LZSTAGG" 1571422 NIL LZSTAGG (NIL T) -9 NIL 1571717 NIL) (-685 1562296 1563469 1564926 "LZSTAGG-" 1564931 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1559383 1560187 1560674 "LWORD" 1561841 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1558959 1559187 1559262 "LSTAST" 1559328 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1551849 1558730 1558864 "LSQM" 1558869 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1551073 1551212 1551440 "LSPP" 1551704 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1548885 1549186 1549642 "LSMP" 1550762 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1545664 1546338 1547068 "LSMP1" 1548187 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1539466 1544754 1544795 "LSAGG" 1544857 NIL LSAGG (NIL T) -9 NIL 1544935 NIL) (-677 1536161 1537085 1538298 "LSAGG-" 1538303 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1533760 1535305 1535554 "LPOLY" 1535956 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1533342 1533427 1533550 "LPEFRAC" 1533669 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1531663 1532436 1532689 "LO" 1533174 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1531275 1531413 1531441 "LOGIC" 1531552 T LOGIC (NIL) -9 NIL 1531633 NIL) (-672 1531137 1531160 1531231 "LOGIC-" 1531236 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1530330 1530470 1530663 "LODOOPS" 1530993 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1527753 1530246 1530312 "LODO" 1530317 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1526291 1526526 1526879 "LODOF" 1527500 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1522495 1524926 1524967 "LODOCAT" 1525405 NIL LODOCAT (NIL T) -9 NIL 1525616 NIL) (-667 1522228 1522286 1522413 "LODOCAT-" 1522418 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1519548 1522069 1522187 "LODO2" 1522192 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1516983 1519485 1519530 "LODO1" 1519535 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1515864 1516029 1516334 "LODEEF" 1516806 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1511142 1514030 1514071 "LNAGG" 1514933 NIL LNAGG (NIL T) -9 NIL 1515368 NIL) (-662 1510289 1510503 1510845 "LNAGG-" 1510850 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1506425 1507214 1507853 "LMOPS" 1509704 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1505814 1506202 1506243 "LMODULE" 1506248 NIL LMODULE (NIL T) -9 NIL 1506274 NIL) (-659 1503015 1505459 1505582 "LMDICT" 1505724 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1502633 1502805 1502846 "LLINSET" 1502907 NIL LLINSET (NIL T) -9 NIL 1502951 NIL) (-657 1502332 1502541 1502601 "LITERAL" 1502606 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1495498 1501266 1501570 "LIST" 1502061 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1495023 1495097 1495236 "LIST3" 1495418 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1494030 1494208 1494436 "LIST2" 1494841 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1492164 1492476 1492875 "LIST2MAP" 1493677 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1491795 1491983 1492024 "LINSET" 1492029 NIL LINSET (NIL T) -9 NIL 1492063 NIL) (-651 1490208 1490822 1490863 "LINEXP" 1491353 NIL LINEXP (NIL T) -9 NIL 1491626 NIL) (-650 1488785 1489045 1489356 "LINDEP" 1489960 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485552 1486271 1487048 "LIMITRF" 1488040 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1483855 1484151 1484560 "LIMITPS" 1485247 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1478283 1483366 1483594 "LIE" 1483676 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1477217 1477686 1477726 "LIECAT" 1477866 NIL LIECAT (NIL T) -9 NIL 1478017 NIL) (-645 1477058 1477085 1477173 "LIECAT-" 1477178 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469651 1476598 1476754 "LIB" 1476922 T LIB (NIL) -8 NIL NIL NIL) (-643 1465286 1466169 1467104 "LGROBP" 1468768 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1463284 1463558 1463908 "LF" 1465007 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1462124 1462816 1462844 "LFCAT" 1463051 T LFCAT (NIL) -9 NIL 1463190 NIL) (-640 1459026 1459656 1460344 "LEXTRIPK" 1461488 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455770 1456596 1457099 "LEXP" 1458606 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1455246 1455491 1455583 "LETAST" 1455698 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453644 1453957 1454358 "LEADCDET" 1454928 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1452834 1452908 1453137 "LAZM3PK" 1453565 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447751 1450911 1451449 "LAUPOL" 1452346 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1447330 1447374 1447535 "LAPLACE" 1447701 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1445269 1446431 1446682 "LA" 1447163 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1444249 1444833 1444874 "LALG" 1444936 NIL LALG (NIL T) -9 NIL 1444995 NIL) (-631 1443963 1444022 1444158 "LALG-" 1444163 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1443798 1443822 1443863 "KVTFROM" 1443925 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442721 1443165 1443350 "KTVLOGIC" 1443633 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442556 1442580 1442621 "KRCFROM" 1442683 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441460 1441647 1441946 "KOVACIC" 1442356 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1441295 1441319 1441360 "KONVERT" 1441422 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1441130 1441154 1441195 "KOERCE" 1441257 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1438961 1439723 1440100 "KERNEL" 1440786 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438457 1438538 1438670 "KERNEL2" 1438875 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1432168 1436934 1436988 "KDAGG" 1437365 NIL KDAGG (NIL T T) -9 NIL 1437571 NIL) (-621 1431697 1431821 1432026 "KDAGG-" 1432031 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1424845 1431358 1431513 "KAFILE" 1431575 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1419273 1424356 1424584 "JORDAN" 1424666 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418652 1418922 1419043 "JOINAST" 1419172 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418498 1418557 1418612 "JAVACODE" 1418617 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414725 1416675 1416729 "IXAGG" 1417658 NIL IXAGG (NIL T T) -9 NIL 1418117 NIL) (-615 1413644 1413950 1414369 "IXAGG-" 1414374 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1409177 1413566 1413625 "IVECTOR" 1413630 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1407943 1408180 1408446 "ITUPLE" 1408944 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406445 1406622 1406917 "ITRIGMNP" 1407765 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1405190 1405394 1405677 "ITFUN3" 1406221 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1404822 1404879 1404988 "ITFUN2" 1405127 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1403981 1404302 1404476 "ITFORM" 1404668 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1401942 1403001 1403279 "ITAYLOR" 1403736 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1390887 1396079 1397242 "ISUPS" 1400812 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1389991 1390131 1390367 "ISUMP" 1390734 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385369 1389936 1389977 "ISTRING" 1389982 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1384845 1385090 1385182 "ISAST" 1385297 T ISAST (NIL) -8 NIL NIL NIL) (-603 1384054 1384136 1384352 "IRURPK" 1384759 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1382990 1383191 1383431 "IRSN" 1383834 T IRSN (NIL) -7 NIL NIL NIL) (-601 1381061 1381416 1381845 "IRRF2F" 1382628 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1380808 1380846 1380922 "IRREDFFX" 1381017 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379423 1379682 1379981 "IROOT" 1380541 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1376027 1377107 1377799 "IR" 1378763 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1375232 1375520 1375671 "IRFORM" 1375896 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1372845 1373340 1373906 "IR2" 1374710 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1371945 1372058 1372272 "IR2F" 1372728 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371736 1371770 1371830 "IPRNTPK" 1371905 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1368317 1371625 1371694 "IPF" 1371699 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366644 1368242 1368299 "IPADIC" 1368304 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1365956 1366204 1366334 "IP4ADDR" 1366534 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365330 1365585 1365717 "IOMODE" 1365844 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364403 1364927 1365054 "IOBFILE" 1365223 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1363891 1364307 1364335 "IOBCON" 1364340 T IOBCON (NIL) -9 NIL 1364361 NIL) (-587 1363402 1363460 1363643 "INVLAPLA" 1363827 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1353050 1355404 1357790 "INTTR" 1361066 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349385 1350127 1350992 "INTTOOLS" 1352235 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1348971 1349062 1349179 "INTSLPE" 1349288 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1346924 1348894 1348953 "INTRVL" 1348958 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344526 1345038 1345613 "INTRF" 1346409 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1343937 1344034 1344176 "INTRET" 1344424 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1341934 1342323 1342793 "INTRAT" 1343545 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1339197 1339780 1340399 "INTPM" 1341419 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1335942 1336541 1337279 "INTPAF" 1338583 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1331121 1332083 1333134 "INTPACK" 1334911 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1327933 1330918 1331027 "INT" 1331032 T INT (NIL) -8 NIL NIL NIL) (-575 1327185 1327337 1327545 "INTHERTR" 1327775 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326624 1326704 1326892 "INTHERAL" 1327099 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324470 1324913 1325370 "INTHEORY" 1326187 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1315876 1317497 1319269 "INTG0" 1322822 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296449 1301239 1306049 "INTFTBL" 1311086 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295698 1295836 1296009 "INTFACT" 1296308 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1293125 1293571 1294128 "INTEF" 1295252 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291478 1292217 1292245 "INTDOM" 1292546 T INTDOM (NIL) -9 NIL 1292753 NIL) (-567 1290847 1291021 1291263 "INTDOM-" 1291268 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1287207 1289136 1289190 "INTCAT" 1289989 NIL INTCAT (NIL T) -9 NIL 1290310 NIL) (-565 1286679 1286782 1286910 "INTBIT" 1287099 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285378 1285532 1285839 "INTALG" 1286524 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1284861 1284951 1285108 "INTAF" 1285282 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1278210 1284671 1284811 "INTABL" 1284816 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277543 1278009 1278074 "INT8" 1278108 T INT8 (NIL) -8 NIL NIL 1278153) (-560 1276875 1277341 1277406 "INT64" 1277440 T INT64 (NIL) -8 NIL NIL 1277485) (-559 1276207 1276673 1276738 "INT32" 1276772 T INT32 (NIL) -8 NIL NIL 1276817) (-558 1275539 1276005 1276070 "INT16" 1276104 T INT16 (NIL) -8 NIL NIL 1276149) (-557 1270234 1273087 1273115 "INS" 1274049 T INS (NIL) -9 NIL 1274714 NIL) (-556 1267474 1268245 1269219 "INS-" 1269292 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1266249 1266476 1266774 "INPSIGN" 1267227 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265367 1265484 1265681 "INPRODPF" 1266129 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264261 1264378 1264615 "INPRODFF" 1265247 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263261 1263413 1263673 "INNMFACT" 1264097 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262458 1262555 1262743 "INMODGCD" 1263160 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1260966 1261211 1261535 "INFSP" 1262203 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1260150 1260267 1260450 "INFPROD0" 1260846 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1257005 1258215 1258730 "INFORM" 1259643 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256615 1256675 1256773 "INFORM1" 1256940 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1256138 1256227 1256341 "INFINITY" 1256521 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255314 1255858 1255959 "INETCLTS" 1256057 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1253930 1254180 1254501 "INEP" 1255062 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1253135 1253827 1253892 "INDE" 1253897 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252699 1252767 1252884 "INCRMAPS" 1253062 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251517 1251968 1252174 "INBFILE" 1252513 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1246816 1247753 1248697 "INBFF" 1250605 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245724 1245993 1246021 "INBCON" 1246534 T INBCON (NIL) -9 NIL 1246800 NIL) (-538 1244976 1245199 1245475 "INBCON-" 1245480 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244455 1244700 1244791 "INAST" 1244905 T INAST (NIL) -8 NIL NIL NIL) (-536 1243882 1244134 1244240 "IMPTAST" 1244369 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240283 1243726 1243830 "IMATRIX" 1243835 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1238991 1239114 1239430 "IMATQF" 1240139 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1237211 1237438 1237775 "IMATLIN" 1238747 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1231792 1237135 1237193 "ILIST" 1237198 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229700 1231652 1231765 "IIARRAY2" 1231770 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1225098 1229611 1229675 "IFF" 1229680 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224445 1224715 1224831 "IFAST" 1225002 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219443 1223737 1223925 "IFARRAY" 1224302 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218623 1219347 1219420 "IFAMON" 1219425 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1218207 1218272 1218326 "IEVALAB" 1218533 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1217882 1217950 1218110 "IEVALAB-" 1218115 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217472 1217796 1217859 "IDPO" 1217864 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216680 1217361 1217436 "IDPOAMS" 1217441 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215945 1216569 1216644 "IDPOAM" 1216649 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214802 1215119 1215172 "IDPC" 1215690 NIL IDPC (NIL T T) -9 NIL 1215881 NIL) (-520 1214230 1214694 1214767 "IDPAM" 1214772 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213324 1213923 1214045 "IDPAG" 1214151 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212969 1213160 1213235 "IDENT" 1213269 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209224 1210072 1210967 "IDECOMP" 1212126 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202061 1203147 1204194 "IDEAL" 1208260 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201221 1201333 1201533 "ICDEN" 1201945 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200292 1200701 1200848 "ICARD" 1201094 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198352 1198665 1199070 "IBPTOOLS" 1199969 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193959 1197972 1198085 "IBITS" 1198271 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190682 1191258 1191953 "IBATOOL" 1193376 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188461 1188923 1189456 "IBACHIN" 1190217 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186293 1188307 1188410 "IARRAY2" 1188415 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182402 1186219 1186276 "IARRAY1" 1186281 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176262 1180814 1181295 "IAN" 1181941 T IAN (NIL) -8 NIL NIL NIL) (-506 1175773 1175830 1176003 "IALGFACT" 1176199 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175301 1175414 1175442 "HYPCAT" 1175649 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174839 1174956 1175142 "HYPCAT-" 1175147 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174434 1174634 1174717 "HOSTNAME" 1174776 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174279 1174316 1174357 "HOMOTOP" 1174362 NIL HOMOTOP (NIL T) -9 NIL 1174395 NIL) (-501 1170836 1172211 1172252 "HOAGG" 1173233 NIL HOAGG (NIL T) -9 NIL 1173962 NIL) (-500 1169430 1169829 1170355 "HOAGG-" 1170360 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163146 1169023 1169173 "HEXADEC" 1169300 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161894 1162116 1162379 "HEUGCD" 1162923 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160970 1161731 1161861 "HELLFDIV" 1161866 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159152 1160747 1160835 "HEAP" 1160914 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158415 1158704 1158838 "HEADAST" 1159038 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152258 1158330 1158392 "HDP" 1158397 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145970 1151893 1152045 "HDMP" 1152159 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145294 1145434 1145598 "HB" 1145826 T HB (NIL) -7 NIL NIL NIL) (-491 1138686 1145140 1145244 "HASHTBL" 1145249 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138162 1138407 1138499 "HASAST" 1138614 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135940 1137784 1137966 "HACKPI" 1138000 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131608 1135793 1135906 "GTSET" 1135911 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125029 1131486 1131584 "GSTBL" 1131589 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117416 1124194 1124450 "GSERIES" 1124829 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116543 1116960 1116988 "GROUP" 1117191 T GROUP (NIL) -9 NIL 1117325 NIL) (-484 1115909 1116068 1116319 "GROUP-" 1116324 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114276 1114597 1114984 "GROEBSOL" 1115586 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113176 1113464 1113515 "GRMOD" 1114044 NIL GRMOD (NIL T T) -9 NIL 1114212 NIL) (-481 1112944 1112980 1113108 "GRMOD-" 1113113 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108234 1109298 1110298 "GRIMAGE" 1111964 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106700 1106961 1107285 "GRDEF" 1107930 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106144 1106260 1106401 "GRAY" 1106579 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105317 1105723 1105774 "GRALG" 1105927 NIL GRALG (NIL T T) -9 NIL 1106020 NIL) (-476 1104978 1105051 1105214 "GRALG-" 1105219 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101755 1104563 1104741 "GPOLSET" 1104885 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101109 1101166 1101424 "GOSPER" 1101692 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096841 1097547 1098073 "GMODPOL" 1100808 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095846 1096030 1096268 "GHENSEL" 1096653 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090002 1090845 1091865 "GENUPS" 1094930 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089699 1089750 1089839 "GENUFACT" 1089945 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089111 1089188 1089353 "GENPGCD" 1089617 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088585 1088620 1088833 "GENMFACT" 1089070 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087151 1087408 1087715 "GENEEZ" 1088328 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081023 1086762 1086924 "GDMP" 1087074 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070366 1074794 1075900 "GCNAALG" 1080006 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068679 1069541 1069569 "GCDDOM" 1069824 T GCDDOM (NIL) -9 NIL 1069981 NIL) (-463 1068149 1068276 1068491 "GCDDOM-" 1068496 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066821 1067006 1067310 "GB" 1067928 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1055437 1057767 1060159 "GBINTERN" 1064512 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053274 1053566 1053987 "GBF" 1055112 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052055 1052220 1052487 "GBEUCLID" 1053090 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1051404 1051529 1051678 "GAUSSFAC" 1051926 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049771 1050073 1050387 "GALUTIL" 1051123 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048079 1048353 1048677 "GALPOLYU" 1049498 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1045444 1045734 1046141 "GALFACTU" 1047776 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037250 1038749 1040357 "GALFACT" 1043876 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034638 1035296 1035324 "FVFUN" 1036480 T FVFUN (NIL) -9 NIL 1037200 NIL) (-452 1033904 1034086 1034114 "FVC" 1034405 T FVC (NIL) -9 NIL 1034588 NIL) (-451 1033547 1033729 1033797 "FUNDESC" 1033856 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033162 1033344 1033425 "FUNCTION" 1033499 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030906 1031484 1031950 "FT" 1032716 T FT (NIL) -8 NIL NIL NIL) (-448 1029697 1030207 1030410 "FTEM" 1030723 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027988 1028277 1028674 "FSUPFACT" 1029388 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1026385 1026674 1027006 "FST" 1027676 T FST (NIL) -8 NIL NIL NIL) (-445 1025584 1025690 1025878 "FSRED" 1026267 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024283 1024539 1024886 "FSPRMELT" 1025299 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021589 1022027 1022513 "FSPECF" 1023846 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002654 1011363 1011404 "FS" 1015288 NIL FS (NIL T) -9 NIL 1017577 NIL) (-441 991297 994290 998347 "FS-" 998647 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990825 990879 991049 "FSINT" 991238 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989117 989818 990121 "FSERIES" 990604 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988159 988275 988499 "FSCINT" 988997 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 984367 987103 987144 "FSAGG" 987514 NIL FSAGG (NIL T) -9 NIL 987773 NIL) (-436 982129 982730 983526 "FSAGG-" 983621 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981171 981314 981541 "FSAGG2" 981982 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978849 979129 979677 "FS2UPS" 980889 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 978483 978526 978655 "FS2" 978800 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977361 977532 977834 "FS2EXPXP" 978308 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976787 976902 977054 "FRUTIL" 977241 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968200 972282 973640 "FR" 975461 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963214 965889 965929 "FRNAALG" 967249 NIL FRNAALG (NIL T) -9 NIL 967847 NIL) (-428 958887 959963 961238 "FRNAALG-" 961988 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958525 958568 958695 "FRNAAF2" 958838 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956900 957374 957670 "FRMOD" 958337 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954643 955275 955593 "FRIDEAL" 956691 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953834 953921 954212 "FRIDEAL2" 954550 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952967 953381 953422 "FRETRCT" 953427 NIL FRETRCT (NIL T) -9 NIL 953603 NIL) (-422 952079 952310 952661 "FRETRCT-" 952666 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949153 950363 950422 "FRAMALG" 951304 NIL FRAMALG (NIL T T) -9 NIL 951596 NIL) (-420 947287 947742 948372 "FRAMALG-" 948595 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940930 946760 947037 "FRAC" 947042 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940566 940623 940730 "FRAC2" 940867 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940202 940259 940366 "FR2" 940503 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934687 937581 937609 "FPS" 938728 T FPS (NIL) -9 NIL 939285 NIL) (-415 934136 934245 934409 "FPS-" 934555 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 931424 933093 933121 "FPC" 933346 T FPC (NIL) -9 NIL 933488 NIL) (-413 931217 931257 931354 "FPC-" 931359 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930007 930705 930746 "FPATMAB" 930751 NIL FPATMAB (NIL T) -9 NIL 930903 NIL) (-411 928246 928749 929096 "FPARFRAC" 929723 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923640 924138 924820 "FORTRAN" 927678 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 921356 921856 922395 "FORT" 923121 T FORT (NIL) -7 NIL NIL NIL) (-408 919032 919594 919622 "FORTFN" 920682 T FORTFN (NIL) -9 NIL 921306 NIL) (-407 918796 918846 918874 "FORTCAT" 918933 T FORTCAT (NIL) -9 NIL 918995 NIL) (-406 916902 917412 917802 "FORMULA" 918426 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916690 916720 916789 "FORMULA1" 916866 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916213 916265 916438 "FORDER" 916632 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 915309 915473 915666 "FOP" 916040 T FOP (NIL) -7 NIL NIL NIL) (-402 913890 914589 914763 "FNLA" 915191 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912605 913020 913048 "FNCAT" 913508 T FNCAT (NIL) -9 NIL 913768 NIL) (-400 912144 912564 912592 "FNAME" 912597 T FNAME (NIL) -8 NIL NIL NIL) (-399 910680 911643 911671 "FMTC" 911676 T FMTC (NIL) -9 NIL 911712 NIL) (-398 909426 910616 910662 "FMONOID" 910667 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906213 907381 907422 "FMONCAT" 908639 NIL FMONCAT (NIL T) -9 NIL 909244 NIL) (-396 905363 905955 906104 "FM" 906109 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902787 903433 903461 "FMFUN" 904605 T FMFUN (NIL) -9 NIL 905313 NIL) (-394 902056 902237 902265 "FMC" 902555 T FMC (NIL) -9 NIL 902737 NIL) (-393 899121 899981 900035 "FMCAT" 901230 NIL FMCAT (NIL T T) -9 NIL 901725 NIL) (-392 897987 898887 898987 "FM1" 899066 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895761 896177 896671 "FLOATRP" 897538 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 889339 893490 894111 "FLOAT" 895160 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886777 887277 887855 "FLOATCP" 888806 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 885425 886369 886410 "FLINEXP" 886415 NIL FLINEXP (NIL T) -9 NIL 886508 NIL) (-387 884579 884814 885142 "FLINEXP-" 885147 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883655 883799 884023 "FLASORT" 884431 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880757 881625 881677 "FLALG" 882904 NIL FLALG (NIL T T) -9 NIL 883371 NIL) (-384 874417 878166 878207 "FLAGG" 879469 NIL FLAGG (NIL T) -9 NIL 880121 NIL) (-383 873143 873482 873972 "FLAGG-" 873977 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872185 872328 872555 "FLAGG2" 872996 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869022 870030 870089 "FINRALG" 871217 NIL FINRALG (NIL T T) -9 NIL 871725 NIL) (-380 868182 868411 868750 "FINRALG-" 868755 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867548 867787 867815 "FINITE" 868011 T FINITE (NIL) -9 NIL 868118 NIL) (-378 859891 862078 862118 "FINAALG" 865785 NIL FINAALG (NIL T) -9 NIL 867238 NIL) (-377 855223 856273 857417 "FINAALG-" 858796 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854591 854978 855081 "FILE" 855153 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853235 853573 853627 "FILECAT" 854311 NIL FILECAT (NIL T T) -9 NIL 854527 NIL) (-374 850937 852465 852493 "FIELD" 852533 T FIELD (NIL) -9 NIL 852613 NIL) (-373 849557 849942 850453 "FIELD-" 850458 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847407 848192 848539 "FGROUP" 849243 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846497 846661 846881 "FGLMICPK" 847239 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842329 846422 846479 "FFX" 846484 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841930 841991 842126 "FFSLPE" 842262 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837920 838702 839498 "FFPOLY" 841166 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837424 837460 837669 "FFPOLY2" 837878 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833270 837343 837406 "FFP" 837411 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828668 833181 833245 "FF" 833250 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823794 828011 828201 "FFNBX" 828522 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818722 822929 823187 "FFNBP" 823648 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813355 818006 818217 "FFNB" 818555 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812187 812385 812700 "FFINTBAS" 813152 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808213 810434 810462 "FFIELDC" 811082 T FFIELDC (NIL) -9 NIL 811458 NIL) (-359 806875 807246 807743 "FFIELDC-" 807748 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806444 806490 806614 "FFHOM" 806817 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804139 804626 805143 "FFF" 805959 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799757 803881 803982 "FFCGX" 804082 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795379 799489 799596 "FFCGP" 799700 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790562 795106 795214 "FFCG" 795315 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770091 780294 780380 "FFCAT" 785545 NIL FFCAT (NIL T T T) -9 NIL 786996 NIL) (-352 765288 766336 767650 "FFCAT-" 768880 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764699 764742 764977 "FFCAT2" 765239 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754022 757671 758891 "FEXPR" 763551 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752984 753419 753460 "FEVALAB" 753544 NIL FEVALAB (NIL T) -9 NIL 753805 NIL) (-348 752143 752353 752691 "FEVALAB-" 752696 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750709 751526 751729 "FDIV" 752042 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747715 748456 748571 "FDIVCAT" 750139 NIL FDIVCAT (NIL T T T T) -9 NIL 750576 NIL) (-345 747477 747504 747674 "FDIVCAT-" 747679 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746697 746784 747061 "FDIV2" 747384 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745671 745992 746194 "FCTRDATA" 746515 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744357 744616 744905 "FCPAK1" 745402 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743456 743857 743998 "FCOMP" 744248 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727161 730606 734144 "FC" 739938 T FC (NIL) -8 NIL NIL NIL) (-339 719454 723482 723522 "FAXF" 725324 NIL FAXF (NIL T) -9 NIL 726016 NIL) (-338 716731 717388 718213 "FAXF-" 718678 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711786 716107 716283 "FARRAY" 716588 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706666 708733 708786 "FAMR" 709809 NIL FAMR (NIL T T) -9 NIL 710269 NIL) (-335 705556 705858 706293 "FAMR-" 706298 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704725 705478 705531 "FAMONOID" 705536 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702497 703207 703260 "FAMONC" 704201 NIL FAMONC (NIL T T) -9 NIL 704587 NIL) (-332 701161 702251 702388 "FAGROUP" 702393 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698956 699275 699678 "FACUTIL" 700842 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698055 698240 698462 "FACTFUNC" 698766 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690477 697358 697557 "EXPUPXS" 697911 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687960 688500 689086 "EXPRTUBE" 689911 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684231 684823 685553 "EXPRODE" 687299 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669715 682880 683309 "EXPR" 683835 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664269 664856 665662 "EXPR2UPS" 669013 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663901 663958 664067 "EXPR2" 664206 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654898 663052 663343 "EXPEXPAN" 663737 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654698 654855 654884 "EXIT" 654889 T EXIT (NIL) -8 NIL NIL NIL) (-321 654178 654422 654513 "EXITAST" 654627 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653805 653867 653980 "EVALCYC" 654110 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653346 653464 653505 "EVALAB" 653675 NIL EVALAB (NIL T) -9 NIL 653779 NIL) (-318 652827 652949 653170 "EVALAB-" 653175 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650181 651483 651511 "EUCDOM" 652066 T EUCDOM (NIL) -9 NIL 652416 NIL) (-316 648586 649028 649618 "EUCDOM-" 649623 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636125 638884 641634 "ESTOOLS" 645856 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635757 635814 635923 "ESTOOLS2" 636062 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635508 635550 635630 "ESTOOLS1" 635709 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629531 631139 631167 "ES" 633935 T ES (NIL) -9 NIL 635345 NIL) (-311 624478 625765 627582 "ES-" 627746 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620852 621613 622393 "ESCONT" 623718 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620597 620629 620711 "ESCONT1" 620814 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620272 620322 620422 "ES2" 620541 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619902 619960 620069 "ES1" 620208 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619118 619247 619423 "ERROR" 619746 T ERROR (NIL) -7 NIL NIL NIL) (-305 612516 618977 619068 "EQTBL" 619073 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605019 607830 609279 "EQ" 611100 NIL -2037 (NIL T) -8 NIL NIL NIL) (-303 604651 604708 604817 "EQ2" 604956 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599942 600989 602082 "EP" 603590 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598542 598833 599139 "ENV" 599656 T ENV (NIL) -8 NIL NIL NIL) (-300 597622 598176 598204 "ENTIRER" 598209 T ENTIRER (NIL) -9 NIL 598255 NIL) (-299 594316 595804 596165 "EMR" 597430 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593446 593631 593685 "ELTAGG" 594065 NIL ELTAGG (NIL T T) -9 NIL 594276 NIL) (-297 593165 593227 593368 "ELTAGG-" 593373 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592929 592958 593012 "ELTAB" 593096 NIL ELTAB (NIL T T) -9 NIL 593148 NIL) (-295 592055 592201 592400 "ELFUTS" 592780 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591797 591853 591881 "ELEMFUN" 591986 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591667 591688 591756 "ELEMFUN-" 591761 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586456 589709 589750 "ELAGG" 590690 NIL ELAGG (NIL T) -9 NIL 591153 NIL) (-291 584741 585175 585838 "ELAGG-" 585843 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584053 584190 584346 "ELABOR" 584605 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582714 582993 583287 "ELABEXPR" 583779 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575548 577351 578180 "EFUPXS" 581989 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568996 570797 571608 "EFULS" 574823 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566481 566839 567311 "EFSTRUC" 568628 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556272 557838 559386 "EF" 564996 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555346 555757 555906 "EAB" 556143 T EAB (NIL) -8 NIL NIL NIL) (-283 554528 555305 555333 "E04UCFA" 555338 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553710 554487 554515 "E04NAFA" 554520 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552892 553669 553697 "E04MBFA" 553702 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552074 552851 552879 "E04JAFA" 552884 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551258 552033 552061 "E04GCFA" 552066 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550442 551217 551245 "E04FDFA" 551250 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549624 550401 550429 "E04DGFA" 550434 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543797 545149 546513 "E04AGNT" 548280 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542555 543098 543138 "DVARCAT" 543479 NIL DVARCAT (NIL T) -9 NIL 543642 NIL) (-274 541759 541971 542285 "DVARCAT-" 542290 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534620 541558 541687 "DSMP" 541692 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533043 533762 533803 "DSEXT" 534166 NIL DSEXT (NIL T) -9 NIL 534460 NIL) (-271 531328 531756 532422 "DSEXT-" 532427 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526109 527273 528341 "DROPT" 530280 T DROPT (NIL) -8 NIL NIL NIL) (-269 525774 525833 525931 "DROPT1" 526044 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520889 522015 523152 "DROPT0" 524657 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519234 519559 519945 "DRAWPT" 520523 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513821 514744 515823 "DRAW" 518208 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513454 513507 513625 "DRAWHACK" 513762 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512185 512454 512745 "DRAWCX" 513183 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511700 511769 511920 "DRAWCURV" 512111 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502168 504130 506245 "DRAWCFUN" 509605 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498907 500833 500874 "DQAGG" 501503 NIL DQAGG (NIL T) -9 NIL 501777 NIL) (-260 486372 493118 493201 "DPOLCAT" 495053 NIL DPOLCAT (NIL T T T T) -9 NIL 495598 NIL) (-259 481209 482557 484515 "DPOLCAT-" 484520 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474556 481070 481168 "DPMO" 481173 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467806 474336 474503 "DPMM" 474508 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467376 467590 467679 "DOMTMPLT" 467737 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466809 467178 467258 "DOMCTOR" 467316 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466021 466289 466440 "DOMAIN" 466678 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459733 465656 465808 "DMP" 465922 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457678 458800 458841 "DMEXT" 458846 NIL DMEXT (NIL T) -9 NIL 459022 NIL) (-251 457278 457334 457478 "DLP" 457616 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451103 456605 456795 "DLIST" 457120 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447875 449928 449969 "DLAGG" 450519 NIL DLAGG (NIL T) -9 NIL 450749 NIL) (-248 446537 447201 447229 "DIVRING" 447321 T DIVRING (NIL) -9 NIL 447404 NIL) (-247 445774 445964 446264 "DIVRING-" 446269 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443876 444233 444639 "DISPLAY" 445388 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437739 443790 443853 "DIRPROD" 443858 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436587 436790 437055 "DIRPROD2" 437532 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425262 431298 431351 "DIRPCAT" 431609 NIL DIRPCAT (NIL NIL T) -9 NIL 432484 NIL) (-242 422588 423230 424111 "DIRPCAT-" 424448 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421875 422035 422221 "DIOSP" 422422 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418505 420759 420800 "DIOPS" 421234 NIL DIOPS (NIL T) -9 NIL 421463 NIL) (-239 418054 418168 418359 "DIOPS-" 418364 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 417105 417733 417761 "DIFRING" 417766 T DIFRING (NIL) -9 NIL 417788 NIL) (-237 416777 416851 416879 "DIFFSPC" 416998 T DIFFSPC (NIL) -9 NIL 417073 NIL) (-236 416422 416500 416652 "DIFFSPC-" 416657 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415478 415956 415997 "DIFFMOD" 416002 NIL DIFFMOD (NIL T) -9 NIL 416100 NIL) (-234 415186 415231 415272 "DIFFDOM" 415393 NIL DIFFDOM (NIL T) -9 NIL 415461 NIL) (-233 415039 415063 415147 "DIFFDOM-" 415152 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412971 414243 414284 "DIFEXT" 414289 NIL DIFEXT (NIL T) -9 NIL 414442 NIL) (-231 410221 412475 412516 "DIAGG" 412521 NIL DIAGG (NIL T) -9 NIL 412541 NIL) (-230 409605 409762 410014 "DIAGG-" 410019 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404977 408564 408841 "DHMATRIX" 409374 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400589 401498 402508 "DFSFUN" 403987 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395667 399520 399832 "DFLOAT" 400297 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393930 394211 394600 "DFINTTLS" 395375 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390959 391951 392351 "DERHAM" 393596 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388763 390734 390823 "DEQUEUE" 390903 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 388017 388150 388333 "DEGRED" 388625 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384447 385192 386038 "DEFINTRF" 387245 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 382002 382471 383063 "DEFINTEF" 383966 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381352 381622 381737 "DEFAST" 381907 T DEFAST (NIL) -8 NIL NIL NIL) (-219 375068 380945 381095 "DECIMAL" 381222 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372580 373038 373544 "DDFACT" 374612 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372176 372219 372370 "DBLRESP" 372531 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 370044 370406 370767 "DBASE" 371942 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369286 369524 369670 "DATAARY" 369943 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368392 369245 369273 "D03FAFA" 369278 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367499 368351 368379 "D03EEFA" 368384 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365449 365915 366404 "D03AGNT" 367030 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364738 365408 365436 "D02EJFA" 365441 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364027 364697 364725 "D02CJFA" 364730 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363316 363986 364014 "D02BHFA" 364019 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362605 363275 363303 "D02BBFA" 363308 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355802 357391 358997 "D02AGNT" 361019 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353570 354093 354639 "D01WGTS" 355276 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352637 353529 353557 "D01TRNS" 353562 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351705 352596 352624 "D01GBFA" 352629 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350773 351664 351692 "D01FCFA" 351697 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349841 350732 350760 "D01ASFA" 350765 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348909 349800 349828 "D01AQFA" 349833 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347977 348868 348896 "D01APFA" 348901 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347045 347936 347964 "D01ANFA" 347969 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346113 347004 347032 "D01AMFA" 347037 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345181 346072 346100 "D01ALFA" 346105 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344249 345140 345168 "D01AKFA" 345173 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343317 344208 344236 "D01AJFA" 344241 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336612 338165 339726 "D01AGNT" 341776 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335949 336077 336229 "CYCLOTOM" 336480 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332682 333397 334124 "CYCLES" 335242 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331994 332128 332299 "CVMP" 332543 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329835 330093 330462 "CTRIGMNP" 331722 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329271 329629 329702 "CTOR" 329782 T CTOR (NIL) -8 NIL NIL NIL) (-188 328780 329002 329103 "CTORKIND" 329190 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328057 328373 328401 "CTORCAT" 328583 T CTORCAT (NIL) -9 NIL 328696 NIL) (-186 327655 327766 327925 "CTORCAT-" 327930 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327117 327329 327437 "CTORCALL" 327579 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326491 326590 326743 "CSTTOOLS" 327014 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322290 322947 323705 "CRFP" 325803 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321765 322011 322103 "CRCEAST" 322218 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320812 320997 321225 "CRAPACK" 321569 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320196 320297 320501 "CPMATCH" 320688 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319921 319949 320055 "CPIMA" 320162 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316269 316941 317660 "COORDSYS" 319256 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315681 315802 315944 "CONTOUR" 316147 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311572 313684 314176 "CONTFRAC" 315221 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311452 311473 311501 "CONDUIT" 311538 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310526 311080 311108 "COMRING" 311113 T COMRING (NIL) -9 NIL 311165 NIL) (-173 309580 309884 310068 "COMPPROP" 310362 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309241 309276 309404 "COMPLPAT" 309539 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298544 309050 309159 "COMPLEX" 309164 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298180 298237 298344 "COMPLEX2" 298481 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297519 297640 297800 "COMPILER" 298040 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297237 297272 297370 "COMPFACT" 297478 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279516 290941 290981 "COMPCAT" 291985 NIL COMPCAT (NIL T) -9 NIL 293333 NIL) (-166 269028 271955 275582 "COMPCAT-" 275938 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268757 268785 268888 "COMMUPC" 268994 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268551 268585 268644 "COMMONOP" 268718 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 268107 268302 268389 "COMM" 268484 T COMM (NIL) -8 NIL NIL NIL) (-162 267683 267911 267986 "COMMAAST" 268052 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266932 267126 267154 "COMBOPC" 267492 T COMBOPC (NIL) -9 NIL 267667 NIL) (-160 265828 266038 266280 "COMBINAT" 266722 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 262285 262859 263486 "COMBF" 265250 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 261043 261401 261636 "COLOR" 262070 T COLOR (NIL) -8 NIL NIL NIL) (-157 260519 260764 260856 "COLONAST" 260971 T COLONAST (NIL) -8 NIL NIL NIL) (-156 260159 260206 260331 "CMPLXRT" 260466 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259607 259859 259958 "CLLCTAST" 260080 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 255109 256137 257217 "CLIP" 258547 T CLIP (NIL) -7 NIL NIL NIL) (-153 253450 254210 254450 "CLIF" 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index a86473ab..b0c434fc 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,36 +1,18 @@ -(731751 . 3486833883) -(((*1 *2 *3 *4 *5 *6 *5) - (-12 (-5 *4 (-171 (-227))) (-5 *5 (-576)) (-5 *6 (-1179)) - (-5 *3 (-227)) (-5 *2 (-1056)) (-5 *1 (-770))))) -(((*1 *2 *3 *3 *3 *3 *4 *3 *5) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) - (-5 *5 (-3 (|:| |fn| (-400)) (|:| |fp| (-79 LSFUN1)))) - (-5 *2 (-1056)) (-5 *1 (-765))))) -(((*1 *1 *1) (-5 *1 (-1084)))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-1312 *3 *4)) (-4 *1 (-385 *3 *4)) (-4 *3 (-861)) - (-4 *4 (-174)))) - ((*1 *1 *1 *1) (|partial| -12 (-4 *1 (-397 *2)) (-4 *2 (-1121)))) - ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-831 *2)) (-4 *2 (-861)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1305 *2 *3)) (-4 *2 (-861)) (-4 *3 (-1070)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-831 *3)) (-4 *1 (-1305 *3 *4)) (-4 *3 (-861)) - 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(((*1 *1 *2) (-12 (-5 *2 (-783)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1070)) (-14 *4 (-656 (-1197))))) @@ -1592,51 +1871,42 @@ (-4 *5 (-174)))) ((*1 *1) (-12 (-4 *2 (-174)) (-4 *1 (-736 *2 *3)) (-4 *3 (-1264 *2))))) (((*1 *1 *2) - (-12 (-5 *2 (-656 (-2 (|:| -4301 *3) (|:| -4440 *4)))) + (-12 (-5 *2 (-656 (-2 (|:| -4300 *3) (|:| -4439 *4)))) (-4 *3 (-1121)) (-4 *4 (-1121)) (-4 *1 (-1214 *3 *4)))) ((*1 *1) (-12 (-4 *1 (-1214 *2 *3)) (-4 *2 (-1121)) (-4 *3 (-1121))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1121)) (-4 *6 (-1121)) + (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-696 *4 *5 *6)) (-4 *4 (-1121))))) (((*1 *2 *1) - (-12 + (-12 (-5 *2 (-1193 (-419 (-971 *3)))) (-5 *1 (-465 *3 *4 *5 *6)) + (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-940)) + (-14 *5 (-656 (-1197))) (-14 *6 (-1288 (-701 *3)))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-4 *1 (-336 *2 *3)) (-4 *2 (-1070)) (-4 *3 (-804))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-656 (-783))) (-5 *3 (-173)) (-5 *1 (-1185 *4 *5)) + (-14 *4 (-940)) (-4 *5 (-1070))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-576)) (-5 *4 (-430 *2)) (-4 *2 (-968 *7 *5 *6)) + (-5 *1 (-754 *5 *6 *7 *2)) (-4 *5 (-805)) (-4 *6 (-861)) + (-4 *7 (-317))))) +(((*1 *2 *2) + (-12 (-5 *2 (-656 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-148)) + (-4 *3 (-317)) (-4 *3 (-568)) (-4 *4 (-805)) (-4 *5 (-861)) + (-5 *1 (-998 *3 *4 *5 *6))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1288 (-326 (-227)))) (-5 *2 - (-1288 - (-2 (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) - (|:| |deltaX| (-227)) (|:| |deltaY| (-227)) (|:| -1793 (-576)) - (|:| -3774 (-576)) (|:| |spline| (-576)) (|:| -1542 (-576)) - (|:| |axesColor| (-888)) (|:| -2328 (-576)) - (|:| |unitsColor| (-888)) (|:| |showing| (-576))))) - (-5 *1 (-1289))))) -(((*1 *2 *1) (-12 (-5 *2 (-576)) (-5 *1 (-876))))) + (-2 (|:| |additions| (-576)) (|:| |multiplications| (-576)) + (|:| |exponentiations| (-576)) (|:| |functionCalls| (-576)))) + (-5 *1 (-315))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-568)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-990 *4 *3)) (-4 *3 (-1264 *4))))) (((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-479)))) ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-479))))) -(((*1 *2 *3) - (-12 (-5 *3 (-971 *4)) (-4 *4 (-13 (-317) (-148))) - (-4 *2 (-968 *4 *6 *5)) (-5 *1 (-943 *4 *5 *6 *2)) - (-4 *5 (-13 (-861) (-626 (-1197)))) (-4 *6 (-805))))) -(((*1 *2 *2 *2 *2 *2) - (-12 (-4 *2 (-13 (-374) (-10 -8 (-15 ** ($ $ (-419 (-576))))))) - (-5 *1 (-1149 *3 *2)) (-4 *3 (-1264 *2))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1238)) (-5 *1 (-386 *4 *2)) - (-4 *2 (-13 (-384 *4) (-10 -7 (-6 -4466))))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4466)) (-4 *1 (-120 *2)) (-4 *2 (-1238))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-946))))) -(((*1 *1 *2) (-12 (-5 *2 (-1288 *3)) (-4 *3 (-374)) (-4 *1 (-339 *3)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1288 *3)) (-4 *3 (-1264 *4)) (-4 *4 (-1242)) - (-4 *1 (-353 *4 *3 *5)) (-4 *5 (-1264 (-419 *3))))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1288 *4)) (-5 *3 (-1288 *1)) (-4 *4 (-174)) - (-4 *1 (-378 *4)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1288 *4)) (-5 *3 (-1288 *1)) (-4 *4 (-174)) - (-4 *1 (-381 *4 *5)) (-4 *5 (-1264 *4)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1288 *3)) (-4 *3 (-174)) (-4 *1 (-421 *3 *4)) - (-4 *4 (-1264 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1288 *3)) (-4 *3 (-174)) (-4 *1 (-429 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-1013 *2)) (-4 *2 (-568)) (-4 *2 (-557)))) - ((*1 *1 *1) (-4 *1 (-1081)))) +(((*1 *1 *2) (-12 (-5 *1 (-229 *2)) (-4 *2 (-13 (-374) (-1223)))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-804)))) @@ -1743,9 +2013,9 @@ (-4 *6 (-374)) (-5 *2 (-598 *6)) (-5 *1 (-596 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -1698 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2451 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-374)) (-4 *6 (-374)) - (-5 *2 (-2 (|:| -1698 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2451 *6) (|:| |coeff| *6))) (-5 *1 (-596 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -1864,7 +2134,7 @@ (-4 *8 (-1070)) (-4 *6 (-805)) (-4 *2 (-13 (-1121) - (-10 -8 (-15 -3030 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-783)))))) + (-10 -8 (-15 -3029 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-783)))))) (-5 *1 (-970 *6 *7 *8 *5 *2)) (-4 *5 (-968 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-977 *5)) (-4 *5 (-1238)) @@ -1880,8 +2150,8 @@ (-4 *2 (-968 (-971 *4) *5 *6)) (-4 *5 (-805)) (-4 *6 (-13 (-861) - (-10 -8 (-15 -4172 ((-1197) $)) - (-15 -3055 ((-3 $ "failed") (-1197)))))) + (-10 -8 (-15 -4171 ((-1197) $)) + (-15 -3054 ((-3 $ "failed") (-1197)))))) (-5 *1 (-1005 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-568)) (-4 *6 (-568)) @@ -1968,38 +2238,66 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1070)) (-5 *1 (-1311 *3 *4)) (-4 *4 (-858))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-783)) (-4 *1 (-1264 *3)) (-4 *3 (-1070)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-940)) (-4 *1 (-1266 *3 *4)) (-4 *3 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*5 *4))) + (-5 *1 (-1135 *4 *5)) (-5 *3 (-1261 *5 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1293)) (-5 *1 (-834))))) +(((*1 *2 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *2 (-1056)) + (-5 *1 (-763))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-576)) (-4 *6 (-805)) (-4 *7 (-861)) (-4 *8 (-317)) + (-4 *9 (-968 *8 *6 *7)) + (-5 *2 (-2 (|:| -3896 (-1193 *9)) (|:| |polval| (-1193 *8)))) + (-5 *1 (-754 *6 *7 *8 *9)) (-5 *3 (-1193 *9)) (-5 *4 (-1193 *8))))) +(((*1 *2 *2 *3 *3) + (|partial| -12 (-5 *3 (-1197)) + (-4 *4 (-13 (-317) (-148) (-1059 (-576)) (-651 (-576)))) + (-5 *1 (-587 *4 *2)) + (-4 *2 (-13 (-1223) (-978) (-1160) (-29 *4)))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2200,27 +2533,35 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *1 *1) - (-12 (-5 *1 (-1161 *2 *3)) (-4 *2 (-13 (-1121) (-34))) - (-4 *3 (-13 (-1121) (-34)))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-115)) (-4 *4 (-1070)) (-5 *1 (-726 *4 *2)) - (-4 *2 (-660 *4)))) - ((*1 *2 *3 *2) (-12 (-5 *3 (-115)) (-5 *1 (-848 *2)) (-4 *2 (-1070))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-805)) - (-4 *4 (-861)) (-4 *2 (-464))))) -(((*1 *2 *1) - (-12 (-5 *2 (-656 (-304 *3))) (-5 *1 (-304 *3)) (-4 *3 (-568)) - (-4 *3 (-1238))))) +(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) + (-12 (-5 *3 (-1179)) (-5 *4 (-576)) (-5 *5 (-701 (-171 (-227)))) + (-5 *2 (-1056)) (-5 *1 (-766))))) (((*1 *2 *3) - (-12 (-5 *2 (-1178 (-656 (-576)))) (-5 *1 (-898)) (-5 *3 (-576))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1233 *3)) (-4 *3 (-995))))) -(((*1 *1 *1 *1) (-4 *1 (-773)))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-1288 *4)) (-5 *3 (-1141)) (-4 *4 (-360)) - (-5 *1 (-540 *4))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-492))))) + (-12 (-5 *3 (-1197)) (-5 *2 (-1 *6 *5)) (-5 *1 (-718 *4 *5 *6)) + (-4 *4 (-626 (-548))) (-4 *5 (-1238)) (-4 *6 (-1238))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1155 *3)) (-4 *3 (-1070)) + (-5 *2 (-656 (-656 (-656 (-783)))))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1238)) (-5 *1 (-1153 *4 *2)) + (-4 *2 (-13 (-616 (-576) *4) (-10 -7 (-6 -4464) (-6 -4465)))))) + ((*1 *2 *2) + (-12 (-4 *3 (-861)) (-4 *3 (-1238)) (-5 *1 (-1153 *3 *2)) + (-4 *2 (-13 (-616 (-576) *3) (-10 -7 (-6 -4464) (-6 -4465))))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-576)) (-5 *1 (-430 *2)) (-4 *2 (-568))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-1092 *4 *5 *6 *3)) (-4 *4 (-464)) (-4 *5 (-805)) + (-4 *6 (-861)) (-4 *3 (-1086 *4 *5 *6)) (-5 *2 (-112))))) +(((*1 *2) (-12 (-5 *2 (-1179)) (-5 *1 (-1207))))) +(((*1 *2 *2) + (-12 (-4 *3 (-568)) (-4 *3 (-174)) (-4 *4 (-384 *3)) + (-4 *5 (-384 *3)) (-5 *1 (-700 *3 *4 *5 *2)) + (-4 *2 (-699 *3 *4 *5))))) +(((*1 *1 *2) + (-12 (-5 *2 (-419 (-576))) (-4 *1 (-566 *3)) + (-4 *3 (-13 (-416) (-1223))))) + ((*1 *1 *2) (-12 (-4 *1 (-566 *2)) (-4 *2 (-13 (-416) (-1223))))) + ((*1 *1 *2 *2) (-12 (-4 *1 (-566 *2)) (-4 *2 (-13 (-416) (-1223)))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1023))))) @@ -2237,66 +2578,53 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *2) - (-12 (-5 *2 (-2 (|:| -3848 (-656 *3)) (|:| -2319 (-656 *3)))) - (-5 *1 (-1239 *3)) (-4 *3 (-1121))))) -(((*1 *2 *2) - (-12 (-4 *3 (-464)) (-5 *1 (-1229 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1223)))))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-171 (-227)))) (-5 *2 (-1056)) - (-5 *1 (-766))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1305 *3 *4)) (-4 *3 (-861)) (-4 *4 (-1070)) + (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1311 *3 *4)) (-4 *3 (-1070)) + (-4 *4 (-858))))) (((*1 *2 *3) - (-12 (-5 *3 (-656 (-227))) (-5 *2 (-1288 (-711))) (-5 *1 (-315))))) -(((*1 *1) (-5 *1 (-142))) ((*1 *1 *1) (-5 *1 (-145))) - ((*1 *1 *1) (-4 *1 (-1165)))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112))))) + (-12 (-4 *4 (-27)) + (-4 *4 (-13 (-374) (-148) (-1059 (-576)) (-1059 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(-1033)))) + ((*1 *2 *3) (-12 (-5 *3 (-971 *1)) (-4 *1 (-1033)) (-5 *2 (-656 *1)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1193 (-576))) (-5 *2 (-656 *1)) (-4 *1 (-1033)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1193 (-419 (-576)))) (-5 *2 (-656 *1)) (-4 *1 (-1033)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1193 *1)) (-4 *1 (-1033)) (-5 *2 (-656 *1)))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-860) (-374))) (-4 *3 (-1264 *4)) (-5 *2 (-656 *1)) + (-4 *1 (-1089 *4 *3))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-985 *2)) (-4 *2 (-1121))))) +(((*1 *2 *3 *4 *2 *5) + (-12 (-5 *3 (-656 *8)) (-5 *4 (-656 (-907 *6))) + (-5 *5 (-1 (-904 *6 *8) *8 (-907 *6) (-904 *6 *8))) (-4 *6 (-1121)) + (-4 *8 (-13 (-1070) (-626 (-907 *6)) (-1059 *7))) + (-5 *2 (-904 *6 *8)) (-4 *7 (-1070)) (-5 *1 (-960 *6 *7 *8))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |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| - (-3 (|:| |str| (-1178 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2951 - (-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 *2 (-1056)) (-5 *1 (-315))))) -(((*1 *2 *1) (-12 (-5 *2 (-1293)) (-5 *1 (-834))))) + (-12 (-5 *3 (-656 *7)) (-4 *7 (-968 *4 *5 *6)) (-4 *6 (-626 (-1197))) + (-4 *4 (-374)) (-4 *5 (-805)) (-4 *6 (-861)) + (-5 *2 (-1186 (-656 (-971 *4)) (-656 (-304 (-971 *4))))) + (-5 *1 (-516 *4 *5 *6 *7))))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *3 (-1 *2 (-783) *2)) (-5 *4 (-783)) (-4 *2 (-1121)) + (-5 *1 (-690 *2)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1 *3 (-783) *3)) (-4 *3 (-1121)) (-5 *1 (-694 *3))))) +(((*1 *2 *2) + (-12 (-5 *2 (-962 *3)) (-4 *3 (-13 (-374) (-1223) (-1023))) + (-5 *1 (-178 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-115))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-732)) (-5 *2 (-940)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-734)) (-5 *2 (-783))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1023))))) @@ -2313,24 +2641,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-568)) (-4 *5 (-805)) (-4 *6 (-861)) (-5 *2 (-656 *3)) - (-5 *1 (-998 *4 *5 *6 *3)) (-4 *3 (-1086 *4 *5 *6))))) -(((*1 *2 *3 *4 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-227)) (-5 *4 (-576)) - (-5 *5 (-3 (|:| |fn| (-400)) (|:| |fp| (-64 -1962)))) - (-5 *2 (-1056)) (-5 *1 (-760))))) -(((*1 *2 *1) (-12 (-4 *1 (-686 *3)) (-4 *3 (-1238)) (-5 *2 (-112))))) -(((*1 *1 *1 *2) - (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1238)) (-4 *3 (-384 *2)) - (-4 *4 (-384 *2)))) - ((*1 *1 *1 *2) - (-12 (|has| *1 (-6 -4466)) (-4 *1 (-616 *3 *2)) (-4 *3 (-1121)) - (-4 *2 (-1238))))) -(((*1 *2 *1) (-12 (-4 *1 (-847 *3)) (-4 *3 (-1121)) (-5 *2 (-55))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-656 *2)) (-4 *2 (-968 *4 *5 *6)) (-4 *4 (-464)) - (-4 *5 (-805)) (-4 *6 (-861)) (-5 *1 (-461 *4 *5 *6 *2))))) +(((*1 *2 *1) + (-12 (-5 *2 (-703 (-887 (-985 *3) (-985 *3)))) (-5 *1 (-985 *3)) + (-4 *3 (-1121))))) +(((*1 *2 *3) + (-12 (-5 *3 (-971 *5)) (-4 *5 (-1070)) (-5 *2 (-253 *4 *5)) + (-5 *1 (-963 *4 *5)) (-14 *4 (-656 (-1197)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-464)) (-4 *4 (-568)) (-4 *5 (-805)) (-4 *6 (-861)) + (-5 *2 (-656 *3)) (-5 *1 (-998 *4 *5 *6 *3)) + (-4 *3 (-1086 *4 *5 *6))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -4249 *6) (|:| |sol?| (-112))) (-576) + *6)) + (-4 *6 (-374)) (-4 *7 (-1264 *6)) + (-5 *2 (-2 (|:| |answer| (-598 (-419 *7))) (|:| |a0| *6))) + (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) +(((*1 *2 *2) (-12 (-5 *2 (-390)) (-5 *1 (-1290)))) + ((*1 *2) (-12 (-5 *2 (-390)) (-5 *1 (-1290))))) +(((*1 *2 *3) + (-12 (-4 *4 (-568)) (-5 *2 (-783)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-429 *4))))) (((*1 *2 *3) (-12 (-5 *2 (-171 (-390))) (-5 *1 (-797 *3)) (-4 *3 (-626 (-390))))) ((*1 *2 *3 *4) @@ -2379,20 +2712,21 @@ (-12 (-5 *3 (-326 (-171 *5))) (-5 *4 (-940)) (-4 *5 (-568)) (-4 *5 (-861)) (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *5))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-1070)) (-4 *2 (-699 *4 *5 *6)) + (-5 *1 (-104 *4 *3 *2 *5 *6)) (-4 *3 (-1264 *4)) (-4 *5 (-384 *4)) + (-4 *6 (-384 *4))))) +(((*1 *1 *1 *1) (-5 *1 (-876)))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *2 *2)) (-4 *5 (-374)) (-4 *6 (-1264 (-419 *2))) - (-4 *2 (-1264 *5)) (-5 *1 (-217 *5 *2 *6 *3)) - (-4 *3 (-353 *5 *2 *6))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-289))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-34)) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-171 (-227))) (-5 *4 (-576)) (-5 *2 (-1056)) - (-5 *1 (-770))))) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1056)) (-5 *1 (-770))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *2)) (-5 *4 (-783)) (-4 *2 (-1121)) (-5 *1 (-690 *2))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1023)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1023))))) ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1279 *3)) @@ -2408,52 +2742,51 @@ (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) (((*1 *2) (-12 (-5 *2 (-656 *3)) (-5 *1 (-1105 *3)) (-4 *3 (-133))))) -(((*1 *2 *1 *1 *3) - (-12 (-5 *3 (-1 (-112) *5 *5)) (-4 *5 (-13 (-1121) (-34))) - (-5 *2 (-112)) (-5 *1 (-1161 *4 *5)) (-4 *4 (-13 (-1121) (-34)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1288 *1)) (-4 *1 (-378 *4)) (-4 *4 (-174)) - (-5 *2 (-656 (-971 *4))))) - ((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-656 (-971 *4))) (-5 *1 (-428 *3 *4)) - (-4 *3 (-429 *4)))) - ((*1 *2) - (-12 (-4 *1 (-429 *3)) (-4 *3 (-174)) (-5 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(-576))) + (|:| |cols| (-656 (-576)))))) + (|:| |fgb| (-656 *7))))) + (-4 *7 (-968 *4 *6 *5)) (-4 *4 (-13 (-317) (-148))) + (-4 *5 (-13 (-861) (-626 (-1197)))) (-4 *6 (-805)) (-5 *2 (-783)) + (-5 *1 (-943 *4 *5 *6 *7))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1023))))) @@ -2474,29 +2807,46 @@ (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-786)) (-5 *1 (-52))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-836))))) -(((*1 *1 *1) (-12 (-4 *1 (-437 *2)) (-4 *2 (-1121)) (-4 *2 (-379))))) -(((*1 *1) - (-12 (-5 *1 (-661 *2 *3 *4)) (-4 *2 (-1121)) (-4 *3 (-23)) - (-14 *4 *3)))) -(((*1 *2 *1) - (-12 (-4 *3 (-13 (-374) (-148))) - (-5 *2 (-656 (-2 (|:| -3422 (-783)) (|:| -2396 *4) (|:| |num| *4)))) - (-5 *1 (-411 *3 *4)) (-4 *4 (-1264 *3))))) -(((*1 *2) - (-12 - (-5 *2 (-2 (|:| -2319 (-656 (-1197))) (|:| -3848 (-656 (-1197))))) - (-5 *1 (-1240))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1231 *3 *4 *5 *2)) (-4 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*1 (-998 *5 *6 *7 *8)) (-5 *4 (-656 *8))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-962 (-227))) (-5 *2 (-1293)) (-5 *1 (-480))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1023))))) @@ -2516,28 +2866,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-375 *3 *4)) (-4 *3 (-1121)) (-4 *4 (-1121)) - (-5 *2 (-1179))))) -(((*1 *2 *3) - (-12 (-4 *4 (-568)) (-5 *2 (-1193 *3)) (-5 *1 (-41 *4 *3)) - (-4 *3 - (-13 (-374) (-312) - (-10 -8 (-15 -1570 ((-1146 *4 (-624 $)) $)) - (-15 -1581 ((-1146 *4 (-624 $)) $)) - (-15 -3570 ($ (-1146 *4 (-624 $)))))))))) -(((*1 *1 *2) (-12 (-5 *2 (-656 (-876))) (-5 *1 (-876))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1070)) (-4 *7 (-1070)) - (-4 *6 (-1264 *5)) (-5 *2 (-1193 (-1193 *7))) - (-5 *1 (-513 *5 *6 *4 *7)) (-4 *4 (-1264 *6))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-794 *2)) (-4 *2 (-1070))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-622 *3 *4)) (-4 *3 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(-5 *2 (-576)) (-5 *1 (-1068))))) +(((*1 *2) (-12 (-5 *2 (-888)) (-5 *1 (-1291)))) + ((*1 *2 *2) (-12 (-5 *2 (-888)) (-5 *1 (-1291))))) (((*1 *2 *1) (-12 (-5 *2 (-656 (-624 *1))) (-4 *1 (-312))))) (((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-529)))) ((*1 *2 *1) (-12 (-4 *2 (-13 (-1121) (-34))) (-5 *1 (-1161 *3 *2)) (-4 *3 (-13 (-1121) (-34))))) ((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-1299))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) - (-12 (-5 *3 (-1 (-390) (-390))) (-5 *4 (-390)) - (-5 *2 - (-2 (|:| -3106 *4) (|:| -3314 *4) (|:| |totalpts| (-576)) - (|:| |success| (-112)))) - (-5 *1 (-801)) (-5 *5 (-576))))) -(((*1 *2 *2) - (-12 (-4 *3 (-464)) (-5 *1 (-1229 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1223)))))) -(((*1 *2 *3 *3 *3 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1056)) (-5 *1 (-770))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-805)) + (-4 *4 (-861)) (-4 *2 (-464))))) +(((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-711)))) + ((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-711))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-518)) (-5 *3 (-656 (-890))) (-5 *1 (-495))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2682,40 +3013,38 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *1 *1) (-12 (-5 *1 (-620 *2)) (-4 *2 (-1121)))) - ((*1 *1 *1) (-5 *1 (-644)))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1197)) (-4 *4 (-464)) (-4 *4 (-1121)) - (-5 *1 (-585 *4 *2)) (-4 *2 (-294)) (-4 *2 (-442 *4))))) -(((*1 *2) - (-12 (-5 *2 (-1293)) (-5 *1 (-1215 *3 *4)) (-4 *3 (-1121)) - (-4 *4 (-1121))))) -(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-264))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 (-1 (-3 (-656 *6) "failed") (-576) *6 *6)) (-4 *6 (-374)) + (-4 *7 (-1264 *6)) + (-5 *2 (-2 (|:| |answer| (-598 (-419 *7))) (|:| |a0| *6))) + (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-888)) (-5 *3 (-656 (-270))) (-5 *1 (-268))))) (((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1070))))) + (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1070)) (-4 *3 (-861)) + (-4 *4 (-275 *3)) (-4 *5 (-805))))) +(((*1 *2 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-390)) (-5 *1 (-97)))) + ((*1 *2 *3 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-390)) (-5 *1 (-97))))) +(((*1 *2 *3 *3 *4) + (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5)) + (-4 *5 (-13 (-374) (-148) (-1059 (-576)))) + (-5 *2 + (-2 (|:| |a| *6) (|:| |b| (-419 *6)) (|:| |c| (-419 *6)) + (|:| -2739 *6))) + (-5 *1 (-1036 *5 *6)) (-5 *3 (-419 *6))))) (((*1 *2 *3 *1) (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1121)) (-4 *4 (-1121)) - (-5 *2 (-2 (|:| -4301 *3) (|:| -4440 *4)))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-390)) (-5 *1 (-97))))) -(((*1 *2 *2 *3) - (-12 (-4 *4 (-805)) - (-4 *3 (-13 (-861) (-10 -8 (-15 -4172 ((-1197) $))))) (-4 *5 (-568)) - (-5 *1 (-744 *4 *3 *5 *2)) (-4 *2 (-968 (-419 (-971 *5)) *4 *3)))) - ((*1 *2 *2 *3) - (-12 (-4 *4 (-1070)) (-4 *5 (-805)) - (-4 *3 - (-13 (-861) - (-10 -8 (-15 -4172 ((-1197) $)) - (-15 -3055 ((-3 $ "failed") (-1197)))))) - (-5 *1 (-1005 *4 *5 *3 *2)) (-4 *2 (-968 (-971 *4) *5 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-656 *6)) - (-4 *6 - (-13 (-861) - (-10 -8 (-15 -4172 ((-1197) $)) - (-15 -3055 ((-3 $ "failed") (-1197)))))) - (-4 *4 (-1070)) (-4 *5 (-805)) (-5 *1 (-1005 *4 *5 *6 *2)) - (-4 *2 (-968 (-971 *4) *5 *6))))) + (-5 *2 (-2 (|:| -4300 *3) (|:| -4439 *4)))))) +(((*1 *1) (-12 (-4 *1 (-339 *2)) (-4 *2 (-379)) (-4 *2 (-374)))) + ((*1 *2 *3) + (-12 (-5 *3 (-940)) (-5 *2 (-1288 *4)) (-5 *1 (-540 *4)) + (-4 *4 (-360))))) +(((*1 *2 *3) + (|partial| -12 (-4 *5 (-1059 (-48))) + (-4 *4 (-13 (-568) (-1059 (-576)))) (-4 *5 (-442 *4)) + (-5 *2 (-430 (-1193 (-48)))) (-5 *1 (-447 *4 *5 *3)) + (-4 *3 (-1264 *5))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2732,30 +3061,14 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-34)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *3 (-464)) (-4 *4 (-861)) (-4 *5 (-805)) (-5 *2 (-112)) - (-5 *1 (-1008 *3 *4 *5 *6)) (-4 *6 (-968 *3 *5 *4)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1161 *3 *4)) (-4 *3 (-13 (-1121) (-34))) - (-4 *4 (-13 (-1121) (-34)))))) +(((*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1238)) (-4 *1 (-107 *3))))) +(((*1 *1) (-5 *1 (-55)))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *5 *7)) (-5 *4 (-1193 *7)) (-4 *5 (-1070)) - (-4 *7 (-1070)) (-4 *2 (-1264 *5)) (-5 *1 (-513 *5 *2 *6 *7)) - (-4 *6 (-1264 *2)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1070)) (-4 *7 (-1070)) - (-4 *4 (-1264 *5)) (-5 *2 (-1193 *7)) (-5 *1 (-513 *5 *4 *6 *7)) - (-4 *6 (-1264 *4))))) + (-12 (-5 *3 (-656 (-701 *5))) (-5 *4 (-1288 *5)) (-4 *5 (-317)) + (-4 *5 (-1070)) (-5 *2 (-701 *5)) (-5 *1 (-1050 *5))))) (((*1 *2 *3) - (-12 (-5 *3 (-624 *5)) (-4 *5 (-442 *4)) (-4 *4 (-1059 (-576))) - (-4 *4 (-568)) (-5 *2 (-1193 *5)) (-5 *1 (-32 *4 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-624 *1)) (-4 *1 (-1070)) (-4 *1 (-312)) - (-5 *2 (-1193 *1))))) -(((*1 *2) - (-12 (-4 *3 (-568)) (-5 *2 (-656 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-429 *3))))) + (-12 (-5 *3 (-783)) (-5 *2 (-701 (-971 *4))) (-5 *1 (-1049 *4)) + (-4 *4 (-1070))))) (((*1 *2 *1) (-12 (-4 *1 (-249 *2)) (-4 *2 (-1238)))) ((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-1117)))) ((*1 *2 *1) @@ -2764,40 +3077,23 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-783)) (-4 *1 (-1276 *3)) (-4 *3 (-1238)))) ((*1 *2 *1) (-12 (-4 *1 (-1276 *2)) (-4 *2 (-1238))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-464) (-1059 (-576)) (-651 (-576)))) - (-5 *2 - (-3 (|:| |%expansion| (-323 *5 *3 *6 *7)) - (|:| |%problem| (-2 (|:| |func| (-1179)) (|:| |prob| (-1179)))))) - (-5 *1 (-432 *5 *3 *6 *7)) (-4 *3 (-13 (-27) (-1223) (-442 *5))) - (-14 *6 (-1197)) (-14 *7 *3)))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-783)) (-4 *1 (-1305 *3 *4)) (-4 *3 (-861)) - (-4 *4 (-1070)) (-4 *4 (-174)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1305 *2 *3)) (-4 *2 (-861)) (-4 *3 (-1070)) - (-4 *3 (-174))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *2 (-1056)) + (-5 *1 (-769))))) +(((*1 *1) (-5 *1 (-1106)))) (((*1 *2 *1) (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1238)) (-4 *4 (-384 *3)) (-4 *5 (-384 *3)) (-5 *2 (-656 *3)))) ((*1 *2 *1) - (-12 (|has| *1 (-6 -4465)) (-4 *1 (-501 *3)) (-4 *3 (-1238)) + (-12 (|has| *1 (-6 -4464)) (-4 *1 (-501 *3)) (-4 *3 (-1238)) (-5 *2 (-656 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-656 (-940))) (-5 *1 (-992))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-390) (-390))) (-5 *4 (-390)) - (-5 *2 - (-2 (|:| -3106 *4) (|:| -3314 *4) (|:| |totalpts| (-576)) - (|:| |success| (-112)))) - (-5 *1 (-801)) (-5 *5 (-576))))) +(((*1 *2 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-390)) (-5 *1 (-798))))) +(((*1 *2 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-1293)) (-5 *1 (-448))))) (((*1 *2 *2 *3) (-12 (-4 *3 (-374)) (-5 *1 (-295 *3 *2)) (-4 *2 (-1279 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-1 (-962 (-227)) (-227) (-227))) - (-5 *3 (-1 (-227) (-227) (-227) (-227))) (-5 *1 (-262))))) -(((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-946))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-783)) (-5 *1 (-59 *3)) (-4 *3 (-1238)))) + ((*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1238)) (-5 *1 (-59 *3))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-227))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2818,40 +3114,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *1 *1) (-12 (-4 *1 (-668 *2)) (-4 *2 (-1070)))) - ((*1 *2 *3) - (-12 (-4 *4 (-568)) (-4 *4 (-174)) (-4 *5 (-384 *4)) - (-4 *6 (-384 *4)) (-5 *2 (-2 (|:| |adjMat| *3) (|:| |detMat| *4))) - (-5 *1 (-700 *4 *5 *6 *3)) (-4 *3 (-699 *4 *5 *6)))) - ((*1 *1 *1 *1) - (-12 (-4 *2 (-174)) (-4 *2 (-1070)) (-5 *1 (-726 *2 *3)) - (-4 *3 (-660 *2)))) - ((*1 *1 *1) - (-12 (-4 *2 (-174)) (-4 *2 (-1070)) (-5 *1 (-726 *2 *3)) - (-4 *3 (-660 *2)))) - ((*1 *1 *1 *1) (-12 (-5 *1 (-848 *2)) (-4 *2 (-174)) (-4 *2 (-1070)))) - ((*1 *1 *1) (-12 (-5 *1 (-848 *2)) (-4 *2 (-174)) (-4 *2 (-1070))))) -(((*1 *1 *2) (-12 (-5 *2 (-783)) (-5 *1 (-135))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-1178 *3)) (-4 *3 (-1070)) (-5 *1 (-1181 *3))))) -(((*1 *2 *3 *3 *3 *3 *4 *5 *5 *6 *7 *8 *8 *3) - (-12 (-5 *6 (-656 (-112))) (-5 *7 (-701 (-227))) - (-5 *8 (-701 (-576))) (-5 *3 (-576)) (-5 *4 (-227)) (-5 *5 (-112)) - (-5 *2 (-1056)) (-5 *1 (-766))))) -(((*1 *2 *3 *3 *4 *3 *4 *4 *4 *5 *5 *5 *5 *4 *4 *6 *7) - (-12 (-5 *4 (-576)) (-5 *5 (-701 (-227))) - (-5 *6 (-3 (|:| |fn| (-400)) (|:| |fp| (-84 FCNF)))) - (-5 *7 (-3 (|:| |fn| (-400)) (|:| |fp| (-85 FCNG)))) (-5 *3 (-227)) - (-5 *2 (-1056)) (-5 *1 (-761))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1070))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1070))))) +(((*1 *2) (-12 (-5 *2 (-888)) (-5 *1 (-1291)))) + ((*1 *2 *2) (-12 (-5 *2 (-888)) (-5 *1 (-1291))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-568)) + (-5 *2 (-2 (|:| -1715 *4) (|:| -1855 *3) (|:| -3891 *3))) + (-5 *1 (-990 *4 *3)) (-4 *3 (-1264 *4)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-1070)) (-4 *4 (-805)) (-4 *5 (-861)) + (-5 *2 (-2 (|:| -1855 *1) (|:| -3891 *1))) (-4 *1 (-1086 *3 *4 *5)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-568)) (-4 *3 (-1070)) + (-5 *2 (-2 (|:| -1715 *3) (|:| -1855 *1) (|:| -3891 *1))) + (-4 *1 (-1264 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-783)) (-4 *4 (-374)) (-4 *5 (-1264 *4)) (-5 *2 (-1293)) - (-5 *1 (-40 *4 *5 *6 *7)) (-4 *6 (-1264 (-419 *5))) (-14 *7 *6)))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1070))))) + (-12 (-5 *3 (-656 (-656 (-962 (-227))))) + (-5 *2 (-656 (-1115 (-227)))) (-5 *1 (-947))))) +(((*1 *2 *1) (-12 (-5 *2 (-1293)) (-5 *1 (-834))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-861)) + (-4 *3 (-1086 *4 *5 *6)) (-5 *2 (-656 *1)) + (-4 *1 (-1092 *4 *5 *6 *3))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-539)) (-5 *3 (-129)) (-5 *2 (-783))))) +(((*1 *2) (-12 (-5 *2 (-656 (-783))) (-5 *1 (-1291)))) + ((*1 *2 *2) (-12 (-5 *2 (-656 (-783))) (-5 *1 (-1291))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 (-656 *5) *6)) + (-4 *5 (-13 (-374) (-148) (-1059 (-419 (-576))))) (-4 *6 (-1264 *5)) + (-5 *2 (-656 (-2 (|:| -1480 *5) (|:| -4026 *3)))) + (-5 *1 (-821 *5 *6 *3 *7)) (-4 *3 (-668 *6)) + (-4 *7 (-668 (-419 *6)))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *3 (-783)) (-4 *4 (-317)) (-4 *6 (-1264 *4)) + (-5 *2 (-1288 (-656 *6))) (-5 *1 (-467 *4 *6)) (-5 *5 (-656 *6))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2871,24 +3166,11 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *2 *1) - (-12 (-4 *2 (-1121)) (-5 *1 (-983 *2 *3)) (-4 *3 (-1121))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-907 *4)) (-4 *4 (-1121)) (-5 *1 (-905 *4 *3)) - (-4 *3 (-1238)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-52)) (-5 *1 (-907 *3)) (-4 *3 (-1121))))) -(((*1 *1 *2 *3) - (-12 (-5 *3 (-1197)) (-5 *1 (-598 *2)) (-4 *2 (-1059 *3)) - (-4 *2 (-374)))) - ((*1 *1 *2 *2) (-12 (-5 *1 (-598 *2)) (-4 *2 (-374)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1197)) (-4 *4 (-568)) (-5 *1 (-642 *4 *2)) - (-4 *2 (-13 (-442 *4) (-1023) (-1223))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1113 *2)) (-4 *2 (-13 (-442 *4) (-1023) (-1223))) - (-4 *4 (-568)) (-5 *1 (-642 *4 *2)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-978)) (-5 *2 (-1197)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1113 *1)) (-4 *1 (-978))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-624 *4)) (-4 *4 (-1121)) (-4 *2 (-1121)) + (-5 *1 (-623 *2 *4))))) +(((*1 *1 *1 *1) (-4 *1 (-557)))) +(((*1 *2) (-12 (-5 *2 (-1179)) (-5 *1 (-771))))) (((*1 *2 *1) (-12 (-5 *2 @@ -2902,10 +3184,10 @@ (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print"))) (-5 *1 (-340))))) (((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -4465)) (-4 *1 (-152 *2)) (-4 *2 (-1238)) + (-12 (|has| *1 (-6 -4464)) (-4 *1 (-152 *2)) (-4 *2 (-1238)) (-4 *2 (-1121)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4465)) (-4 *1 (-152 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4464)) (-4 *1 (-152 *3)) (-4 *3 (-1238)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-686 *3)) (-4 *3 (-1238)))) @@ -2917,27 +3199,46 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1161 *3 *4)) (-4 *3 (-13 (-1121) (-34))) (-4 *4 (-13 (-1121) (-34))) (-5 *1 (-1162 *3 *4))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-115)) (-5 *3 (-656 (-1 *4 (-656 *4)))) (-4 *4 (-1121)) +(((*1 *1 *2) + (-12 (-5 *2 (-425 *3 *4 *5 *6)) (-4 *6 (-1059 *4)) (-4 *3 (-317)) + (-4 *4 (-1013 *3)) (-4 *5 (-1264 *4)) (-4 *6 (-421 *4 *5)) + (-14 *7 (-1288 *6)) (-5 *1 (-426 *3 *4 *5 *6 *7)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1288 *6)) (-4 *6 (-421 *4 *5)) (-4 *4 (-1013 *3)) + (-4 *5 (-1264 *4)) (-4 *3 (-317)) (-5 *1 (-426 *3 *4 *5 *6 *7)) + (-14 *7 *2)))) +(((*1 *1 *1 *1) (-5 *1 (-876))) ((*1 *1 *1) (-5 *1 (-876))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1193 (-576))) (-5 *3 (-576)) (-4 *1 (-883 *4))))) +(((*1 *2 *3 *3 *2) + (|partial| -12 (-5 *2 (-783)) + (-4 *3 (-13 (-738) (-379) (-10 -7 (-15 ** (*3 *3 (-576)))))) + (-5 *1 (-251 *3))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-115)) (-5 *4 (-656 *2)) (-5 *1 (-114 *2)) + (-4 *2 (-1121)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 (-656 *4))) (-4 *4 (-1121)) (-5 *1 (-114 *4)))) ((*1 *2 *2 *3) (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1121)) (-5 *1 (-114 *4)))) ((*1 *2 *3) - (|partial| -12 (-5 *3 (-115)) (-5 *2 (-656 (-1 *4 (-656 *4)))) - (-5 *1 (-114 *4)) (-4 *4 (-1121))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-888)) (-5 *3 (-656 (-270))) (-5 *1 (-268))))) -(((*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1238)) (-4 *1 (-107 *3))))) -(((*1 *2) (-12 (-5 *2 (-888)) (-5 *1 (-1291)))) - ((*1 *2 *2) (-12 (-5 *2 (-888)) (-5 *1 (-1291))))) -(((*1 *1 *1 *1) (-4 *1 (-557)))) -(((*1 *1 *1) (-5 *1 (-112)))) + (|partial| -12 (-5 *3 (-115)) (-5 *2 (-1 *4 (-656 *4))) + (-5 *1 (-114 *4)) (-4 *4 (-1121)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-660 *3)) (-4 *3 (-1070)) + (-5 *1 (-726 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1070)) (-5 *1 (-848 *3))))) (((*1 *2 *3) - (-12 (-4 *4 (-568)) (-4 *5 (-805)) (-4 *6 (-861)) - (-4 *7 (-1086 *4 *5 *6)) - (-5 *2 (-2 (|:| |goodPols| (-656 *7)) (|:| |badPols| (-656 *7)))) - (-5 *1 (-998 *4 *5 *6 *7)) (-5 *3 (-656 *7))))) + (-12 (-5 *3 (-1193 *7)) (-4 *7 (-968 *6 *4 *5)) (-4 *4 (-805)) + (-4 *5 (-861)) (-4 *6 (-1070)) (-5 *2 (-1193 *6)) + (-5 *1 (-331 *4 *5 *6 *7))))) +(((*1 *1 *1) (-5 *1 (-112)))) +(((*1 *2 *2) + (-12 (-4 *3 (-464)) (-5 *1 (-1229 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1223)))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -2957,28 +3258,31 @@ ((*1 *2 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1183 *3))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) +(((*1 *2 *1) (-12 (-5 *2 (-656 (-1179))) (-5 *1 (-406)))) + ((*1 *2 *1) (-12 (-5 *2 (-656 (-1179))) (-5 *1 (-1218))))) +(((*1 *2 *3) + (-12 (-4 *4 (-568)) (-4 *5 (-805)) (-4 *6 (-861)) + (-4 *7 (-1086 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-656 *7)) (|:| |badPols| (-656 *7)))) + (-5 *1 (-998 *4 *5 *6 *7)) (-5 *3 (-656 *7))))) +(((*1 *2 *3) + (-12 (-5 *3 (-940)) (-5 *2 (-1193 *4)) (-5 *1 (-600 *4)) + (-4 *4 (-360))))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1070))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-390) (-390))) (-5 *4 (-390)) (-5 *2 - (-2 (|:| -3106 *4) (|:| -3314 *4) (|:| |totalpts| (-576)) + (-2 (|:| -3104 *4) (|:| -3313 *4) (|:| |totalpts| (-576)) (|:| |success| (-112)))) (-5 *1 (-801)) (-5 *5 (-576))))) -(((*1 *2 *1) - (-12 (-4 *1 (-375 *3 *2)) (-4 *3 (-1121)) (-4 *2 (-1121))))) -(((*1 *2 *1) (-12 (-4 *1 (-1155 *3)) (-4 *3 (-1070)) (-5 *2 (-783))))) -(((*1 *2 *1 *3 *3 *3 *2) - (-12 (-5 *3 (-783)) (-5 *1 (-687 *2)) (-4 *2 (-1121))))) +(((*1 *1) (-12 (-4 *1 (-339 *2)) (-4 *2 (-379)) (-4 *2 (-374))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |lfn| (-656 (-326 (-227)))) (|:| -3540 (-656 (-227))))) - (-5 *2 (-390)) (-5 *1 (-276)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1288 (-326 (-227)))) (-5 *2 (-390)) (-5 *1 (-315))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-940)) (-5 *3 (-656 (-270))) (-5 *1 (-268)))) - ((*1 *1 *2) (-12 (-5 *2 (-940)) (-5 *1 (-270))))) -(((*1 *2) (-12 (-5 *2 (-1293)) (-5 *1 (-815))))) + (-12 (-4 *4 (-13 (-374) (-10 -8 (-15 ** ($ $ (-419 (-576))))))) + (-5 *2 (-656 *4)) (-5 *1 (-1149 *3 *4)) (-4 *3 (-1264 *4)))) + ((*1 *2 *3 *3 *3) + (-12 (-4 *3 (-13 (-374) (-10 -8 (-15 ** ($ $ (-419 (-576))))))) + (-5 *2 (-656 *3)) (-5 *1 (-1149 *4 *3)) (-4 *4 (-1264 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1023))))) @@ -2996,66 +3300,46 @@ (-5 *1 (-1183 *3)))) ((*1 *1 *1) (-4 *1 (-1226)))) (((*1 *2 *3 *3) - (-12 (-5 *3 (-656 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-568)) - (-4 *5 (-805)) (-4 *6 (-861)) (-5 *2 (-112)) - (-5 *1 (-998 *4 *5 *6 *7))))) -(((*1 *2 *3 *3) - (-12 (|has| *2 (-6 (-4467 "*"))) (-4 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(|:| -4350 (-656 (-340))))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-1288 (-711))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1201)) (|:| -4349 (-656 (-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1201)) (|:| -4350 (-656 (-340))))) (-4 *1 (-453)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-453)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-453)))) @@ -5301,7 +5566,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-656 (-2 (|:| -1714 *3) (|:| -3685 *4)))) + (-12 (-5 *2 (-656 (-2 (|:| -1715 *3) (|:| -3684 *4)))) (-4 *3 (-1070)) (-4 *4 (-738)) (-5 *1 (-747 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-576)) (-4 *1 (-775)))) ((*1 *1 *2) @@ -5310,25 +5575,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-227))) - (|:| -2951 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -3417 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-227))) - (|:| -2951 (-656 (-1115 (-855 (-227))))) + (|:| -3417 (-656 (-1115 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-781)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-227))) - (|:| -2951 (-656 (-1115 (-855 (-227))))) (|:| |abserr| (-227)) + (|:| -3417 (-656 (-1115 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-781)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-227))) - (|:| -2951 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -3417 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-781)))) ((*1 *2 *3) (-12 (-5 *2 (-786)) (-5 *1 (-785 *3)) (-4 *3 (-1238)))) @@ -5346,23 +5611,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-227))) (|:| -3540 (-656 (-227))) + (-2 (|:| |fn| (-326 (-227))) (|:| -3539 (-656 (-227))) (|:| |lb| (-656 (-855 (-227)))) (|:| |cf| 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infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-571)))) + ((*1 *2 *1) + (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1121)) (-4 *4 (-1238)) + (-5 *2 (-656 *4))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-783)) (-5 *1 (-103 *3)) (-4 *3 (-1121))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1070)) (-5 *1 (-1260 *3 *2)) (-4 *2 (-1264 *3))))) +(((*1 *2 *3 *2) + (-12 + (-5 *2 + (-656 + (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-783)) (|:| |poli| *3) + (|:| |polj| *3)))) + (-4 *5 (-805)) (-4 *3 (-968 *4 *5 *6)) (-4 *4 (-464)) (-4 *6 (-861)) + (-5 *1 (-461 *4 *5 *6 *3))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-576)) (|has| *1 (-6 -4465)) (-4 *1 (-1276 *3)) + (-4 *3 (-1238))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-568)) (-4 *3 (-1070)) + (-5 *2 (-2 (|:| -1855 *1) (|:| -3891 *1))) (-4 *1 (-866 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-568)) (-4 *5 (-1070)) + (-5 *2 (-2 (|:| -1855 *3) (|:| -3891 *3))) (-5 *1 (-867 *5 *3)) + (-4 *3 (-866 *5))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-227)) (-5 *2 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+ (|:| -3539 (-656 (-227))))))) (-5 *1 (-853)))) ((*1 *2 *1) (-12 @@ -9112,7 +9398,7 @@ (-4 *4 (-805)) (-4 *5 (-861)) (-4 *1 (-997 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1059 *2)) (-4 *2 (-1238)))) ((*1 *1 *2) - (-2760 + (-2759 (-12 (-5 *2 (-971 *3)) (-12 (-2663 (-4 *3 (-38 (-419 (-576))))) (-2663 (-4 *3 (-38 (-576)))) (-4 *5 (-626 (-1197)))) @@ -9129,7 +9415,7 @@ (-4 *3 (-1070)) (-4 *1 (-1086 *3 *4 *5)) (-4 *4 (-805)) (-4 *5 (-861))))) ((*1 *1 *2) - (-2760 + (-2759 (-12 (-5 *2 (-971 (-576))) (-4 *1 (-1086 *3 *4 *5)) (-12 (-2663 (-4 *3 (-38 (-419 (-576))))) (-4 *3 (-38 (-576))) (-4 *5 (-626 (-1197)))) @@ -9141,38 +9427,55 @@ (-12 (-5 *2 (-971 (-419 (-576)))) (-4 *1 (-1086 *3 *4 *5)) (-4 *3 (-38 (-419 (-576)))) (-4 *5 (-626 (-1197))) (-4 *3 (-1070)) (-4 *4 (-805)) (-4 *5 (-861))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1264 *5)) (-4 *5 (-374)) - (-5 *2 (-2 (|:| -3014 (-430 *3)) (|:| |special| (-430 *3)))) - (-5 *1 (-739 *5 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-656 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singularities not yet evaluated"))) + (|:| -3417 + (-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 (-571))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-1165)) (-5 *2 (-142)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1165)) (-5 *2 (-145))))) -(((*1 *2 *1 *2) - (-12 (|has| *1 (-6 -4466)) (-4 *1 (-1031 *2)) (-4 *2 (-1238))))) -(((*1 *2 *2 *3 *4) - (|partial| -12 (-5 *2 (-656 (-1193 *7))) (-5 *3 (-1193 *7)) - (-4 *7 (-968 *5 *6 *4)) (-4 *5 (-928)) (-4 *6 (-805)) - (-4 *4 (-861)) (-5 *1 (-925 *5 *6 *4 *7))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *2 (-656 (-576))) (-5 *1 (-1131)) (-5 *3 (-576))))) +(((*1 *2) (-12 (-5 *2 (-1293)) (-5 *1 (-97))))) +(((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-333 *3 *4)) (-4 *3 (-1121)) + (-4 *4 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(|:| -4213 (-656 (-2 (|:| |irr| *3) (|:| -3012 (-576))))))) + (-5 *1 (-454 *3)) (-4 *3 (-1264 (-576))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) + (-5 *2 + (-2 (|:| |contp| (-576)) + (|:| -4213 (-656 (-2 (|:| |irr| *3) (|:| -3012 (-576))))))) + (-5 *1 (-1253 *3)) (-4 *3 (-1264 (-576)))))) +(((*1 *2) + (-12 (-5 *2 (-783)) (-5 *1 (-121 *3)) (-4 *3 (-1264 (-576))))) + ((*1 *2 *2) + (-12 (-5 *2 (-783)) (-5 *1 (-121 *3)) (-4 *3 (-1264 (-576)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-701 (-419 (-971 (-576))))) + (-5 *2 (-656 (-701 (-326 (-576))))) (-5 *1 (-1052))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-924 *4)) (-4 *4 (-1121)) (-5 *2 (-656 (-783))) + (-5 *1 (-923 *4))))) (((*1 *2 *1) (-12 (-5 *2 (-656 (-185 (-140)))) (-5 *1 (-141))))) (((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-96)))) ((*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-109)))) @@ -10606,18 +10767,41 @@ ((*1 *2 *1) (-12 (-5 *2 (-1197)) (-5 *1 (-1096 *3)) (-14 *3 *2))) ((*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-1136)))) ((*1 *1 *1) (-5 *1 (-1197)))) 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(-1197)))) @@ -10628,81 +10812,67 @@ ((*1 *2 *3) (-12 (-5 *3 (-876)) (-5 *2 (-1293)) (-5 *1 (-1159)))) ((*1 *2 *3) (-12 (-5 *3 (-656 (-876))) (-5 *2 (-1293)) (-5 *1 (-1159))))) -(((*1 *2 *2 *3 *4) - (-12 (-5 *3 (-656 (-624 *6))) (-5 *4 (-1197)) (-5 *2 (-624 *6)) - (-4 *6 (-442 *5)) (-4 *5 (-1121)) (-5 *1 (-585 *5 *6))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1031 *3)) (-4 *3 (-1238)) (-4 *3 (-1121)) - (-5 *2 (-112))))) -(((*1 *2 *1) - (-12 (-4 *1 (-997 *3 *4 *2 *5)) (-4 *3 (-1070)) (-4 *4 (-805)) - (-4 *5 (-1086 *3 *4 *2)) (-4 *2 (-861)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1086 *3 *4 *2)) (-4 *3 (-1070)) (-4 *4 (-805)) - (-4 *2 (-861))))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-493 *4 *5))) (-14 *4 (-656 (-1197))) - (-4 *5 (-464)) - (-5 *2 - (-2 (|:| |gblist| (-656 (-253 *4 *5))) - (|:| |gvlist| (-656 (-576))))) - (-5 *1 (-643 *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-659 *3)) (-4 *3 (-1121))))) -(((*1 *2 *3) - (-12 (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-861)) (-5 *2 (-576)) - (-5 *1 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(-419 (-576)))) (-4 *5 (-1264 (-419 *4))) + (-4 *6 (-353 (-419 (-576)) *4 *5)) (-5 *2 (-112)) + (-5 *1 (-931 *4 *5 *6))))) +(((*1 *2 *3) + (-12 (-5 *3 (-304 (-971 (-576)))) + (-5 *2 + (-2 (|:| |varOrder| (-656 (-1197))) + (|:| |inhom| (-3 (-656 (-1288 (-783))) "failed")) + (|:| |hom| (-656 (-1288 (-783)))))) + (-5 *1 (-241))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1197)) (-5 *2 (-1293)) (-5 *1 (-834))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-227))) - (|:| -2951 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -3417 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 @@ -10720,7 +10890,7 @@ (-3 (|:| |str| (-1178 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2951 + (|:| -3417 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -10728,94 +10898,132 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-571))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-1197)) - (-4 *6 (-13 (-317) (-1059 (-576)) (-651 (-576)) (-148))) - (-4 *4 (-13 (-29 *6) (-1223) (-978))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -1593 (-656 *4)))) - (-5 *1 (-813 *6 *4 *3)) (-4 *3 (-668 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1238)) (-5 *1 (-337 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-656 *3)) (-4 *3 (-1238)) (-5 *1 (-528 *3 *4)) + (-14 *4 (-576))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-518)) (-5 *1 (-289))))) +(((*1 *1 *2) (-12 (-5 *2 (-1179)) (-5 *1 (-503))))) (((*1 *2 *3) (-12 (-5 *3 (-400)) (-5 *2 (-1293)) (-5 *1 (-403)))) ((*1 *2 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-1293)) (-5 *1 (-403))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-1193 *3)) (-4 *3 (-360)) (-5 *1 (-368 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-419 (-971 *3))) (-5 *1 (-465 *3 *4 *5 *6)) - (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-940)) - (-14 *5 (-656 (-1197))) (-14 *6 (-1288 (-701 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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| + (-3 (|:| |str| (-1178 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3417 + (-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 *2 (-1056)) (-5 *1 (-315))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-1070)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-962 (-227))) (-5 *1 (-1234)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1286 *2)) (-4 *2 (-1238)) (-4 *2 (-1070))))) +(((*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1238))))) +(((*1 *2 *1) + (|partial| -12 (-4 *3 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(-5 *2 (-656 *1)) (-4 *1 (-968 *3 *4 *5))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-656 (-701 *5))) (-5 *4 (-1288 *5)) (-4 *5 (-317)) - (-4 *5 (-1070)) (-5 *2 (-701 *5)) (-5 *1 (-1050 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-656 (-962 (-227))))) - (-5 *2 (-656 (-1115 (-227)))) (-5 *1 (-947))))) -(((*1 *2 *3 *3 *2) - (|partial| -12 (-5 *2 (-783)) - (-4 *3 (-13 (-738) (-379) (-10 -7 (-15 ** (*3 *3 (-576)))))) - (-5 *1 (-251 *3))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1004 *2)) (-4 *2 (-1223))))) +(((*1 *1) + (-12 (-5 *1 (-661 *2 *3 *4)) (-4 *2 (-1121)) (-4 *3 (-23)) + (-14 *4 *3)))) +(((*1 *1 *1 *2) + (|partial| -12 (-4 *1 (-1231 *3 *4 *5 *2)) (-4 *3 (-568)) + (-4 *4 (-805)) (-4 *5 (-861)) (-4 *2 (-1086 *3 *4 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-656 (-326 (-227)))) (-5 *1 (-276))))) +(((*1 *2 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-52)) (-5 *1 (-841))))) (((*1 *2) (-12 (-14 *4 *2) (-4 *5 (-1238)) (-5 *2 (-783)) (-5 *1 (-242 *3 *4 *5)) (-4 *3 (-243 *4 *5)))) @@ -12875,29 +13229,19 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-860) (-374))) (-5 *1 (-1082 *2 *3)) (-4 *3 (-1264 *2))))) -(((*1 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) - ((*1 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) - ((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) - ((*1 *1 *1) (-4 *1 (-1160)))) -(((*1 *1 *2) - (-12 (-5 *2 (-656 (-2 (|:| |gen| *3) (|:| -4104 *4)))) - (-4 *3 (-1121)) (-4 *4 (-23)) (-14 *5 *4) (-5 *1 (-661 *3 *4 *5))))) -(((*1 *2 *3 *3 *2 *4) - (-12 (-5 *3 (-701 *2)) (-5 *4 (-576)) - (-4 *2 (-13 (-317) (-10 -8 (-15 -3921 ((-430 $) $))))) - (-4 *5 (-1264 *2)) (-5 *1 (-511 *2 *5 *6)) (-4 *6 (-421 *2 *5))))) -(((*1 *2) (-12 (-5 *2 (-1293)) (-5 *1 (-448))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| -3498 (-794 *3)) (|:| |coef1| (-794 *3)) - (|:| |coef2| (-794 *3)))) - (-5 *1 (-794 *3)) (-4 *3 (-568)) (-4 *3 (-1070)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-568)) (-4 *3 (-1070)) (-4 *4 (-805)) (-4 *5 (-861)) - (-5 *2 (-2 (|:| -3498 *1) (|:| |coef1| *1) (|:| |coef2| *1))) - (-4 *1 (-1086 *3 *4 *5))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1004 *2)) (-4 *2 (-1223))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-783)) (-4 *5 (-568)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-990 *5 *3)) (-4 *3 (-1264 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-656 (-701 (-326 (-576))))) (-5 *1 (-1052))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-1121)) (-4 *3 (-917 *5)) (-5 *2 (-1288 *3)) + (-5 *1 (-704 *5 *3 *6 *4)) (-4 *6 (-384 *3)) + (-4 *4 (-13 (-384 *5) (-10 -7 (-6 -4464))))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1271 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-1248 *3)) + (-5 *2 (-419 (-576)))))) (((*1 *2 *1) (-12 (-5 *2 (-656 (-518))) (-5 *1 (-49)))) ((*1 *2 *1) (-12 (-5 *2 (-656 (-890))) (-5 *1 (-495))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-804)) (-4 *2 (-1070)))) @@ -12909,10 +13253,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-393 *2 *3)) (-4 *3 (-1121)) (-4 *2 (-1070)))) ((*1 *2 *1) - (-12 (-14 *3 (-656 (-1197))) (-4 *5 (-243 (-3503 *3) (-783))) + (-12 (-14 *3 (-656 (-1197))) (-4 *5 (-243 (-3502 *3) (-783))) (-14 *6 - (-1 (-112) (-2 (|:| -3224 *4) (|:| -3422 *5)) - (-2 (|:| -3224 *4) (|:| -3422 *5)))) + (-1 (-112) (-2 (|:| -3223 *4) (|:| -2508 *5)) + (-2 (|:| -3223 *4) (|:| -2508 *5)))) (-4 *2 (-174)) (-5 *1 (-473 *3 *2 *4 *5 *6 *7)) (-4 *4 (-861)) (-4 *7 (-968 *2 *5 (-878 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-521 *2 *3)) (-4 *3 (-861)) (-4 *2 (-1121)))) @@ -12929,54 +13273,41 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1086 *3 *4 *2)) (-4 *3 (-1070)) (-4 *4 (-805)) (-4 *2 (-861))))) -(((*1 *2 *1 *2 *3) - (|partial| -12 (-5 *2 (-1179)) (-5 *3 (-576)) (-5 *1 (-1084))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1160)))) -(((*1 *2 *3) - (-12 (-5 *3 (-598 *2)) (-4 *2 (-13 (-29 *4) (-1223))) - (-5 *1 (-595 *4 *2)) - (-4 *4 (-13 (-464) (-1059 (-576)) (-651 (-576)))))) - ((*1 *2 *3) - (-12 (-5 *3 (-598 (-419 (-971 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*5 *6 *7)) (-4 *3 (-1121)) (-4 *4 (-1121)) + (-4 *5 (-1121)) (-4 *6 (-1121)) (-4 *7 (-1121)) (-5 *2 (-112))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1070)) (-4 *3 (-804)))) ((*1 *2 *1) (-12 (-4 *1 (-393 *3 *2)) (-4 *3 (-1070)) (-4 *2 (-1121)))) ((*1 *2 *1) (-12 (-14 *3 (-656 (-1197))) (-4 *4 (-174)) - (-4 *6 (-243 (-3503 *3) (-783))) + (-4 *6 (-243 (-3502 *3) (-783))) (-14 *7 - (-1 (-112) (-2 (|:| -3224 *5) (|:| -3422 *6)) - (-2 (|:| -3224 *5) (|:| -3422 *6)))) + (-1 (-112) (-2 (|:| -3223 *5) (|:| -2508 *6)) + (-2 (|:| -3223 *5) (|:| -2508 *6)))) (-5 *2 (-725 *5 *6 *7)) (-5 *1 (-473 *3 *4 *5 *6 *7 *8)) (-4 *5 (-861)) (-4 *8 (-968 *4 *6 (-878 *3))))) ((*1 *2 *1) @@ -12985,134 +13316,136 @@ ((*1 *1 *1) (-12 (-4 *1 (-994 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-804)) (-4 *4 (-861))))) -(((*1 *1 *2) (-12 (-5 *2 (-419 (-576))) (-5 *1 (-219))))) -(((*1 *2 *3 *2) +(((*1 *2) (-12 - (-5 *2 - (-656 - (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-783)) (|:| |poli| *6) - (|:| |polj| *6)))) - (-4 *3 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(-4 *1 (-1155 *3))))) +(((*1 *2 *3 *4 *5 *3) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -4249 *6) (|:| |sol?| (-112))) (-576) + *6)) + (-4 *6 (-374)) (-4 *7 (-1264 *6)) + (-5 *2 + (-3 (-2 (|:| |answer| (-419 *7)) (|:| |a0| *6)) + (-2 (|:| -2451 (-419 *7)) (|:| |coeff| (-419 *7))) "failed")) + (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4465)) (-4 *1 (-152 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4464)) (-4 *1 (-152 *3)) (-4 *3 (-1238)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1238)) (-5 *1 (-613 *3)))) @@ -13730,24 +13883,19 @@ (-4 *5 (-805)) (-4 *3 (-861)) (-4 *2 (-1086 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-783)) (-5 *1 (-1235 *2)) (-4 *2 (-1238))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) - (-4 *2 (-13 (-442 *3) (-1023)))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-656 (-656 *8))) (-5 *3 (-656 *8)) - (-4 *8 (-968 *5 *7 *6)) (-4 *5 (-13 (-317) (-148))) - (-4 *6 (-13 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+13917,7 @@ (-5 *1 (-969 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-374) - (-10 -8 (-15 -3570 ($ *7)) (-15 -1570 (*7 $)) (-15 -1581 (*7 $))))))) + (-10 -8 (-15 -3569 ($ *7)) (-15 -1570 (*7 $)) (-15 -1581 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-994 *3 *4 *5)) (-4 *3 (-1070)) (-4 *4 (-804)) (-4 *5 (-861)) (-5 *2 (-656 *5)))) @@ -13779,47 +13927,32 @@ ((*1 *2 *3) (-12 (-5 *3 (-419 (-971 *4))) (-4 *4 (-568)) (-5 *2 (-656 (-1197))) (-5 *1 (-1064 *4))))) -(((*1 *1 *2 *3 *4) - (-12 (-5 *3 (-576)) (-5 *4 (-3 "nil" "sqfr" "irred" "prime")) - (-5 *1 (-430 *2)) (-4 *2 (-568))))) -(((*1 *2 *1) (-12 (-4 *1 (-317)) (-5 *2 (-783))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1056)) (-5 *1 (-770))))) +(((*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-861)) (-5 *1 (-122 *3))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1238)) (-5 *1 (-613 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1238)) (-5 *1 (-1178 *3))))) -(((*1 *2 *2 *3) (-12 (-5 *2 (-576)) (-5 *3 (-783)) (-5 *1 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+14021,10 @@ (-4 *2 (-374)) (-14 *5 (-1014 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-725 *5 *6 *7)) (-4 *5 (-861)) - (-4 *6 (-243 (-3503 *4) (-783))) + (-4 *6 (-243 (-3502 *4) (-783))) (-14 *7 - (-1 (-112) (-2 (|:| -3224 *5) (|:| -3422 *6)) - (-2 (|:| -3224 *5) (|:| -3422 *6)))) + (-1 (-112) (-2 (|:| -3223 *5) (|:| -2508 *6)) + (-2 (|:| -3223 *5) (|:| -2508 *6)))) (-14 *4 (-656 (-1197))) (-4 *2 (-174)) (-5 *1 (-473 *4 *2 *5 *6 *7 *8)) (-4 *8 (-968 *2 *6 (-878 *4))))) ((*1 *1 *2 *3) @@ -13923,11 +14054,9 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-994 *4 *3 *2)) (-4 *4 (-1070)) (-4 *3 (-804)) (-4 *2 (-861))))) -(((*1 *2 *1) (-12 (-4 *1 (-187)) (-5 *2 (-656 (-112)))))) -(((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-1 *3 *3 *3 *3 *3)) (-4 *3 (-1121)) (-5 *1 (-103 *3)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1 *2 *2 *2)) (-5 *1 (-103 *2)) (-4 *2 (-1121))))) +(((*1 *2 *3 *3 *4 *3 *5 *3 *5 *4 *5 *5 *4 *4 *5 *3) + (-12 (-5 *4 (-701 (-227))) (-5 *5 (-701 (-576))) (-5 *3 (-576)) + (-5 *2 (-1056)) (-5 *1 (-768))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-940)) (-4 *6 (-568)) (-5 *2 (-656 (-326 *6))) (-5 *1 (-223 *5 *6)) (-5 *3 (-326 *6)) (-4 *5 (-1070)))) @@ -13953,72 +14082,64 @@ ((*1 *2 *1) (-12 (-5 *2 (-1303 *3 *4)) (-5 *1 (-1312 *3 *4)) (-4 *3 (-861)) (-4 *4 (-1070))))) -(((*1 *2 *3) (-12 (-5 *3 (-1179)) (-5 *2 (-940)) (-5 *1 (-798))))) -(((*1 *1 *1 *1) - (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-576)) (-14 *3 (-783)) - (-4 *4 (-174)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1197)) (-4 *4 (-568)) (-5 *1 (-159 *4 *2)) - (-4 *2 (-442 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1113 *2)) (-4 *2 (-442 *4)) (-4 *4 (-568)) - (-5 *1 (-159 *4 *2)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1113 *1)) (-4 *1 (-161)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-161)) (-5 *2 (-1197)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-477 *2 *3)) (-4 *2 (-174)) (-4 *3 (-23)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-783)) (-5 *1 (-1308 *3 *4)) (-4 *3 (-861)) - (-4 *4 (-174))))) -(((*1 *2) - (-12 (-5 *2 (-940)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-576))))) - ((*1 *2 *2) - (-12 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(-270)))) + ((*1 *1 *2) (-12 (-5 *2 (-390)) (-5 *1 (-270))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-861)) + (-4 *3 (-1086 *4 *5 *6)) (-5 *2 (-3 (-112) (-656 *1))) + (-4 *1 (-1092 *4 *5 *6 *3))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1288 (-326 (-227)))) (|:| |yinit| (-656 (-227))) + (|:| |intvals| (-656 (-227))) (|:| |g| (-326 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (-5 *2 (-390)) (-5 *1 (-207))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4465)) (-4 *1 (-120 *2)) (-4 *2 (-1238))))) (((*1 *1 *1) (-12 (-5 *1 (-350 *2 *3 *4)) (-14 *2 (-656 (-1197))) (-14 *3 (-656 (-1197))) (-4 *4 (-399)))) @@ -14500,10 +14559,16 @@ ((*1 *1 *2) (-12 (-5 *2 (-419 (-576))) (-4 *1 (-1033)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1033)) (-5 *2 (-940)))) ((*1 *1 *1) (-4 *1 (-1033)))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1070))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-656 *3)) (-4 *3 (-317)) (-5 *1 (-181 *3))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *5 (-783)) (-4 *6 (-1121)) (-4 *7 (-917 *6)) + (-5 *2 (-701 *7)) (-5 *1 (-704 *6 *7 *3 *4)) (-4 *3 (-384 *7)) + (-4 *4 (-13 (-384 *6) (-10 -7 (-6 -4464))))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-836)) (-5 *3 (-656 (-1197))) (-5 *1 (-837))))) +(((*1 *2 *3 *4 *3) + (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5)) (-4 *5 (-374)) + (-5 *2 (-2 (|:| -2451 (-419 *6)) (|:| |coeff| (-419 *6)))) + (-5 *1 (-586 *5 *6)) (-5 *3 (-419 *6))))) (((*1 *2 *3) (-12 (-5 *3 (-940)) (-5 *2 (-1193 *4)) (-5 *1 (-368 *4)) (-4 *4 (-360)))) @@ -14521,25 +14586,24 @@ (-12 (-5 *3 (-576)) (-5 *2 (-924 *4)) (-5 *1 (-923 *4)) (-4 *4 (-1121)))) ((*1 *1) (-12 (-4 *1 (-1013 *2)) (-4 *2 (-557)) (-4 *2 (-568))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-783)) (-4 *4 (-13 (-568) (-148))) + (-5 *1 (-1258 *4 *2)) (-4 *2 (-1264 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-836)) (-5 *1 (-837))))) (((*1 *2 *3) - (-12 (-4 *3 (-1264 *2)) (-4 *2 (-1264 *4)) - (-5 *1 (-1006 *4 *2 *3 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*2 *4 *3))))) + (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1023)))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-946))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-568)) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4334 *4))) + (-5 *1 (-990 *4 *3)) (-4 *3 (-1264 *4))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-656 (-48))) (-5 *2 (-430 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1264 (-48))))) @@ -14588,8 +14652,8 @@ (-12 (-4 *4 (-13 (-861) - (-10 -8 (-15 -4172 ((-1197) $)) - (-15 -3055 ((-3 $ "failed") (-1197)))))) + (-10 -8 (-15 -4171 ((-1197) $)) + (-15 -3054 ((-3 $ "failed") (-1197)))))) (-4 *5 (-805)) (-4 *7 (-568)) (-5 *2 (-430 *3)) (-5 *1 (-468 *4 *5 *6 *7 *3)) (-4 *6 (-568)) (-4 *3 (-968 *7 *5 *4)))) @@ -14638,13 +14702,13 @@ (-12 (-4 *4 (-805)) (-4 *5 (-13 (-861) - (-10 -8 (-15 -4172 ((-1197) $)) - (-15 -3055 ((-3 $ "failed") (-1197)))))) + (-10 -8 (-15 -4171 ((-1197) $)) + (-15 -3054 ((-3 $ "failed") (-1197)))))) (-4 *6 (-317)) (-5 *2 (-430 *3)) (-5 *1 (-742 *4 *5 *6 *3)) (-4 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25780) (-4323 . 24203) (-4324 . 24055) (-4325 . 23930) + (-4326 . 23703) (-4327 . 23372) (-4328 . 23079) (-4329 . 22836) + (-4330 . 22618) (-4331 . 22535) (-4332 . 22303) (-4333 . 22220) + (-4334 . 21833) (-4335 . 21708) (-4336 . 21579) (-4337 . 21395) + (-4338 . 21313) (-4339 . 21192) (-4340 . 21107) (-4341 . 20822) + (-4342 . 20743) (-4343 . 20316) (-4344 . 20185) (-4345 . 20128) + (-4346 . 19939) (-4347 . 19858) (-4348 . 19799) (-4349 . 19722) + (-4350 . 18541) (-4351 . 18480) (-4352 . 18219) (-4353 . 17904) + (-4354 . 17746) (-4355 . 17673) (-4356 . 17279) (-4357 . 17120) + (-4358 . 17001) (-4359 . 16367) (-4360 . 16269) (-4361 . 15925) + (-4362 . 15832) (-4363 . 15609) (-4364 . 15557) (-4365 . 15300) + (-4366 . 15185) (-4367 . 14887) (-4368 . 14809) (-4369 . 14427) + (-4370 . 14045) (-4371 . 13961) (-4372 . 13873) (-4373 . 13757) + (-4374 . 13649) (-4375 . 13085) (-4376 . 13002) (-4377 . 12916) + (-4378 . 12819) (-4379 . 12742) (-4380 . 12669) (-4381 . 12616) + (-4382 . 12539) (-4383 . 12462) (-4384 . 12358) (-4385 . 12159) + (-4386 . 12022) (-4387 . 11459) (-4388 . 11431) (-4389 . 11335) + (-4390 . 11280) (-4391 . 10907) (-4392 . 10757) (-4393 . 10639) + (-4394 . 10135) (-4395 . 10035) (-4396 . 9947) (-4397 . 9796) + (-4398 . 9561) (-4399 . 9487) (-4400 . 9342) (-4401 . 9208) + (-4402 . 9158) (-4403 . 9043) (-4404 . 8890) (-4405 . 8524) + (-4406 . 8080) (-4407 . 7595) (-4408 . 7349) (-4409 . 6977) + (-4410 . 6585) (-4411 . 6531) (-4412 . 6397) (-4413 . 6344) + (-4414 . 6265) (-4415 . 6159) (-4416 . 6125) (-4417 . 6006) + (-4418 . 5950) (-4419 . 5710) (-4420 . 5550) (-4421 . 5005) + (-4422 . 4855) (-4423 . 4345) (-4424 . 4138) (-4425 . 4035) + (-4426 . 3858) (-4427 . 3806) (-4428 . 3653) (-4429 . 3415) + (-4430 . 3250) (-4431 . 3011) (-4432 . 2503) (-4433 . 2284) + (-4434 . 2037) (-4435 . 1777) (-4436 . 1745) (-4437 . 1665) + (-4438 . 1549) (-4439 . 347) (-4440 . 313) (-4441 . 279) (-4442 . 222) + (-4443 . 118) (-4444 . 30))
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