diff options
| -rw-r--r-- | src/ChangeLog | 4 | ||||
| -rw-r--r-- | src/algebra/any.spad.pamphlet | 41 | ||||
| -rw-r--r-- | src/interp/sys-utility.boot | 3 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1282 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1222 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1306 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8825 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 30254 |
8 files changed, 21473 insertions, 21464 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 8053d465..cb93a17d 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,9 @@ 2009-01-06 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/any.spad.pamphlet (Maybe): Rework. + +2009-01-06 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/sys-utility.boot (getVMType): IndexList are lists. * interp/g-util.boot (isSubDomain): Tidy. * interp/g-opt.boot (isVMConstantForm): New. diff --git a/src/algebra/any.spad.pamphlet b/src/algebra/any.spad.pamphlet index 7bc2d368..b877b958 100644 --- a/src/algebra/any.spad.pamphlet +++ b/src/algebra/any.spad.pamphlet @@ -41,45 +41,42 @@ None():SetCategory == add \section{The Maybe domain} <<domain MAYBE Maybe>>= -import UnionType import CoercibleTo OutputForm import Boolean )abbrev domain MAYBE Maybe ++ Author: Gabriel Dos Reis ++ Date Created: August 20, 2008 -++ Also See: Union(T,"failed") +++ Date Last Modified: January 06, 2009 ++ Description: -++ This domain implements the notion of optional vallue, where +++ This domain implements the notion of optional value, where ++ a computation may fail to produce expected value. -++ Note: Ideally, this domain definition should be a one-liner. -++ That is currently impossible because of mismatch between -++ the `old representation' and `new representation' for domains. Maybe(T: CoercibleTo OutputForm): Public == Private where - Public == Join(UnionType,CoercibleTo OutputForm) with + Public == Join(UnionType,RetractableTo T, CoercibleTo OutputForm) with + just: T -> % + ++ maybe(x) injects the value `x' into %. _case: (%,[| T |]) -> Boolean ++ x case T returns true if x is actually a data of type T. _case: (%,[| nothing |]) -> Boolean ++ x case nothing evaluates true if the value for x is missing. - coerce: T -> % - ++ x::T injects the value x into %. - coerce: % -> T - ++ x::T tries to extract the value of T from the computation x. - ++ Produces a runtime error when the computation fails. autoCoerce: % -> T - ++ same as above but implicitly called by the compiler. + ++ autoCoerce is a courtesy coercion function used by the compiler + ++ in case it knows that `x' really is a T. nothing: % ++ represents failure. Private == add - Rep == Union(T,"nothing") - nothing == per("nothing"::Rep) - coerce(x: T): % == per(x::Rep) - coerce(x: %): T == rep(x)::T - autoCoerce x == rep(x)::T - x case T == rep x case T - x case nothing == rep x case "nothing" + nothing == %nothing$Lisp + just x == x : % + x case nothing == EQ(x,%nothing$Lisp)$Lisp + x case T == not(x case nothing) + autoCoerce x == x : T + coerce(x: T): % == just x + retractIfCan x == + x case T => x@T + "failed" coerce(x: %): OutputForm == - x case T => x::T::OutputForm - paren(empty()$OutputForm)$OutputForm + x case nothing => paren(empty()$OutputForm)$OutputForm + (x@T)::OutputForm + @ diff --git a/src/interp/sys-utility.boot b/src/interp/sys-utility.boot index d34cc4b8..3fcbdf9c 100644 --- a/src/interp/sys-utility.boot +++ b/src/interp/sys-utility.boot @@ -40,6 +40,9 @@ namespace BOOT --% $COMBLOCKLIST := nil +++ No value marker for the Maybe domain. +%nothing == KEYWORD::%OpenAxiomNoValue + --% diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 06dabb7d..81ffe67b 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2276553 . 3439752255) +(2276389 . 3440274381) (-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."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -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(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . 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(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4379 . T) (-4377 . T) (-4376 . T) ((-4384 "*") . T) (-4375 . T) (-4380 . T) (-4374 . T)) +((-4380 . T) (-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4376 . T) (-4381 . T) (-4375 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3160) +(-32 R -3198) ((|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 -1028) (QUOTE (-558))))) (-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 -4382))) +((|HasAttribute| |#1| (QUOTE -4383))) (-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}."))) -((-4382 . T) (-4383 . T)) +((-4383 . T) (-4384 . 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"))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . 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 -3160 UP UPUP -4169) +(-40 -3198 UP UPUP -1783) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4375 |has| (-406 |#2|) (-362)) (-4380 |has| (-406 |#2|) (-362)) (-4374 |has| (-406 |#2|) (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3986 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3986 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3986 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3986 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) -(-41 R -3160) +((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3996 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3996 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3996 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3996 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +(-41 R -3198) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-306)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4379 |has| |#1| (-550)) (-4377 . T) (-4376 . T)) +((-4380 |has| |#1| (-550)) (-4378 . T) (-4377 . T)) ((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-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."))) -((-4382 . T) (-4383 . T)) -((-3986 (-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|))))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|))))))) +((-4383 . T) (-4384 . T)) +((-3996 (-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|))))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4379 . T)) +((-4380 . 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 -3160) +(-54 |Base| R -3198) ((|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"))) -((-4382 . T) (-4383 . T)) +((-4383 . T) (-4384 . 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}"))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|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}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-61 -3072) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +(-61 -3149) ((|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 -3072) +(-62 -3149) ((|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 -3072) +(-63 -3149) ((|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 -3072) +(-64 -3149) ((|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 -3072) +(-65 -3149) ((|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 -3072) +(-66 -3149) ((|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 -3072) +(-67 -3149) ((|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 -3072) +(-68 -3149) ((|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 -3072) +(-69 -3149) ((|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 -3072) +(-70 -3149) ((|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 -3072) +(-71 -3149) ((|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 -3072) +(-72 -3149) ((|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 -3072) +(-73 -3149) ((|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 -3072) +(-74 -3149) ((|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 -3072) +(-77 -3149) ((|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 -3072) +(-78 -3149) ((|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 -3072) +(-79 -3149) ((|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 -3072) +(-80 -3149) ((|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 -3072) +(-81 -3149) ((|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 -3072) +(-82 -3149) ((|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 -3072) +(-83 -3149) ((|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 -3072) +(-84 -3149) ((|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 -3072) +(-85 -3149) ((|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 -3072) +(-86 -3149) ((|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 -3072) +(-87 -3149) ((|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 -3072) +(-88 -3149) ((|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 -3072) +(-89 -3149) ((|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 (-362)))) (-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}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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\"."))) -((-4382 . T)) +((-4383 . 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."))) -((-4382 . T) ((-4384 "*") . T) (-4383 . T) (-4379 . T) (-4377 . T) (-4376 . T) (-4375 . T) (-4380 . T) (-4374 . T) (-4373 . T) (-4372 . T) (-4371 . T) (-4370 . T) (-4378 . T) (-4381 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4369 . T)) +((-4383 . T) ((-4385 "*") . T) (-4384 . T) (-4380 . T) (-4378 . T) (-4377 . T) (-4376 . T) (-4381 . T) (-4375 . T) (-4374 . T) (-4373 . T) (-4372 . T) (-4371 . T) (-4379 . T) (-4382 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4370 . 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}."))) -((-4379 . T)) +((-4380 . 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{\\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}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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 (-4384 "*")))) +((|HasAttribute| |#1| (QUOTE (-4385 "*")))) (-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"))) -((-4382 . T)) +((-4383 . 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."))) -((-4383 . T)) +((-4384 . 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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3986 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3996 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-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| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1087))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-112) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-112) (QUOTE (-1087))) (|HasCategory| (-112) (LIST (QUOTE -605) (QUOTE (-853))))) (-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}"))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -388,22 +388,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3160 UP) +(-115 -3198 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 (-116 |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}."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-899))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1012))) (|HasCategory| (-116 |#1|) (QUOTE (-811))) (-3986 (|HasCategory| (-116 |#1|) (QUOTE (-811))) (|HasCategory| (-116 |#1|) (QUOTE (-841)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-1138))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-543))) (|HasCategory| (-116 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-899))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1012))) (|HasCategory| (-116 |#1|) (QUOTE (-811))) (-3996 (|HasCategory| (-116 |#1|) (QUOTE (-811))) (|HasCategory| (-116 |#1|) (QUOTE (-841)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-1138))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-543))) (|HasCategory| (-116 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4383))) +((|HasAttribute| |#1| (QUOTE -4384))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -414,15 +414,15 @@ NIL NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,22 +430,22 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4382 . T) (-4383 . T)) +((-4383 . T) (-4384 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|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'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-3986 (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-129) (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087)))) (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-3996 (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-129) (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087)))) (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-129) -((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) +((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|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 NIL (-130) @@ -462,13 +462,13 @@ NIL NIL (-133) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4384 "*") . T)) +(((-4385 "*") . T)) NIL -(-134 |minix| -4269 S T$) +(-134 |minix| -4352 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -4269 R) +(-135 |minix| -4352 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -490,8 +490,8 @@ NIL NIL (-140) ((|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}."))) -((-4382 . T) (-4372 . T) (-4383 . T)) -((-3986 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-4383 . T) (-4373 . T) (-4384 . T)) +((-3996 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-141 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -506,7 +506,7 @@ NIL NIL (-144) ((|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."))) -((-4379 . T)) +((-4380 . T)) NIL (-145 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}."))) @@ -514,9 +514,9 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4379 . T)) +((-4380 . T)) NIL -(-147 -3160 UP UPUP) +(-147 -3198 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 @@ -527,14 +527,14 @@ NIL (-149 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 -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasAttribute| |#1| (QUOTE -4382))) +((|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasAttribute| |#1| (QUOTE -4383))) (-150 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 (-151 |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."))) -((-4377 . T) (-4376 . T) (-4379 . T)) +((-4378 . T) (-4377 . T) (-4380 . T)) NIL (-152) ((|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."))) @@ -556,7 +556,7 @@ 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 -(-157 R -3160) +(-157 R -3198) ((|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 @@ -587,10 +587,10 @@ NIL (-164 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| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) NIL -((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-992))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4378)) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-841)))) +((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-992))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4379)) (|HasAttribute| |#2| (QUOTE -4382)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-841)))) (-165 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| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) -((-4375 -3986 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4378 |has| |#1| (-6 -4378)) (-4381 |has| |#1| (-6 -4381)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 -3996 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4379 |has| |#1| (-6 -4379)) (-4382 |has| |#1| (-6 -4382)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-166 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."))) @@ -602,8 +602,8 @@ NIL NIL (-168 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}."))) -((-4375 -3986 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4378 |has| |#1| (-6 -4378)) (-4381 |has| |#1| (-6 -4381)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-819)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-841)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1012)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1185)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -606) 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T) (-4377 . T) (-4378 . T) (-4380 . 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(|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-348))))) (-169 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 @@ -614,7 +614,7 @@ NIL NIL (-171) ((|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."))) -(((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-172) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -622,7 +622,7 @@ NIL NIL (-173 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4384 "*") . T) (-4375 . T) (-4380 . T) (-4374 . T) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") . T) (-4376 . T) (-4381 . T) (-4375 . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-174) ((|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| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -676,7 +676,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors."))) NIL NIL -(-187 R -3160) +(-187 R -3198) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -784,23 +784,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-214 -3160 UP UPUP R) +(-214 -3198 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 -(-215 -3160 FP) +(-215 -3198 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 (-216) ((|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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3986 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3996 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-217) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-218 R -3160) +(-218 R -3198) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -814,19 +814,19 @@ NIL NIL (-221 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-222 |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}."))) -((-4379 . T)) +((-4380 . T)) NIL -(-223 R -3160) +(-223 R -3198) ((|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 (-224) ((|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}."))) -((-1399 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1394 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-225) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -834,15 +834,15 @@ NIL NIL (-226 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}"))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-227 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 (-228 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."))) -((-4383 . T)) +((-4384 . T)) NIL (-229 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -850,7 +850,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (-230 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4379 . T)) +((-4380 . T)) NIL (-231 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -858,36 +858,36 @@ NIL NIL (-232) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4379 . T)) +((-4380 . T)) NIL (-233 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4382))) +((|HasAttribute| |#1| (QUOTE -4383))) (-234 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}."))) -((-4383 . T)) +((-4384 . T)) NIL (-235) ((|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 -(-236 S -4269 R) +(-236 S -4352 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-784))) (|HasCategory| |#3| (QUOTE (-839))) (|HasAttribute| |#3| (QUOTE -4379)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (QUOTE (-1087)))) -(-237 -4269 R) +((|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-784))) (|HasCategory| |#3| (QUOTE (-839))) (|HasAttribute| |#3| (QUOTE -4380)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (QUOTE (-1087)))) +(-237 -4352 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4376 |has| |#2| (-1039)) (-4377 |has| |#2| (-1039)) (-4379 |has| |#2| (-6 -4379)) ((-4384 "*") |has| |#2| (-171)) (-4382 . T)) +((-4377 |has| |#2| (-1039)) (-4378 |has| |#2| (-1039)) (-4380 |has| |#2| (-6 -4380)) ((-4385 "*") |has| |#2| (-171)) (-4383 . T)) NIL -(-238 -4269 A B) +(-238 -4352 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 -(-239 -4269 R) +(-239 -4352 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."))) -((-4376 |has| |#2| (-1039)) (-4377 |has| |#2| (-1039)) (-4379 |has| |#2| (-6 -4379)) ((-4384 "*") |has| |#2| (-171)) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-839))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST 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(|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 @@ -898,7 +898,7 @@ NIL NIL (-242) ((|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}."))) -((-4375 . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-243 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."))) @@ -906,16 +906,16 @@ NIL NIL (-244 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}"))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-245 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 (-246 |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"))) -(((-4384 "*") |has| |#2| (-171)) (-4375 |has| |#2| (-550)) (-4380 |has| |#2| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3986 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3986 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +(((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#2| (QUOTE (-899))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-247) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) NIL @@ -926,23 +926,23 @@ NIL NIL (-249 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4379 -3986 (-2146 (|has| |#4| (-1039)) (|has| |#4| (-232))) (-2146 (|has| |#4| (-1039)) (|has| |#4| (-890 (-1163)))) (|has| |#4| (-6 -4379)) (-2146 (|has| |#4| (-1039)) (|has| |#4| (-631 (-558))))) (-4376 |has| |#4| (-1039)) (-4377 |has| |#4| (-1039)) ((-4384 "*") |has| |#4| (-171)) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#4| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-232))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-784))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-839))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1039))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|))) 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(QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-251 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 (-232)))) (-252 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."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL (-253 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}."))) -((-4382 . T) (-4383 . T)) +((-4383 . T) (-4384 . T)) NIL (-254) ((|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."))) @@ -982,8 +982,8 @@ NIL NIL (-263 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"))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-264 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1028,11 +1028,11 @@ 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 -(-275 R -3160) +(-275 R -3198) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-276 R -3160) +(-276 R -3198) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1054,7 +1054,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087)))) (-281 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}."))) -((-4383 . T)) +((-4384 . T)) NIL (-282 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}."))) @@ -1075,18 +1075,18 @@ NIL (-286 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 -4383))) +((|HasAttribute| |#1| (QUOTE -4384))) (-287 |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 -(-288 S R |Mod| -4218 -2596 |exactQuo|) +(-288 S R |Mod| -4160 -3743 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-289) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4375 . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-290) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1102,21 +1102,21 @@ NIL NIL (-293 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.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-295) ((|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 -(-296 -3160 S) +(-296 -3198 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 -(-297 E -3160) +(-297 E -3198) ((|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 @@ -1154,7 +1154,7 @@ NIL NIL (-306) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-307 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1164,7 +1164,7 @@ 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 -(-309 -3160) +(-309 -3198) ((|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 @@ -1178,8 +1178,8 @@ NIL NIL (-312 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}.")) 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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 @@ -1190,9 +1190,9 @@ NIL NIL (-315 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) 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(-25))) (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))))) (-3996 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-1039)))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) +(-316 R -3198) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1202,8 +1202,8 @@ NIL NIL (-318 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."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3710) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-319 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 @@ -1214,7 +1214,7 @@ NIL NIL (-321 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) ((|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-783)))) (-322 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1230,19 +1230,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171)))) (-325 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-326 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."))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-327 S -3160) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-327 S -3198) ((|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 (-367)))) -(-328 -3160) +(-328 -3198) ((|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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-329) ((|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."))) @@ -1260,15 +1260,15 @@ 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 -(-333 S -3160 UP UPUP R) +(-333 S -3198 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 -(-334 -3160 UP UPUP R) +(-334 -3198 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 -(-335 -3160 UP UPUP R) +(-335 -3198 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 @@ -1282,32 +1282,32 @@ NIL NIL (-338 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-378)))) (|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) (-339 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 -(-340 S -3160 UP UPUP) +(-340 S -3198 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-362)))) -(-341 -3160 UP UPUP) +(-341 -3198 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4375 |has| (-406 |#2|) (-362)) (-4380 |has| (-406 |#2|) (-362)) (-4374 |has| (-406 |#2|) (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-342 |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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) (-343 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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-344 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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-345 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 @@ -1322,33 +1322,33 @@ NIL NIL (-348) ((|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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL -(-349 R UP -3160) +(-349 R UP -3198) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-350 |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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) (-351 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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-352 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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-353 |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}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) (-354 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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) -(-355 -3160 GF) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +(-355 -3198 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 @@ -1356,21 +1356,21 @@ 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 -(-357 -3160 FP FPP) +(-357 -3198 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-358 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}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-359 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 (-360 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4379 . T)) +((-4380 . T)) NIL (-361 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1378,7 +1378,7 @@ NIL NIL (-362) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-363 |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."))) @@ -1394,7 +1394,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-550)))) (-366 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4379 |has| |#1| (-550)) (-4377 . T) (-4376 . T)) +((-4380 |has| |#1| (-550)) (-4378 . T) (-4377 . T)) NIL (-367) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1406,7 +1406,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-362)))) (-369 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) NIL (-370 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1415,14 +1415,14 @@ NIL (-371 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4383)) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087)))) +((|HasAttribute| |#1| (QUOTE -4384)) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087)))) (-372 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4382 . T)) +((-4383 . T)) NIL (-373 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4377 . T) (-4376 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4378 . T) (-4377 . T)) NIL (-374 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."))) @@ -1434,7 +1434,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-376 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4379 . T)) +((-4380 . T)) NIL (-377 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1442,7 +1442,7 @@ NIL NIL (-378) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4365 . T) (-4373 . T) (-1399 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4366 . T) (-4374 . T) (-1394 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-379 |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}."))) @@ -1450,11 +1450,11 @@ NIL NIL (-380 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}"))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) ((|HasCategory| |#1| (QUOTE (-171)))) (-381 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}."))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) NIL (-382) ((|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}."))) @@ -1466,7 +1466,7 @@ NIL NIL (-384 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."))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) ((|HasCategory| |#1| (QUOTE (-171)))) (-385 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1474,7 +1474,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-841)))) (-386) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-387) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1486,13 +1486,13 @@ NIL NIL (-389 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) NIL (-390) ((|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 -(-391 -3160 UP UPUP R) +(-391 -3198 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 @@ -1516,11 +1516,11 @@ 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 -(-397 -3072 |returnType| -3987 |symbols|) +(-397 -3149 |returnType| -1315 |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 -(-398 -3160 UP) +(-398 -3198 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1534,15 +1534,15 @@ NIL NIL (-401) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-402 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4365)) (|HasAttribute| |#1| (QUOTE -4373))) +((|HasAttribute| |#1| (QUOTE -4366)) (|HasAttribute| |#1| (QUOTE -4374))) (-403) ((|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\"."))) -((-1399 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1394 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-404 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."))) @@ -1554,15 +1554,15 @@ NIL NIL (-406 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."))) -((-4369 -12 (|has| |#1| (-6 -4380)) (|has| |#1| (-450)) (|has| |#1| (-6 -4369))) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-811))) (-3986 (|HasCategory| |#1| (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-841)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4380)) (|HasAttribute| |#1| (QUOTE -4369)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((-4370 -12 (|has| |#1| (-6 -4381)) (|has| |#1| (-450)) (|has| |#1| (-6 -4370))) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-811))) (-3996 (|HasCategory| |#1| (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-841)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4381)) (|HasAttribute| |#1| (QUOTE -4370)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-407 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-408 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) NIL (-409 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-412 R -3160 UP A) +(-412 R -3198 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4379 . T)) +((-4380 . T)) NIL -(-413 R -3160 UP A |ibasis|) +(-413 R -3198 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1028) (|devaluate| |#2|)))) @@ -1594,12 +1594,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-416 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4379 |has| |#1| (-550)) (-4377 . T) (-4376 . T)) +((-4380 |has| |#1| (-550)) (-4378 . T) (-4377 . T)) NIL (-417 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."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1204))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1204))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) (-418 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 @@ -1626,17 +1626,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-367)))) (-424 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4382 . T) (-4372 . T) (-4383 . T)) +((-4383 . T) (-4373 . T) (-4384 . T)) NIL -(-425 R -3160) +(-425 R -3198) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-426 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4369 -12 (|has| |#1| (-6 -4369)) (|has| |#2| (-6 -4369))) (-4376 . T) (-4377 . T) (-4379 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4369)) (|HasAttribute| |#2| (QUOTE -4369)))) -(-427 R -3160) +((-4370 -12 (|has| |#1| (-6 -4370)) (|has| |#2| (-6 -4370))) (-4377 . T) (-4378 . T) (-4380 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4370)) (|HasAttribute| |#2| (QUOTE -4370)))) +(-427 R -3198) ((|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 @@ -1646,17 +1646,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (-429 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4379 -3986 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) ((-4384 "*") |has| |#1| (-550)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-550)) (-4374 |has| |#1| (-550))) +((-4380 -3996 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) ((-4385 "*") |has| |#1| (-550)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-550)) (-4375 |has| |#1| (-550))) NIL -(-430 R -3160) +(-430 R -3198) ((|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 -(-431 R -3160) +(-431 R -3198) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-432 R -3160) +(-432 R -3198) ((|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 @@ -1664,7 +1664,7 @@ 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 -(-434 R -3160 UP) +(-434 R -3198 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 -1028) (QUOTE (-48))))) @@ -1692,7 +1692,7 @@ 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 -(-441 R UP -3160) +(-441 R UP -3198) ((|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 @@ -1730,16 +1730,16 @@ NIL NIL (-450) ((|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}."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-451 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"))) -((-4379 |has| (-406 (-942 |#1|)) (-550)) (-4377 . T) (-4376 . T)) +((-4380 |has| (-406 (-942 |#1|)) (-550)) (-4378 . T) (-4377 . T)) ((|HasCategory| (-406 (-942 |#1|)) (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| (-406 (-942 |#1|)) (QUOTE (-550)))) (-452 |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"))) -(((-4384 "*") |has| |#2| (-171)) (-4375 |has| |#2| (-550)) (-4380 |has| |#2| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3986 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3986 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +(((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#2| (QUOTE (-899))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-453 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 @@ -1766,7 +1766,7 @@ NIL NIL (-459 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) NIL (-460 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1774,7 +1774,7 @@ NIL NIL (-461 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) (-462 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}."))) @@ -1804,7 +1804,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-469 |lv| -3160 R) +(-469 |lv| -3198 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1814,23 +1814,23 @@ NIL NIL (-471) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4379 . T)) +((-4380 . T)) NIL (-472 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3710) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-473 |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."))) -((-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087)))) +((-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087)))) (-474 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)}"))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) (-475) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-476) ((|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'."))) @@ -1838,29 +1838,29 @@ NIL NIL (-477 |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."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-478) ((|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 (-479 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4384 "*") |has| |#2| (-171)) (-4375 |has| |#2| (-550)) (-4380 |has| |#2| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . 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(|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3996 (|HasCategory| |#2| (QUOTE (-1039))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-481) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL NIL (-482 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-483 -3160 UP UPUP R) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +(-483 -3198 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1870,12 +1870,12 @@ NIL NIL (-485) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3986 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3996 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-486 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 -4382)) (|HasAttribute| |#1| (QUOTE -4383)) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) +((|HasAttribute| |#1| (QUOTE -4383)) (|HasAttribute| |#1| (QUOTE -4384)) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (-487 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1896,33 +1896,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-492 -3160 UP |AlExt| |AlPol|) +(-492 -3198 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-493) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) (-494 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-495 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."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-496 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 -(-497 R UP -3160) +(-497 R UP -3198) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-498 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1087))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-112) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-112) (QUOTE (-1087))) (|HasCategory| (-112) (LIST (QUOTE -605) (QUOTE (-853))))) (-499 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)}."))) @@ -1936,7 +1936,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-502 -3160 |Expon| |VarSet| |DPoly|) +(-502 -3198 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-1163))))) @@ -1986,36 +1986,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-783)))) (-514 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-515) ((|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 (-516 |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}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((-3986 (|HasCategory| (-575 |#1|) (QUOTE (-144))) (|HasCategory| (-575 |#1|) (QUOTE (-367)))) (|HasCategory| (-575 |#1|) (QUOTE (-146))) (|HasCategory| (-575 |#1|) (QUOTE (-367))) (|HasCategory| (-575 |#1|) (QUOTE (-144)))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-3996 (|HasCategory| (-575 |#1|) (QUOTE (-144))) (|HasCategory| (-575 |#1|) (QUOTE (-367)))) (|HasCategory| (-575 |#1|) (QUOTE (-146))) (|HasCategory| (-575 |#1|) (QUOTE (-367))) (|HasCategory| (-575 |#1|) (QUOTE (-144)))) (-517 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}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-518 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."))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-519 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 -4383))) +((|HasAttribute| |#3| (QUOTE -4384))) (-520 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 -4383))) +((|HasAttribute| |#7| (QUOTE -4384))) (-521 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."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-522) ((|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 @@ -2048,7 +2048,7 @@ 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 -(-530 K -3160 |Par|) +(-530 K -3198 |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 @@ -2072,7 +2072,7 @@ 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 -(-536 K -3160 |Par|) +(-536 K -3198 |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 @@ -2102,17 +2102,17 @@ NIL NIL (-543) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4380 . T) (-4381 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4381 . T) (-4382 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-544 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) -(-545 R -3160) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +(-545 R -3198) ((|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 -(-546 R0 -3160 UP UPUP R) +(-546 R0 -3198 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 @@ -2122,7 +2122,7 @@ NIL NIL (-548 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."))) -((-1399 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1394 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-549 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."))) @@ -2130,9 +2130,9 @@ NIL NIL (-550) ((|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."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL -(-551 R -3160) +(-551 R -3198) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2144,7 +2144,7 @@ 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 -(-554 R -3160 L) +(-554 R -3198 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -646) (|devaluate| |#2|)))) @@ -2152,31 +2152,31 @@ 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 -(-556 -3160 UP UPUP R) +(-556 -3198 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 -(-557 -3160 UP) +(-557 -3198 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 (-558) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4364 . T) (-4370 . T) (-4374 . T) (-4369 . T) (-4380 . T) (-4381 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4365 . T) (-4371 . T) (-4375 . T) (-4370 . T) (-4381 . T) (-4382 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-559) ((|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 -(-560 R -3160 L) +(-560 R -3198 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -646) (|devaluate| |#2|)))) -(-561 R -3160) +(-561 R -3198) ((|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 -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1126)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-621))))) -(-562 -3160 UP) +(-562 -3198 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2184,27 +2184,27 @@ 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 -(-564 -3160) +(-564 -3198) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-565 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."))) -((-1399 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1394 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-566) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-567 R -3160) +(-567 R -3198) ((|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 -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-621))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-283)))) (|HasCategory| |#1| (QUOTE (-550)))) -(-568 -3160 UP) +(-568 -3198 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-569 R -3160) +(-569 R -3198) ((|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 @@ -2226,27 +2226,27 @@ NIL NIL (-574 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-575 |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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) (-576) ((|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 -(-577 R -3160) +(-577 R -3198) ((|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 -(-578 E -3160) +(-578 E -3198) ((|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 -(-579 -3160) +(-579 -3198) ((|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}."))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) ((|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163))))) (-580 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"))) @@ -2274,19 +2274,19 @@ NIL NIL (-586 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-3986 (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-3996 (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-587 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 (-588 |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}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) (-589 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4377 |has| |#1| (-550)) (-4376 |has| |#1| (-550)) ((-4384 "*") |has| |#1| (-550)) (-4375 |has| |#1| (-550)) (-4379 . T)) +((-4378 |has| |#1| (-550)) (-4377 |has| |#1| (-550)) ((-4385 "*") |has| |#1| (-550)) (-4376 |has| |#1| (-550)) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-550)))) (-590 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) @@ -2296,7 +2296,7 @@ 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 -(-592 R -3160 FG) +(-592 R -3198 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2306,12 +2306,12 @@ NIL NIL (-594 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-595 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 -4383)) (|HasCategory| |#2| (QUOTE (-841))) (|HasAttribute| |#1| (QUOTE -4382)) (|HasCategory| |#3| (QUOTE (-1087)))) +((|HasAttribute| |#1| (QUOTE -4384)) (|HasCategory| |#2| (QUOTE (-841))) (|HasAttribute| |#1| (QUOTE -4383)) (|HasCategory| |#3| (QUOTE (-1087)))) (-596 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2326,19 +2326,19 @@ NIL NIL (-599 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4379 -3986 (-2146 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4377 . T) (-4376 . T)) -((-3986 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +((-4380 -3996 (-2113 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4378 . T) (-4377 . T)) +((-3996 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-600 |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."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-601 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 (-602 |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}."))) -((-4383 . T)) +((-4384 . T)) NIL (-603 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"))) @@ -2356,7 +2356,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-607 -3160 UP) +(-607 -3198 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2378,19 +2378,19 @@ NIL NIL (-612 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."))) -((-4379 . T)) +((-4380 . T)) NIL (-613 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}."))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-839)))) -(-614 R -3160) +(-614 R -3198) ((|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 (-615 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"))) -((-4377 . T) (-4376 . T) ((-4384 "*") . T) (-4375 . T) (-4379 . T)) +((-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4376 . T) (-4380 . T)) ((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (-616 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."))) @@ -2406,7 +2406,7 @@ NIL NIL (-619 |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}}."))) -((-4379 . T)) +((-4380 . T)) NIL (-620 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}}."))) @@ -2416,30 +2416,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-622 R -3160) +(-622 R -3198) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-623 |lv| -3160) +(-623 |lv| -3198) ((|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 (-624) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -2957) (QUOTE (-52))))))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1145) (QUOTE (-841))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (QUOTE (-1087)))) +((-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -3528) (QUOTE (-52))))))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1145) (QUOTE (-841))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (QUOTE (-1087)))) (-625 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-626 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4377 . T) (-4376 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4378 . T) (-4377 . T)) NIL (-627 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4379 -3986 (-2146 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4377 . T) (-4376 . T)) -((-3986 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +((-4380 -3996 (-2113 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4378 . T) (-4377 . T)) +((-3996 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-628 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 @@ -2451,10 +2451,10 @@ NIL (-630 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2137 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) +((-2104 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) (-631 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4379 . T)) +((-4380 . T)) NIL (-632 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) @@ -2470,16 +2470,16 @@ NIL NIL (-635 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-636 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL (-637 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-638 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2491,22 +2491,22 @@ NIL (-640 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#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 -4383))) +((|HasAttribute| |#1| (QUOTE -4384))) (-641 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-642 R -3160 L) +(-642 R -3198 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 (-643 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}}"))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) (-644 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) (-645 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2514,15 +2514,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-646 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}."))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) NIL -(-647 -3160 UP) +(-647 -3198 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)))) -(-648 A -3058) +(-648 A -2680) ((|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}}"))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) (-649 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."))) @@ -2538,7 +2538,7 @@ NIL NIL (-652 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}."))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) ((|HasCategory| |#1| (QUOTE (-782)))) (-653 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2546,7 +2546,7 @@ NIL NIL (-654 |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) (-4377 . T) (-4376 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4378 . T) (-4377 . T)) ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-171)))) (-655 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}."))) @@ -2554,13 +2554,13 @@ NIL NIL (-656 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}."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL -(-657 -3160) +(-657 -3198) ((|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 -(-658 -3160 |Row| |Col| M) +(-658 -3198 |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 @@ -2570,8 +2570,8 @@ NIL NIL (-660 |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."))) -((-4379 . T) (-4382 . T) (-4376 . T) (-4377 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550))) (-3986 (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((-4380 . T) (-4383 . T) (-4377 . T) (-4378 . T)) +((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550))) (-3996 (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-661) ((|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 @@ -2591,7 +2591,7 @@ NIL (-665 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 -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-666) ((|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 @@ -2635,10 +2635,10 @@ NIL (-676 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550)))) +((|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550)))) (-677 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4382 . T) (-4383 . T)) +((-4383 . T) (-4384 . T)) NIL (-678 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."))) @@ -2646,17 +2646,17 @@ NIL ((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550)))) (-679 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."))) -((-4382 . T) (-4383 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4384 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4383 . T) (-4384 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-680 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 NIL (-681 T$) -((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}."))) +((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "autoCoerce is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spad{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "maybe(\\spad{x}) injects the value \\spad{`x'} into \\%."))) NIL NIL -(-682 S -3160 FLAF FLAS) +(-682 S -3198 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 @@ -2666,11 +2666,11 @@ NIL NIL (-684) ((|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"))) -((-4375 . T) (-4380 |has| (-689) (-362)) (-4374 |has| (-689) (-362)) (-4381 |has| (-689) (-6 -4381)) (-4378 |has| (-689) (-6 -4378)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . 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T)) +((|HasCategory| (-689) (QUOTE (-146))) (|HasCategory| (-689) (QUOTE (-144))) (|HasCategory| (-689) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-689) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-689) (QUOTE (-367))) (|HasCategory| (-689) (QUOTE (-362))) (-3996 (|HasCategory| (-689) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-689) (QUOTE (-362)))) (|HasCategory| (-689) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-689) (QUOTE (-232))) (-3996 (|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-348)))) (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (LIST (QUOTE -285) (QUOTE (-689)) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -308) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-689) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-689) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-689) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3996 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-348)))) (|HasCategory| (-689) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-689) (QUOTE (-1012))) (|HasCategory| (-689) (QUOTE (-1185))) (-12 (|HasCategory| (-689) (QUOTE (-992))) (|HasCategory| (-689) (QUOTE (-1185)))) (-3996 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-362))) (-12 (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (QUOTE (-899))))) (-3996 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (-12 (|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-899)))) (-12 (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (QUOTE (-899))))) (|HasCategory| (-689) (QUOTE (-543))) (-12 (|HasCategory| (-689) (QUOTE (-1048))) (|HasCategory| (-689) (QUOTE (-1185)))) (|HasCategory| (-689) (QUOTE (-1048))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899))) (-3996 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-362)))) (-3996 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-550)))) (-12 (|HasCategory| (-689) (QUOTE (-232))) (|HasCategory| (-689) (QUOTE (-362)))) (-12 (|HasCategory| (-689) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-689) (QUOTE (-362)))) (|HasCategory| (-689) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-689) (QUOTE (-841))) (|HasCategory| (-689) (QUOTE (-550))) (|HasAttribute| (-689) (QUOTE -4382)) (|HasAttribute| (-689) (QUOTE -4379)) (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-144)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-348))))) (-685 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}."))) -((-4383 . T)) +((-4384 . T)) NIL (-686 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}."))) @@ -2680,13 +2680,13 @@ 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 -(-688 OV E -3160 PG) +(-688 OV E -3198 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 (-689) ((|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}"))) -((-1399 . T) (-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-1394 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-690 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."))) @@ -2694,7 +2694,7 @@ NIL NIL (-691) ((|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}"))) -((-4381 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4382 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-692 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"))) @@ -2716,7 +2716,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-697 S -2897 I) +(-697 S -2922 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2726,7 +2726,7 @@ NIL NIL (-699 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)}.}"))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) NIL (-700 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}."))) @@ -2736,25 +2736,25 @@ 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 -(-702 R |Mod| -4218 -2596 |exactQuo|) +(-702 R |Mod| -4160 -3743 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-703 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4378 |has| |#1| (-362)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4379 |has| |#1| (-362)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . 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(|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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) (-4379 . T)) +((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) -(-706 R |Mod| -4218 -2596 |exactQuo|) +(-706 R |Mod| -4160 -3743 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4379 . T)) +((-4380 . T)) NIL (-707 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2762,11 +2762,11 @@ NIL NIL (-708 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) NIL -(-709 -3160) +(-709 -3198) ((|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]]}."))) -((-4379 . T)) +((-4380 . T)) NIL (-710 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."))) @@ -2790,7 +2790,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-348))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-367)))) (-715 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."))) -((-4375 |has| |#1| (-362)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 |has| |#1| (-362)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-716 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."))) @@ -2800,7 +2800,7 @@ 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 -(-718 -3160 UP) +(-718 -3198 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 @@ -2818,8 +2818,8 @@ NIL NIL (-722 |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."))) -(((-4384 "*") |has| |#2| (-171)) (-4375 |has| |#2| (-550)) (-4380 |has| |#2| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . 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T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#2| (QUOTE (-899))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-723 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2834,15 +2834,15 @@ NIL NIL (-726 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) (-4379 . T)) +((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-841)))) (-727 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4372 . T) (-4383 . T)) +((-4373 . T) (-4384 . T)) NIL (-728 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}."))) -((-4382 . T) (-4372 . T) (-4383 . T)) +((-4383 . T) (-4373 . T) (-4384 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-729) ((|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."))) @@ -2854,7 +2854,7 @@ NIL NIL (-731 |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}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4377 . T) (-4376 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL (-732 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"))) @@ -2870,7 +2870,7 @@ NIL NIL (-735 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}."))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) NIL (-736) ((|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}."))) @@ -2952,11 +2952,11 @@ 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 -(-756 -3160) +(-756 -3198) ((|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 -(-757 P -3160) +(-757 P -3198) ((|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 @@ -2964,7 +2964,7 @@ NIL NIL NIL NIL -(-759 UP -3160) +(-759 UP -3198) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -2978,9 +2978,9 @@ NIL NIL (-762) ((|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."))) -(((-4384 "*") . T)) +(((-4385 "*") . T)) NIL -(-763 R -3160) +(-763 R -3198) ((|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 @@ -3000,7 +3000,7 @@ 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 -(-768 -3160 |ExtF| |SUEx| |ExtP| |n|) +(-768 -3198 |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 @@ -3014,23 +3014,23 @@ NIL NIL (-771 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."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . 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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 (-773 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.")) 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T)) +((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-774 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 -406) (QUOTE (-558)))))) (-775 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.}"))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-776 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}."))) @@ -3082,25 +3082,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-367)))) (-788 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) NIL -(-789 -3986 R OS S) +(-789 -3996 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-790 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-3986 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) +((-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-3996 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (-791) ((|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 -(-792 R -3160 L) +(-792 R -3198 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-793 R -3160) +(-793 R -3198) ((|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 @@ -3108,7 +3108,7 @@ 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 -(-795 R -3160) +(-795 R -3198) ((|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 @@ -3116,11 +3116,11 @@ 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 -(-797 -3160 UP UPUP R) +(-797 -3198 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 -(-798 -3160 UP L LQ) +(-798 -3198 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 @@ -3128,41 +3128,41 @@ 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 -(-800 -3160 UP L LQ) +(-800 -3198 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-801 -3160 UP) +(-801 -3198 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 -(-802 -3160 L UP A LO) +(-802 -3198 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 -(-803 -3160 UP) +(-803 -3198 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-804 -3160 LO) +(-804 -3198 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 -(-805 -3160 LODO) +(-805 -3198 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-806 -4269 S |f|) +(-806 -4352 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}."))) -((-4376 |has| |#2| (-1039)) (-4377 |has| |#2| (-1039)) (-4379 |has| |#2| (-6 -4379)) ((-4384 "*") |has| |#2| (-171)) (-4382 . 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(LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-839))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| (-558) (QUOTE (-841))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (QUOTE (-1039)))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3996 (|HasCategory| |#2| (QUOTE (-1039))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-807 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-808 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4384 "*") |has| |#2| (-362)) (-4375 |has| |#2| (-362)) (-4380 |has| |#2| (-362)) (-4374 |has| |#2| (-362)) (-4379 . T) (-4377 . T) (-4376 . T)) +(((-4385 "*") |has| |#2| (-362)) (-4376 |has| |#2| (-362)) (-4381 |has| |#2| (-362)) (-4375 |has| |#2| (-362)) (-4380 . T) (-4378 . T) (-4377 . T)) ((|HasCategory| |#2| (QUOTE (-362)))) (-809 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}))."))) @@ -3174,7 +3174,7 @@ NIL NIL (-811) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-812) ((|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}"))) @@ -3202,7 +3202,7 @@ NIL NIL (-818 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}."))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-232)))) (-819) ((|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."))) @@ -3214,7 +3214,7 @@ NIL NIL (-821 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4382 . T) (-4372 . T) (-4383 . T)) +((-4383 . T) (-4373 . T) (-4384 . T)) NIL (-822) ((|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."))) @@ -3226,8 +3226,8 @@ NIL NIL (-824 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."))) -((-4379 |has| |#1| (-839))) -((|HasCategory| |#1| (QUOTE (-839))) (-3986 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3986 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4380 |has| |#1| (-839))) +((|HasCategory| |#1| (QUOTE (-839))) (-3996 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3996 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-825 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.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL @@ -3238,7 +3238,7 @@ NIL NIL (-827 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) (-4379 . T)) +((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) (-828) ((|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)."))) @@ -3266,13 +3266,13 @@ NIL NIL (-834 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4379 |has| |#1| (-839))) -((|HasCategory| |#1| (QUOTE (-839))) (-3986 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3986 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4380 |has| |#1| (-839))) +((|HasCategory| |#1| (QUOTE (-839))) (-3996 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3996 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-835) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-836 -4269 S) +(-836 -4352 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3286,7 +3286,7 @@ NIL NIL (-839) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4379 . T)) +((-4380 . T)) NIL (-840 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3302,19 +3302,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171)))) (-843 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) NIL (-844 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 (-362))) (|HasCategory| |#1| (QUOTE (-550)))) -(-845 R |sigma| -1310) +(-845 R |sigma| -4151) ((|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."))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) -(-846 |x| R |sigma| -1310) +(-846 |x| R |sigma| -4151) ((|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}."))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-362)))) (-847 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..)}."))) @@ -3354,7 +3354,7 @@ NIL NIL (-856 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) (-4379 . T)) +((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) (-857 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3366,24 +3366,24 @@ NIL NIL (-859 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-860 |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)."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-861 |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)."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-860 |#1|) (QUOTE (-899))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-146))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-860 |#1|) (QUOTE (-1012))) (|HasCategory| (-860 |#1|) (QUOTE (-811))) (-3986 (|HasCategory| (-860 |#1|) (QUOTE (-811))) (|HasCategory| (-860 |#1|) (QUOTE (-841)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-1138))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-232))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -860) (|devaluate| |#1|)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (QUOTE (-306))) (|HasCategory| (-860 |#1|) (QUOTE (-543))) (|HasCategory| (-860 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-860 |#1|) (QUOTE (-899))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-146))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-860 |#1|) (QUOTE (-1012))) (|HasCategory| (-860 |#1|) (QUOTE (-811))) (-3996 (|HasCategory| (-860 |#1|) (QUOTE (-811))) (|HasCategory| (-860 |#1|) (QUOTE (-841)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-1138))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-232))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -860) (|devaluate| |#1|)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (QUOTE (-306))) (|HasCategory| (-860 |#1|) (QUOTE (-543))) (|HasCategory| (-860 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))))) (-862 |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)}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (-3986 (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (-3996 (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-863 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 (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-864) ((|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 @@ -3439,7 +3439,7 @@ NIL (-877 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2137 (|HasCategory| |#2| (QUOTE (-1039)))) (-2137 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (-2137 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) +((-12 (-2104 (|HasCategory| |#2| (QUOTE (-1039)))) (-2104 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (-2104 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) (-878 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3448,7 +3448,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-880 R -2897) +(-880 R -2922) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3472,7 +3472,7 @@ 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 -(-886 UP -3160) +(-886 UP -3198) ((|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 @@ -3490,19 +3490,19 @@ NIL NIL (-890 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4379 . T)) +((-4380 . T)) NIL (-891 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 (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-892 |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 (-893 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4379 . T)) +((-4380 . T)) NIL (-894 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3510,8 +3510,8 @@ NIL NIL (-895 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4379 . T)) -((-3986 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) +((-4380 . T)) +((-3996 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (-896 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3526,13 +3526,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-144)))) (-899) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-900 |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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) -(-901 R0 -3160 UP UPUP R) +(-901 R0 -3198 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 @@ -3546,7 +3546,7 @@ NIL NIL (-904 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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-905 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."))) @@ -3560,7 +3560,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-908 -3160) +(-908 -3198) ((|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 @@ -3570,17 +3570,17 @@ NIL NIL (-910) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-911) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4384 "*") . T)) +(((-4385 "*") . T)) NIL -(-912 -3160 P) +(-912 -3198 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-913 |xx| -3160) +(-913 |xx| -3198) ((|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 @@ -3604,7 +3604,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-919 R -3160) +(-919 R -3198) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3616,7 +3616,7 @@ 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 -(-922 S R -3160) +(-922 S R -3198) ((|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 @@ -3636,11 +3636,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -876) (|devaluate| |#1|)))) -(-927 R -3160 -2897) +(-927 R -3198 -2922) ((|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 -(-928 -2897) +(-928 -2922) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3662,8 +3662,8 @@ NIL NIL (-933 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-934 |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 @@ -3683,12 +3683,12 @@ NIL (-938 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 (-899))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#4| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-841)))) +((|HasCategory| |#2| (QUOTE (-899))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#4| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-841)))) (-939 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}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL -(-940 E V R P -3160) +(-940 E V R P -3198) ((|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 @@ -3698,9 +3698,9 @@ NIL NIL (-942 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}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-943 E V R P -3160) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . 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(|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 (-450)))) @@ -3722,13 +3722,13 @@ NIL NIL (-948 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"))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-949) ((|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 -(-950 -3160) +(-950 -3198) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3742,12 +3742,12 @@ NIL NIL (-953 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}"))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4380))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4381))) (-954 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"))) -((-4379 -12 (|has| |#2| (-471)) (|has| |#1| (-471)))) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE 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(|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) +((-4380 -12 (|has| |#2| (-471)) (|has| |#1| (-471)))) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) (-955) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3762,7 +3762,7 @@ NIL NIL (-958 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4382 . T) (-4383 . T)) +((-4383 . T) (-4384 . T)) NIL (-959 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}}"))) @@ -3782,7 +3782,7 @@ NIL NIL (-963 |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}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-964) ((|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}."))) @@ -3794,7 +3794,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-550)))) (-966 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."))) -((-4382 . T)) +((-4383 . T)) NIL (-967 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."))) @@ -3810,7 +3810,7 @@ NIL NIL (-970 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}."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-971 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3828,7 +3828,7 @@ 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 -(-975 K R UP -3160) +(-975 K R UP -3198) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3858,7 +3858,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138)))) (-982 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}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-983 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3870,7 +3870,7 @@ NIL NIL (-985 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."))) -((-4382 . T) (-4383 . T)) +((-4383 . T) (-4384 . T)) NIL (-986 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}."))) @@ -3878,7 +3878,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-289)))) (-987 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}."))) -((-4375 |has| |#1| (-289)) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 |has| |#1| (-289)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-988 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}."))) @@ -3886,12 +3886,12 @@ NIL NIL (-989 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.}"))) -((-4375 |has| |#1| (-289)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543)))) +((-4376 |has| |#1| (-289)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543)))) (-990 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}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-991 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3900,14 +3900,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-993 -3160 UP UPUP |radicnd| |n|) +(-993 -3198 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4375 |has| (-406 |#2|) (-362)) (-4380 |has| (-406 |#2|) (-362)) (-4374 |has| (-406 |#2|) (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3986 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3986 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3986 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3986 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3996 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3996 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3996 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3996 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) (-994 |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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3986 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3996 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-995) ((|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 @@ -3927,7 +3927,7 @@ NIL (-999 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 -4383)) (|HasCategory| |#2| (QUOTE (-1087)))) +((|HasAttribute| |#1| (QUOTE -4384)) (|HasCategory| |#2| (QUOTE (-1087)))) (-1000 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 @@ -3938,21 +3938,21 @@ NIL NIL (-1002) ((|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}}"))) -((-4375 . T) (-4380 . T) (-4374 . T) (-4377 . T) (-4376 . T) ((-4384 "*") . T) (-4379 . T)) +((-4376 . T) (-4381 . T) (-4375 . T) (-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4380 . T)) NIL -(-1003 R -3160) +(-1003 R -3198) ((|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 -(-1004 R -3160) +(-1004 R -3198) ((|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 -(-1005 -3160 UP) +(-1005 -3198 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 -(-1006 -3160 UP) +(-1006 -3198 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 @@ -3986,9 +3986,9 @@ NIL NIL (-1014 |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"))) -((-4375 . T) (-4380 . T) (-4374 . T) (-4377 . T) (-4376 . T) ((-4384 "*") . T) (-4379 . T)) -((-3986 (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558))))) -(-1015 -3160 L) +((-4376 . T) (-4381 . T) (-4375 . T) (-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4380 . T)) +((-3996 (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558))))) +(-1015 -3198 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -3998,12 +3998,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1087)))) (-1017 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."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) (-1018 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4384 "*")))) +((|HasAttribute| |#1| (QUOTE (-4385 "*")))) (-1019 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 @@ -4024,14 +4024,14 @@ 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 -(-1024 -3160 |Expon| |VarSet| |FPol| |LFPol|) +(-1024 -3198 |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"))) -(((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1025) ((|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.}"))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -2957) (QUOTE (-52))))))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -3528) (QUOTE (-52))))))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) (-1026) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4074,7 +4074,7 @@ NIL NIL (-1036 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}."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) ((-12 (|HasCategory| (-771 |#1| (-855 |#2|)) (QUOTE (-1087))) (|HasCategory| (-771 |#1| (-855 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -771) (|devaluate| |#1|) (LIST (QUOTE -855) (|devaluate| |#2|)))))) (|HasCategory| (-771 |#1| (-855 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-771 |#1| (-855 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| (-855 |#2|) (QUOTE (-367))) (|HasCategory| (-771 |#1| (-855 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-1037) ((|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"))) @@ -4086,9 +4086,9 @@ NIL NIL (-1039) ((|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."))) -((-4379 . T)) +((-4380 . T)) NIL -(-1040 |xx| -3160) +(-1040 |xx| -3198) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4098,12 +4098,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-306))) (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (QUOTE (-550))) (|HasCategory| |#4| (QUOTE (-171)))) (-1042 |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"))) -((-4382 . T) (-4377 . T) (-4376 . T)) +((-4383 . T) (-4378 . T) (-4377 . T)) NIL (-1043 |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}."))) -((-4382 . T) (-4377 . T) (-4376 . T)) -((-3986 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4378 . T) (-4377 . T)) +((-3996 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853))))) (-1044 |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 @@ -4122,7 +4122,7 @@ NIL NIL (-1048) ((|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."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1049 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4130,19 +4130,19 @@ NIL NIL (-1050) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4370 . T) (-4374 . T) (-4369 . T) (-4380 . T) (-4381 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4371 . T) (-4375 . T) (-4370 . T) (-4381 . T) (-4382 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1051) ((|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}"))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -2957) (QUOTE (-52))))))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -3528) (QUOTE (-52))))))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) (-1052 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -982) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-1163))))) (-1053 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL (-1054) ((|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'."))) @@ -4166,7 +4166,7 @@ NIL NIL (-1059 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-1060 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."))) @@ -4180,11 +4180,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1063 |Base| R -3160) +(-1063 |Base| R -3198) ((|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 -(-1064 |Base| R -3160) +(-1064 |Base| R -3198) ((|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 @@ -4198,8 +4198,8 @@ NIL NIL (-1067 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."))) -((-4375 |has| |#1| (-362)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) +((-4376 |has| |#1| (-362)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) (-1068 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 @@ -4226,8 +4226,8 @@ NIL NIL (-1074 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"))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1075 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1075 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4270,7 +4270,7 @@ NIL NIL (-1085 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}."))) -((-4372 . T)) +((-4373 . T)) NIL (-1086 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}."))) @@ -4286,8 +4286,8 @@ NIL NIL (-1089 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)}}"))) -((-4382 . T) (-4372 . T) (-4383 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4383 . T) (-4373 . T) (-4384 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-1090 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4314,7 +4314,7 @@ NIL NIL (-1096 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.}"))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-1097) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4330,8 +4330,8 @@ NIL NIL (-1100 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-784))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-839))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| (-558) (QUOTE (-841))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1039)))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3996 (|HasCategory| |#3| (QUOTE (-1039))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1087)))) (|HasAttribute| |#3| (QUOTE -4380)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-1101 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 @@ -4340,7 +4340,7 @@ 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 -(-1103 R -3160) +(-1103 R -3198) ((|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 @@ -4358,19 +4358,19 @@ NIL NIL (-1107) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|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."))) -((-4370 . T) (-4374 . T) (-4369 . T) (-4380 . T) (-4381 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4371 . T) (-4375 . T) (-4370 . T) (-4381 . T) (-4382 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1108 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4382 . T) (-4383 . T)) +((-4383 . T) (-4384 . T)) NIL (-1109 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-362))) (|HasAttribute| |#3| (QUOTE (-4384 "*"))) (|HasCategory| |#3| (QUOTE (-171)))) +((|HasCategory| |#3| (QUOTE (-362))) (|HasAttribute| |#3| (QUOTE (-4385 "*"))) (|HasCategory| |#3| (QUOTE (-171)))) (-1110 |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."))) -((-4382 . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4383 . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1111 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}."))) @@ -4378,17 +4378,17 @@ NIL NIL (-1112 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. 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T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3986 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1113 |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}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) (-1114 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}"))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL -(-1115 UP -3160) +(-1115 UP -3198) ((|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 @@ -4442,19 +4442,19 @@ NIL NIL (-1128 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))) (-3986 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))))) (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))) (-3996 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))))) (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853))))) (-1129 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4379 . T) (-4371 |has| |#2| (-6 (-4384 "*"))) (-4382 . T) (-4376 . T) (-4377 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3986 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (-3986 (|HasAttribute| |#2| (QUOTE (-4384 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((-4380 . T) (-4372 |has| |#2| (-6 (-4385 "*"))) (-4383 . T) (-4377 . T) (-4378 . T)) +((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (-3996 (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-1130 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1131) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-1132 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.}"))) @@ -4462,12 +4462,12 @@ NIL NIL (-1133 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."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) (-1134 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}."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-1135 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 @@ -4478,8 +4478,8 @@ NIL NIL (-1137 |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."))) -((-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087)))) +((-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087)))) (-1138) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4502,20 +4502,20 @@ NIL NIL (-1143 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4383 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4384 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-1144) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-1145) NIL -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-1146 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#1|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#1|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-1147 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4546,9 +4546,9 @@ NIL NIL (-1154 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4384 "*") -3986 (-2146 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-811))) (|has| |#1| (-171)) (-2146 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-899)))) (-4375 -3986 (-2146 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-811))) (|has| |#1| (-550)) (-2146 (|has| |#1| (-362)) (|has| (-1161 |#1| |#2| |#3|) (-899)))) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3710) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1161 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3710) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1162) ((|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 @@ -4590,8 +4590,8 @@ NIL NIL (-1165 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-6 -4380)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3986 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| (-961) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasAttribute| |#1| (QUOTE -4380))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| (-961) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasAttribute| |#1| (QUOTE -4381))) (-1166) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4622,8 +4622,8 @@ NIL NIL (-1173 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4382 . T) (-4383 . T)) -((-12 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2045) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2957) (|devaluate| |#2|)))))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3986 (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-4383 . T) (-4384 . T)) +((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-1174 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4634,7 +4634,7 @@ NIL NIL (-1176 |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})}."))) -((-4383 . T)) +((-4384 . T)) NIL (-1177 |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."))) @@ -4674,8 +4674,8 @@ NIL NIL (-1186 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4383 . T) (-4382 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-4384 . T) (-4383 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-1187 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4684,7 +4684,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1189 R -3160) +(-1189 R -3198) ((|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 @@ -4692,7 +4692,7 @@ 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 -(-1191 R -3160) +(-1191 R -3198) ((|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 -606) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -876) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -876) (|devaluate| |#1|))))) @@ -4702,12 +4702,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-367)))) (-1193 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-1194 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) (-1195 |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 @@ -4720,7 +4720,7 @@ 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 (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-1198 -3160) +(-1198 -3198) ((|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 @@ -4746,7 +4746,7 @@ NIL NIL (-1204) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1205 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) @@ -4754,7 +4754,7 @@ NIL NIL (-1206 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1207 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)}."))) @@ -4762,16 +4762,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-1208 |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)}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1209 |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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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 @@ -4806,8 +4806,8 @@ NIL NIL (-1219 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4818,15 +4818,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-1138)))) (-1222 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}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4378 |has| |#1| (-362)) (-4380 |has| |#1| (-6 -4380)) (-4377 . T) (-4376 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4379 |has| |#1| (-362)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL (-1223 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2540) (LIST (|devaluate| |#2|) (QUOTE (-1163)))))) +((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2560) (LIST (|devaluate| |#2|) (QUOTE (-1163)))))) (-1224 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1225 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4838,7 +4838,7 @@ NIL NIL (-1227 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1228 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)}."))) @@ -4846,24 +4846,24 @@ NIL NIL (-1229 |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)}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1230 |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)}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3710) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-1231 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4380 |has| |#1| (-362)) (-4374 |has| |#1| (-362)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3986 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3710) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1232 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))}."))) -(((-4384 "*") |has| (-1231 |#2| |#3| |#4|) (-171)) (-4375 |has| (-1231 |#2| |#3| |#4|) (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-171))) (-3986 (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-550)))) +(((-4385 "*") |has| (-1231 |#2| |#3| |#4|) (-171)) (-4376 |has| (-1231 |#2| |#3| |#4|) (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-171))) (-3996 (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-550)))) (-1233 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4383))) +((|HasAttribute| |#1| (QUOTE -4384))) (-1234 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4875,20 +4875,20 @@ NIL (-1236 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2296) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3710) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) (-1237 |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."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1238 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4384 "*") |has| |#1| (-171)) (-4375 |has| |#1| (-550)) (-4376 . T) (-4377 . T) (-4379 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3986 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3986 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -3826) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +(((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3710) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1239 |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 -(-1240 -3160 UP L UTS) +(-1240 -3198 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 (-550)))) @@ -4906,7 +4906,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-992))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1244 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) NIL (-1245 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4914,8 +4914,8 @@ NIL NIL (-1246 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4383 . T) (-4382 . T)) -((-3986 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3986 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3986 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4384 . T) (-4383 . T)) +((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-1247) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4942,13 +4942,13 @@ NIL NIL (-1253 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4377 . T) (-4376 . T)) +((-4378 . T) (-4377 . T)) NIL (-1254 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 -(-1255 K R UP -3160) +(-1255 K R UP -3198) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -4962,56 +4962,56 @@ NIL NIL (-1258 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)"))) -((-4377 |has| |#1| (-171)) (-4376 |has| |#1| (-171)) (-4379 . T)) +((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) (-1259 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}}."))) -((-4383 . T) (-4382 . T)) +((-4384 . T) (-4383 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -605) (QUOTE (-853))))) (-1260 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})"))) -((-4376 . T) (-4377 . T) (-4379 . T)) +((-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1261 |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."))) -((-4379 . T) (-4375 |has| |#2| (-6 -4375)) (-4377 . T) (-4376 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4375))) +((-4380 . T) (-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4376))) (-1262 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 (-1263 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4375 |has| |#2| (-6 -4375)) (-4377 . T) (-4376 . T) (-4379 . T)) +((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL -(-1264 S -3160) +(-1264 S -3198) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1265 -3160) +(-1265 -3198) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4374 . T) (-4380 . T) (-4375 . T) ((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1266 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4375 |has| |#2| (-6 -4375)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -708) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4375))) +((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -708) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4376))) (-1267 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4375 |has| |#2| (-6 -4375)) (-4377 . T) (-4376 . T) (-4379 . T)) +((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL (-1268 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4375 |has| |#1| (-6 -4375)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4375))) +((-4376 |has| |#1| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4376))) (-1269 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4379 . T) (-4380 |has| |#1| (-6 -4380)) (-4375 |has| |#1| (-6 -4375)) (-4377 . T) (-4376 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4379)) (|HasAttribute| |#1| (QUOTE -4380)) (|HasAttribute| |#1| (QUOTE -4375))) +((-4380 . T) (-4381 |has| |#1| (-6 -4381)) (-4376 |has| |#1| (-6 -4376)) (-4378 . T) (-4377 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4380)) (|HasAttribute| |#1| (QUOTE -4381)) (|HasAttribute| |#1| (QUOTE -4376))) (-1270 |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."))) -((-4375 |has| |#2| (-6 -4375)) (-4377 . T) (-4376 . T) (-4379 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4375))) +((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4376))) (-1271 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,{}n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL @@ -5026,7 +5026,7 @@ NIL NIL (-1274 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4384 "*") . T) (-4376 . T) (-4377 . T) (-4379 . T)) +(((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL NIL NIL @@ -5044,4 +5044,4 @@ NIL NIL NIL NIL -((-3 NIL 2276533 2276538 2276543 2276548) (-2 NIL 2276513 2276518 2276523 2276528) (-1 NIL 2276493 2276498 2276503 2276508) (0 NIL 2276473 2276478 2276483 2276488) (-1274 "ZMOD.spad" 2276282 2276295 2276411 2276468) (-1273 "ZLINDEP.spad" 2275326 2275337 2276272 2276277) (-1272 "ZDSOLVE.spad" 2265175 2265197 2275316 2275321) (-1271 "YSTREAM.spad" 2264668 2264679 2265165 2265170) (-1270 "XRPOLY.spad" 2263888 2263908 2264524 2264593) (-1269 "XPR.spad" 2261679 2261692 2263606 2263705) (-1268 "XPOLY.spad" 2261234 2261245 2261535 2261604) (-1267 "XPOLYC.spad" 2260551 2260567 2261160 2261229) (-1266 "XPBWPOLY.spad" 2258988 2259008 2260331 2260400) (-1265 "XF.spad" 2257449 2257464 2258890 2258983) (-1264 "XF.spad" 2255890 2255907 2257333 2257338) (-1263 "XFALG.spad" 2252914 2252930 2255816 2255885) (-1262 "XEXPPKG.spad" 2252165 2252191 2252904 2252909) (-1261 "XDPOLY.spad" 2251779 2251795 2252021 2252090) (-1260 "XALG.spad" 2251439 2251450 2251735 2251774) (-1259 "WUTSET.spad" 2247278 2247295 2251085 2251112) (-1258 "WP.spad" 2246477 2246521 2247136 2247203) (-1257 "WHILEAST.spad" 2246275 2246284 2246467 2246472) (-1256 "WHEREAST.spad" 2245946 2245955 2246265 2246270) (-1255 "WFFINTBS.spad" 2243509 2243531 2245936 2245941) (-1254 "WEIER.spad" 2241723 2241734 2243499 2243504) (-1253 "VSPACE.spad" 2241396 2241407 2241691 2241718) (-1252 "VSPACE.spad" 2241089 2241102 2241386 2241391) (-1251 "VOID.spad" 2240766 2240775 2241079 2241084) (-1250 "VIEW.spad" 2238388 2238397 2240756 2240761) (-1249 "VIEWDEF.spad" 2233585 2233594 2238378 2238383) (-1248 "VIEW3D.spad" 2217420 2217429 2233575 2233580) (-1247 "VIEW2D.spad" 2205157 2205166 2217410 2217415) (-1246 "VECTOR.spad" 2203832 2203843 2204083 2204110) (-1245 "VECTOR2.spad" 2202459 2202472 2203822 2203827) (-1244 "VECTCAT.spad" 2200359 2200370 2202427 2202454) (-1243 "VECTCAT.spad" 2198067 2198080 2200137 2200142) (-1242 "VARIABLE.spad" 2197847 2197862 2198057 2198062) (-1241 "UTYPE.spad" 2197491 2197500 2197837 2197842) (-1240 "UTSODETL.spad" 2196784 2196808 2197447 2197452) (-1239 "UTSODE.spad" 2194972 2194992 2196774 2196779) (-1238 "UTS.spad" 2189761 2189789 2193439 2193536) (-1237 "UTSCAT.spad" 2187212 2187228 2189659 2189756) (-1236 "UTSCAT.spad" 2184307 2184325 2186756 2186761) (-1235 "UTS2.spad" 2183900 2183935 2184297 2184302) (-1234 "URAGG.spad" 2178532 2178543 2183890 2183895) (-1233 "URAGG.spad" 2173128 2173141 2178488 2178493) (-1232 "UPXSSING.spad" 2170771 2170797 2172209 2172342) (-1231 "UPXS.spad" 2167919 2167947 2168903 2169052) (-1230 "UPXSCONS.spad" 2165676 2165696 2166051 2166200) (-1229 "UPXSCCA.spad" 2164241 2164261 2165522 2165671) (-1228 "UPXSCCA.spad" 2162948 2162970 2164231 2164236) (-1227 "UPXSCAT.spad" 2161529 2161545 2162794 2162943) (-1226 "UPXS2.spad" 2161070 2161123 2161519 2161524) (-1225 "UPSQFREE.spad" 2159482 2159496 2161060 2161065) (-1224 "UPSCAT.spad" 2157075 2157099 2159380 2159477) (-1223 "UPSCAT.spad" 2154374 2154400 2156681 2156686) (-1222 "UPOLYC.spad" 2149352 2149363 2154216 2154369) (-1221 "UPOLYC.spad" 2144222 2144235 2149088 2149093) (-1220 "UPOLYC2.spad" 2143691 2143710 2144212 2144217) (-1219 "UP.spad" 2140848 2140863 2141241 2141394) (-1218 "UPMP.spad" 2139738 2139751 2140838 2140843) (-1217 "UPDIVP.spad" 2139301 2139315 2139728 2139733) (-1216 "UPDECOMP.spad" 2137538 2137552 2139291 2139296) (-1215 "UPCDEN.spad" 2136745 2136761 2137528 2137533) (-1214 "UP2.spad" 2136107 2136128 2136735 2136740) (-1213 "UNISEG.spad" 2135460 2135471 2136026 2136031) (-1212 "UNISEG2.spad" 2134953 2134966 2135416 2135421) (-1211 "UNIFACT.spad" 2134054 2134066 2134943 2134948) (-1210 "ULS.spad" 2124606 2124634 2125699 2126128) (-1209 "ULSCONS.spad" 2117000 2117020 2117372 2117521) (-1208 "ULSCCAT.spad" 2114729 2114749 2116846 2116995) (-1207 "ULSCCAT.spad" 2112566 2112588 2114685 2114690) (-1206 "ULSCAT.spad" 2110782 2110798 2112412 2112561) (-1205 "ULS2.spad" 2110294 2110347 2110772 2110777) (-1204 "UFD.spad" 2109359 2109368 2110220 2110289) (-1203 "UFD.spad" 2108486 2108497 2109349 2109354) (-1202 "UDVO.spad" 2107333 2107342 2108476 2108481) (-1201 "UDPO.spad" 2104760 2104771 2107289 2107294) (-1200 "TYPE.spad" 2104692 2104701 2104750 2104755) (-1199 "TYPEAST.spad" 2104611 2104620 2104682 2104687) (-1198 "TWOFACT.spad" 2103261 2103276 2104601 2104606) (-1197 "TUPLE.spad" 2102745 2102756 2103160 2103165) (-1196 "TUBETOOL.spad" 2099582 2099591 2102735 2102740) (-1195 "TUBE.spad" 2098223 2098240 2099572 2099577) (-1194 "TS.spad" 2096812 2096828 2097788 2097885) (-1193 "TSETCAT.spad" 2083939 2083956 2096780 2096807) (-1192 "TSETCAT.spad" 2071052 2071071 2083895 2083900) (-1191 "TRMANIP.spad" 2065418 2065435 2070758 2070763) (-1190 "TRIMAT.spad" 2064377 2064402 2065408 2065413) (-1189 "TRIGMNIP.spad" 2062894 2062911 2064367 2064372) (-1188 "TRIGCAT.spad" 2062406 2062415 2062884 2062889) (-1187 "TRIGCAT.spad" 2061916 2061927 2062396 2062401) (-1186 "TREE.spad" 2060487 2060498 2061523 2061550) (-1185 "TRANFUN.spad" 2060318 2060327 2060477 2060482) (-1184 "TRANFUN.spad" 2060147 2060158 2060308 2060313) (-1183 "TOPSP.spad" 2059821 2059830 2060137 2060142) (-1182 "TOOLSIGN.spad" 2059484 2059495 2059811 2059816) (-1181 "TEXTFILE.spad" 2058041 2058050 2059474 2059479) (-1180 "TEX.spad" 2055173 2055182 2058031 2058036) (-1179 "TEX1.spad" 2054729 2054740 2055163 2055168) (-1178 "TEMUTL.spad" 2054284 2054293 2054719 2054724) (-1177 "TBCMPPK.spad" 2052377 2052400 2054274 2054279) (-1176 "TBAGG.spad" 2051413 2051436 2052357 2052372) (-1175 "TBAGG.spad" 2050457 2050482 2051403 2051408) (-1174 "TANEXP.spad" 2049833 2049844 2050447 2050452) (-1173 "TABLE.spad" 2048244 2048267 2048514 2048541) (-1172 "TABLEAU.spad" 2047725 2047736 2048234 2048239) (-1171 "TABLBUMP.spad" 2044508 2044519 2047715 2047720) (-1170 "SYSTEM.spad" 2043782 2043791 2044498 2044503) (-1169 "SYSSOLP.spad" 2041255 2041266 2043772 2043777) (-1168 "SYNTAX.spad" 2037525 2037534 2041245 2041250) (-1167 "SYMTAB.spad" 2035581 2035590 2037515 2037520) (-1166 "SYMS.spad" 2031566 2031575 2035571 2035576) (-1165 "SYMPOLY.spad" 2030573 2030584 2030655 2030782) (-1164 "SYMFUNC.spad" 2030048 2030059 2030563 2030568) (-1163 "SYMBOL.spad" 2027475 2027484 2030038 2030043) (-1162 "SWITCH.spad" 2024232 2024241 2027465 2027470) (-1161 "SUTS.spad" 2021131 2021159 2022699 2022796) (-1160 "SUPXS.spad" 2018266 2018294 2019263 2019412) (-1159 "SUP.spad" 2015035 2015046 2015816 2015969) (-1158 "SUPFRACF.spad" 2014140 2014158 2015025 2015030) (-1157 "SUP2.spad" 2013530 2013543 2014130 2014135) (-1156 "SUMRF.spad" 2012496 2012507 2013520 2013525) (-1155 "SUMFS.spad" 2012129 2012146 2012486 2012491) (-1154 "SULS.spad" 2002668 2002696 2003774 2004203) (-1153 "SUCHTAST.spad" 2002437 2002446 2002658 2002663) (-1152 "SUCH.spad" 2002117 2002132 2002427 2002432) (-1151 "SUBSPACE.spad" 1994124 1994139 2002107 2002112) (-1150 "SUBRESP.spad" 1993284 1993298 1994080 1994085) (-1149 "STTF.spad" 1989383 1989399 1993274 1993279) (-1148 "STTFNC.spad" 1985851 1985867 1989373 1989378) (-1147 "STTAYLOR.spad" 1978249 1978260 1985732 1985737) (-1146 "STRTBL.spad" 1976754 1976771 1976903 1976930) (-1145 "STRING.spad" 1976163 1976172 1976177 1976204) (-1144 "STRICAT.spad" 1975951 1975960 1976131 1976158) (-1143 "STREAM.spad" 1972809 1972820 1975476 1975491) (-1142 "STREAM3.spad" 1972354 1972369 1972799 1972804) (-1141 "STREAM2.spad" 1971422 1971435 1972344 1972349) (-1140 "STREAM1.spad" 1971126 1971137 1971412 1971417) (-1139 "STINPROD.spad" 1970032 1970048 1971116 1971121) (-1138 "STEP.spad" 1969233 1969242 1970022 1970027) (-1137 "STBL.spad" 1967759 1967787 1967926 1967941) (-1136 "STAGG.spad" 1966834 1966845 1967749 1967754) (-1135 "STAGG.spad" 1965907 1965920 1966824 1966829) (-1134 "STACK.spad" 1965258 1965269 1965514 1965541) (-1133 "SREGSET.spad" 1962962 1962979 1964904 1964931) (-1132 "SRDCMPK.spad" 1961507 1961527 1962952 1962957) (-1131 "SRAGG.spad" 1956604 1956613 1961475 1961502) (-1130 "SRAGG.spad" 1951721 1951732 1956594 1956599) (-1129 "SQMATRIX.spad" 1949337 1949355 1950253 1950340) (-1128 "SPLTREE.spad" 1943889 1943902 1948773 1948800) (-1127 "SPLNODE.spad" 1940477 1940490 1943879 1943884) (-1126 "SPFCAT.spad" 1939254 1939263 1940467 1940472) (-1125 "SPECOUT.spad" 1937804 1937813 1939244 1939249) (-1124 "SPADXPT.spad" 1929943 1929952 1937794 1937799) (-1123 "spad-parser.spad" 1929408 1929417 1929933 1929938) (-1122 "SPADAST.spad" 1929109 1929118 1929398 1929403) (-1121 "SPACEC.spad" 1913122 1913133 1929099 1929104) (-1120 "SPACE3.spad" 1912898 1912909 1913112 1913117) (-1119 "SORTPAK.spad" 1912443 1912456 1912854 1912859) (-1118 "SOLVETRA.spad" 1910200 1910211 1912433 1912438) (-1117 "SOLVESER.spad" 1908720 1908731 1910190 1910195) (-1116 "SOLVERAD.spad" 1904730 1904741 1908710 1908715) (-1115 "SOLVEFOR.spad" 1903150 1903168 1904720 1904725) (-1114 "SNTSCAT.spad" 1902750 1902767 1903118 1903145) (-1113 "SMTS.spad" 1901010 1901036 1902315 1902412) (-1112 "SMP.spad" 1898449 1898469 1898839 1898966) (-1111 "SMITH.spad" 1897292 1897317 1898439 1898444) (-1110 "SMATCAT.spad" 1895402 1895432 1897236 1897287) (-1109 "SMATCAT.spad" 1893444 1893476 1895280 1895285) (-1108 "SKAGG.spad" 1892405 1892416 1893412 1893439) (-1107 "SINT.spad" 1891231 1891240 1892271 1892400) (-1106 "SIMPAN.spad" 1890959 1890968 1891221 1891226) (-1105 "SIG.spad" 1890287 1890296 1890949 1890954) (-1104 "SIGNRF.spad" 1889395 1889406 1890277 1890282) (-1103 "SIGNEF.spad" 1888664 1888681 1889385 1889390) (-1102 "SIGAST.spad" 1888045 1888054 1888654 1888659) (-1101 "SHP.spad" 1885963 1885978 1888001 1888006) (-1100 "SHDP.spad" 1875674 1875701 1876183 1876314) (-1099 "SGROUP.spad" 1875282 1875291 1875664 1875669) (-1098 "SGROUP.spad" 1874888 1874899 1875272 1875277) (-1097 "SGCF.spad" 1867769 1867778 1874878 1874883) (-1096 "SFRTCAT.spad" 1866697 1866714 1867737 1867764) (-1095 "SFRGCD.spad" 1865760 1865780 1866687 1866692) (-1094 "SFQCMPK.spad" 1860397 1860417 1865750 1865755) (-1093 "SFORT.spad" 1859832 1859846 1860387 1860392) (-1092 "SEXOF.spad" 1859675 1859715 1859822 1859827) (-1091 "SEX.spad" 1859567 1859576 1859665 1859670) (-1090 "SEXCAT.spad" 1857118 1857158 1859557 1859562) (-1089 "SET.spad" 1855418 1855429 1856539 1856578) (-1088 "SETMN.spad" 1853852 1853869 1855408 1855413) (-1087 "SETCAT.spad" 1853337 1853346 1853842 1853847) (-1086 "SETCAT.spad" 1852820 1852831 1853327 1853332) (-1085 "SETAGG.spad" 1849341 1849352 1852800 1852815) (-1084 "SETAGG.spad" 1845870 1845883 1849331 1849336) (-1083 "SEQAST.spad" 1845573 1845582 1845860 1845865) (-1082 "SEGXCAT.spad" 1844695 1844708 1845563 1845568) (-1081 "SEG.spad" 1844508 1844519 1844614 1844619) (-1080 "SEGCAT.spad" 1843415 1843426 1844498 1844503) (-1079 "SEGBIND.spad" 1842487 1842498 1843370 1843375) (-1078 "SEGBIND2.spad" 1842183 1842196 1842477 1842482) (-1077 "SEGAST.spad" 1841897 1841906 1842173 1842178) (-1076 "SEG2.spad" 1841322 1841335 1841853 1841858) (-1075 "SDVAR.spad" 1840598 1840609 1841312 1841317) (-1074 "SDPOL.spad" 1837988 1837999 1838279 1838406) (-1073 "SCPKG.spad" 1836067 1836078 1837978 1837983) (-1072 "SCOPE.spad" 1835212 1835221 1836057 1836062) (-1071 "SCACHE.spad" 1833894 1833905 1835202 1835207) (-1070 "SASTCAT.spad" 1833803 1833812 1833884 1833889) (-1069 "SAOS.spad" 1833675 1833684 1833793 1833798) (-1068 "SAERFFC.spad" 1833388 1833408 1833665 1833670) (-1067 "SAE.spad" 1831563 1831579 1832174 1832309) (-1066 "SAEFACT.spad" 1831264 1831284 1831553 1831558) (-1065 "RURPK.spad" 1828905 1828921 1831254 1831259) (-1064 "RULESET.spad" 1828346 1828370 1828895 1828900) (-1063 "RULE.spad" 1826550 1826574 1828336 1828341) (-1062 "RULECOLD.spad" 1826402 1826415 1826540 1826545) (-1061 "RSTRCAST.spad" 1826119 1826128 1826392 1826397) (-1060 "RSETGCD.spad" 1822497 1822517 1826109 1826114) (-1059 "RSETCAT.spad" 1812281 1812298 1822465 1822492) (-1058 "RSETCAT.spad" 1802085 1802104 1812271 1812276) (-1057 "RSDCMPK.spad" 1800537 1800557 1802075 1802080) (-1056 "RRCC.spad" 1798921 1798951 1800527 1800532) (-1055 "RRCC.spad" 1797303 1797335 1798911 1798916) (-1054 "RPTAST.spad" 1797005 1797014 1797293 1797298) (-1053 "RPOLCAT.spad" 1776365 1776380 1796873 1797000) (-1052 "RPOLCAT.spad" 1755439 1755456 1775949 1775954) (-1051 "ROUTINE.spad" 1751302 1751311 1754086 1754113) (-1050 "ROMAN.spad" 1750630 1750639 1751168 1751297) (-1049 "ROIRC.spad" 1749710 1749742 1750620 1750625) (-1048 "RNS.spad" 1748613 1748622 1749612 1749705) (-1047 "RNS.spad" 1747602 1747613 1748603 1748608) (-1046 "RNG.spad" 1747337 1747346 1747592 1747597) (-1045 "RMODULE.spad" 1746975 1746986 1747327 1747332) (-1044 "RMCAT2.spad" 1746383 1746440 1746965 1746970) (-1043 "RMATRIX.spad" 1745207 1745226 1745550 1745589) (-1042 "RMATCAT.spad" 1740740 1740771 1745163 1745202) (-1041 "RMATCAT.spad" 1736163 1736196 1740588 1740593) (-1040 "RINTERP.spad" 1736051 1736071 1736153 1736158) (-1039 "RING.spad" 1735521 1735530 1736031 1736046) (-1038 "RING.spad" 1734999 1735010 1735511 1735516) (-1037 "RIDIST.spad" 1734383 1734392 1734989 1734994) (-1036 "RGCHAIN.spad" 1732962 1732978 1733868 1733895) (-1035 "RGBCSPC.spad" 1732743 1732755 1732952 1732957) (-1034 "RGBCMDL.spad" 1732273 1732285 1732733 1732738) (-1033 "RF.spad" 1729887 1729898 1732263 1732268) (-1032 "RFFACTOR.spad" 1729349 1729360 1729877 1729882) (-1031 "RFFACT.spad" 1729084 1729096 1729339 1729344) (-1030 "RFDIST.spad" 1728072 1728081 1729074 1729079) (-1029 "RETSOL.spad" 1727489 1727502 1728062 1728067) (-1028 "RETRACT.spad" 1726917 1726928 1727479 1727484) (-1027 "RETRACT.spad" 1726343 1726356 1726907 1726912) (-1026 "RETAST.spad" 1726155 1726164 1726333 1726338) (-1025 "RESULT.spad" 1724215 1724224 1724802 1724829) (-1024 "RESRING.spad" 1723562 1723609 1724153 1724210) (-1023 "RESLATC.spad" 1722886 1722897 1723552 1723557) (-1022 "REPSQ.spad" 1722615 1722626 1722876 1722881) (-1021 "REP.spad" 1720167 1720176 1722605 1722610) (-1020 "REPDB.spad" 1719872 1719883 1720157 1720162) (-1019 "REP2.spad" 1709444 1709455 1719714 1719719) (-1018 "REP1.spad" 1703434 1703445 1709394 1709399) (-1017 "REGSET.spad" 1701231 1701248 1703080 1703107) (-1016 "REF.spad" 1700560 1700571 1701186 1701191) (-1015 "REDORDER.spad" 1699736 1699753 1700550 1700555) (-1014 "RECLOS.spad" 1698519 1698539 1699223 1699316) (-1013 "REALSOLV.spad" 1697651 1697660 1698509 1698514) (-1012 "REAL.spad" 1697523 1697532 1697641 1697646) (-1011 "REAL0Q.spad" 1694805 1694820 1697513 1697518) (-1010 "REAL0.spad" 1691633 1691648 1694795 1694800) (-1009 "RDUCEAST.spad" 1691354 1691363 1691623 1691628) (-1008 "RDIV.spad" 1691005 1691030 1691344 1691349) (-1007 "RDIST.spad" 1690568 1690579 1690995 1691000) (-1006 "RDETRS.spad" 1689364 1689382 1690558 1690563) (-1005 "RDETR.spad" 1687471 1687489 1689354 1689359) (-1004 "RDEEFS.spad" 1686544 1686561 1687461 1687466) (-1003 "RDEEF.spad" 1685540 1685557 1686534 1686539) (-1002 "RCFIELD.spad" 1682726 1682735 1685442 1685535) (-1001 "RCFIELD.spad" 1679998 1680009 1682716 1682721) (-1000 "RCAGG.spad" 1677910 1677921 1679988 1679993) (-999 "RCAGG.spad" 1675750 1675762 1677829 1677834) (-998 "RATRET.spad" 1675111 1675121 1675740 1675745) (-997 "RATFACT.spad" 1674804 1674815 1675101 1675106) (-996 "RANDSRC.spad" 1674124 1674132 1674794 1674799) (-995 "RADUTIL.spad" 1673879 1673887 1674114 1674119) (-994 "RADIX.spad" 1670781 1670794 1672346 1672439) (-993 "RADFF.spad" 1669195 1669231 1669313 1669469) (-992 "RADCAT.spad" 1668789 1668797 1669185 1669190) (-991 "RADCAT.spad" 1668381 1668391 1668779 1668784) (-990 "QUEUE.spad" 1667724 1667734 1667988 1668015) (-989 "QUAT.spad" 1666306 1666316 1666648 1666713) (-988 "QUATCT2.spad" 1665925 1665943 1666296 1666301) (-987 "QUATCAT.spad" 1664090 1664100 1665855 1665920) (-986 "QUATCAT.spad" 1662006 1662018 1663773 1663778) (-985 "QUAGG.spad" 1660832 1660842 1661974 1662001) (-984 "QQUTAST.spad" 1660601 1660609 1660822 1660827) (-983 "QFORM.spad" 1660064 1660078 1660591 1660596) (-982 "QFCAT.spad" 1658767 1658777 1659966 1660059) (-981 "QFCAT.spad" 1657061 1657073 1658262 1658267) (-980 "QFCAT2.spad" 1656752 1656768 1657051 1657056) (-979 "QEQUAT.spad" 1656309 1656317 1656742 1656747) (-978 "QCMPACK.spad" 1651056 1651075 1656299 1656304) (-977 "QALGSET.spad" 1647131 1647163 1650970 1650975) (-976 "QALGSET2.spad" 1645127 1645145 1647121 1647126) (-975 "PWFFINTB.spad" 1642437 1642458 1645117 1645122) (-974 "PUSHVAR.spad" 1641766 1641785 1642427 1642432) (-973 "PTRANFN.spad" 1637892 1637902 1641756 1641761) (-972 "PTPACK.spad" 1634980 1634990 1637882 1637887) (-971 "PTFUNC2.spad" 1634801 1634815 1634970 1634975) (-970 "PTCAT.spad" 1634050 1634060 1634769 1634796) (-969 "PSQFR.spad" 1633357 1633381 1634040 1634045) (-968 "PSEUDLIN.spad" 1632215 1632225 1633347 1633352) (-967 "PSETPK.spad" 1617648 1617664 1632093 1632098) (-966 "PSETCAT.spad" 1611568 1611591 1617628 1617643) (-965 "PSETCAT.spad" 1605462 1605487 1611524 1611529) (-964 "PSCURVE.spad" 1604445 1604453 1605452 1605457) (-963 "PSCAT.spad" 1603212 1603241 1604343 1604440) (-962 "PSCAT.spad" 1602069 1602100 1603202 1603207) (-961 "PRTITION.spad" 1601014 1601022 1602059 1602064) (-960 "PRTDAST.spad" 1600733 1600741 1601004 1601009) (-959 "PRS.spad" 1590295 1590312 1600689 1600694) (-958 "PRQAGG.spad" 1589726 1589736 1590263 1590290) (-957 "PROPLOG.spad" 1589129 1589137 1589716 1589721) (-956 "PROPFRML.spad" 1587047 1587058 1589119 1589124) (-955 "PROPERTY.spad" 1586541 1586549 1587037 1587042) (-954 "PRODUCT.spad" 1584221 1584233 1584507 1584562) (-953 "PR.spad" 1582607 1582619 1583312 1583439) (-952 "PRINT.spad" 1582359 1582367 1582597 1582602) (-951 "PRIMES.spad" 1580610 1580620 1582349 1582354) (-950 "PRIMELT.spad" 1578591 1578605 1580600 1580605) (-949 "PRIMCAT.spad" 1578214 1578222 1578581 1578586) (-948 "PRIMARR.spad" 1577219 1577229 1577397 1577424) (-947 "PRIMARR2.spad" 1575942 1575954 1577209 1577214) (-946 "PREASSOC.spad" 1575314 1575326 1575932 1575937) (-945 "PPCURVE.spad" 1574451 1574459 1575304 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1036109) (-643 "LODO1.spad" 1035063 1035073 1035343 1035382) (-642 "LODEEF.spad" 1033835 1033853 1035053 1035058) (-641 "LNAGG.spad" 1029637 1029647 1033825 1033830) (-640 "LNAGG.spad" 1025403 1025415 1029593 1029598) (-639 "LMOPS.spad" 1022139 1022156 1025393 1025398) (-638 "LMODULE.spad" 1021781 1021791 1022129 1022134) (-637 "LMDICT.spad" 1021064 1021074 1021332 1021359) (-636 "LITERAL.spad" 1020970 1020981 1021054 1021059) (-635 "LIST.spad" 1018688 1018698 1020117 1020144) (-634 "LIST3.spad" 1017979 1017993 1018678 1018683) (-633 "LIST2.spad" 1016619 1016631 1017969 1017974) (-632 "LIST2MAP.spad" 1013496 1013508 1016609 1016614) (-631 "LINEXP.spad" 1012928 1012938 1013476 1013491) (-630 "LINDEP.spad" 1011705 1011717 1012840 1012845) (-629 "LIMITRF.spad" 1009619 1009629 1011695 1011700) (-628 "LIMITPS.spad" 1008502 1008515 1009609 1009614) (-627 "LIE.spad" 1006516 1006528 1007792 1007937) (-626 "LIECAT.spad" 1005992 1006002 1006442 1006511) (-625 "LIECAT.spad" 1005496 1005508 1005948 1005953) (-624 "LIB.spad" 1003544 1003552 1004155 1004170) (-623 "LGROBP.spad" 1000897 1000916 1003534 1003539) (-622 "LF.spad" 999816 999832 1000887 1000892) (-621 "LFCAT.spad" 998835 998843 999806 999811) (-620 "LEXTRIPK.spad" 994338 994353 998825 998830) (-619 "LEXP.spad" 992341 992368 994318 994333) (-618 "LETAST.spad" 992040 992048 992331 992336) (-617 "LEADCDET.spad" 990424 990441 992030 992035) (-616 "LAZM3PK.spad" 989128 989150 990414 990419) (-615 "LAUPOL.spad" 987817 987830 988721 988790) (-614 "LAPLACE.spad" 987390 987406 987807 987812) (-613 "LA.spad" 986830 986844 987312 987351) (-612 "LALG.spad" 986606 986616 986810 986825) (-611 "LALG.spad" 986390 986402 986596 986601) (-610 "KVTFROM.spad" 986125 986135 986380 986385) (-609 "KTVLOGIC.spad" 985548 985556 986115 986120) (-608 "KRCFROM.spad" 985286 985296 985538 985543) (-607 "KOVACIC.spad" 983999 984016 985276 985281) (-606 "KONVERT.spad" 983721 983731 983989 983994) (-605 "KOERCE.spad" 983458 983468 983711 983716) (-604 "KERNEL.spad" 981993 982003 983242 983247) (-603 "KERNEL2.spad" 981696 981708 981983 981988) (-602 "KDAGG.spad" 980799 980821 981676 981691) (-601 "KDAGG.spad" 979910 979934 980789 980794) (-600 "KAFILE.spad" 978873 978889 979108 979135) (-599 "JORDAN.spad" 976700 976712 978163 978308) (-598 "JOINAST.spad" 976394 976402 976690 976695) (-597 "JAVACODE.spad" 976260 976268 976384 976389) (-596 "IXAGG.spad" 974383 974407 976250 976255) (-595 "IXAGG.spad" 972361 972387 974230 974235) (-594 "IVECTOR.spad" 971132 971147 971287 971314) (-593 "ITUPLE.spad" 970277 970287 971122 971127) (-592 "ITRIGMNP.spad" 969088 969107 970267 970272) (-591 "ITFUN3.spad" 968582 968596 969078 969083) (-590 "ITFUN2.spad" 968312 968324 968572 968577) (-589 "ITAYLOR.spad" 966104 966119 968148 968273) (-588 "ISUPS.spad" 958515 958530 965078 965175) (-587 "ISUMP.spad" 958012 958028 958505 958510) (-586 "ISTRING.spad" 957015 957028 957181 957208) (-585 "ISAST.spad" 956734 956742 957005 957010) (-584 "IRURPK.spad" 955447 955466 956724 956729) (-583 "IRSN.spad" 953407 953415 955437 955442) (-582 "IRRF2F.spad" 951882 951892 953363 953368) (-581 "IRREDFFX.spad" 951483 951494 951872 951877) (-580 "IROOT.spad" 949814 949824 951473 951478) (-579 "IR.spad" 947603 947617 949669 949696) (-578 "IR2.spad" 946623 946639 947593 947598) (-577 "IR2F.spad" 945823 945839 946613 946618) (-576 "IPRNTPK.spad" 945583 945591 945813 945818) (-575 "IPF.spad" 945148 945160 945388 945481) (-574 "IPADIC.spad" 944909 944935 945074 945143) (-573 "IP4ADDR.spad" 944457 944465 944899 944904) (-572 "IOMODE.spad" 944078 944086 944447 944452) (-571 "IOBFILE.spad" 943439 943447 944068 944073) (-570 "IOBCON.spad" 943304 943312 943429 943434) (-569 "INVLAPLA.spad" 942949 942965 943294 943299) (-568 "INTTR.spad" 936195 936212 942939 942944) (-567 "INTTOOLS.spad" 933906 933922 935769 935774) (-566 "INTSLPE.spad" 933212 933220 933896 933901) (-565 "INTRVL.spad" 932778 932788 933126 933207) (-564 "INTRF.spad" 931142 931156 932768 932773) (-563 "INTRET.spad" 930574 930584 931132 931137) (-562 "INTRAT.spad" 929249 929266 930564 930569) (-561 "INTPM.spad" 927612 927628 928892 928897) (-560 "INTPAF.spad" 925380 925398 927544 927549) (-559 "INTPACK.spad" 915690 915698 925370 925375) (-558 "INT.spad" 915051 915059 915544 915685) (-557 "INTHERTR.spad" 914317 914334 915041 915046) (-556 "INTHERAL.spad" 913983 914007 914307 914312) (-555 "INTHEORY.spad" 910396 910404 913973 913978) (-554 "INTG0.spad" 903859 903877 910328 910333) (-553 "INTFTBL.spad" 897888 897896 903849 903854) (-552 "INTFACT.spad" 896947 896957 897878 897883) (-551 "INTEF.spad" 895262 895278 896937 896942) (-550 "INTDOM.spad" 893877 893885 895188 895257) (-549 "INTDOM.spad" 892554 892564 893867 893872) (-548 "INTCAT.spad" 890807 890817 892468 892549) (-547 "INTBIT.spad" 890310 890318 890797 890802) (-546 "INTALG.spad" 889492 889519 890300 890305) (-545 "INTAF.spad" 888984 889000 889482 889487) (-544 "INTABL.spad" 887502 887533 887665 887692) (-543 "INS.spad" 884969 884977 887404 887497) (-542 "INS.spad" 882522 882532 884959 884964) (-541 "INPSIGN.spad" 881956 881969 882512 882517) (-540 "INPRODPF.spad" 881022 881041 881946 881951) (-539 "INPRODFF.spad" 880080 880104 881012 881017) (-538 "INNMFACT.spad" 879051 879068 880070 880075) (-537 "INMODGCD.spad" 878535 878565 879041 879046) (-536 "INFSP.spad" 876820 876842 878525 878530) (-535 "INFPROD0.spad" 875870 875889 876810 876815) (-534 "INFORM.spad" 873031 873039 875860 875865) (-533 "INFORM1.spad" 872656 872666 873021 873026) (-532 "INFINITY.spad" 872208 872216 872646 872651) (-531 "INETCLTS.spad" 872185 872193 872198 872203) (-530 "INEP.spad" 870717 870739 872175 872180) (-529 "INDE.spad" 870446 870463 870707 870712) (-528 "INCRMAPS.spad" 869867 869877 870436 870441) (-527 "INBFILE.spad" 868939 868947 869857 869862) (-526 "INBFF.spad" 864709 864720 868929 868934) (-525 "INBCON.spad" 863953 863961 864699 864704) (-524 "INBCON.spad" 863195 863205 863943 863948) (-523 "INAST.spad" 862860 862868 863185 863190) (-522 "IMPTAST.spad" 862568 862576 862850 862855) (-521 "IMATRIX.spad" 861513 861539 862025 862052) (-520 "IMATQF.spad" 860607 860651 861469 861474) (-519 "IMATLIN.spad" 859212 859236 860563 860568) (-518 "ILIST.spad" 857868 857883 858395 858422) (-517 "IIARRAY2.spad" 857256 857294 857475 857502) (-516 "IFF.spad" 856666 856682 856937 857030) (-515 "IFAST.spad" 856280 856288 856656 856661) (-514 "IFARRAY.spad" 853767 853782 855463 855490) (-513 "IFAMON.spad" 853629 853646 853723 853728) (-512 "IEVALAB.spad" 853018 853030 853619 853624) (-511 "IEVALAB.spad" 852405 852419 853008 853013) (-510 "IDPO.spad" 852203 852215 852395 852400) (-509 "IDPOAMS.spad" 851959 851971 852193 852198) (-508 "IDPOAM.spad" 851679 851691 851949 851954) (-507 "IDPC.spad" 850613 850625 851669 851674) (-506 "IDPAM.spad" 850358 850370 850603 850608) (-505 "IDPAG.spad" 850105 850117 850348 850353) (-504 "IDENT.spad" 849877 849885 850095 850100) (-503 "IDECOMP.spad" 847114 847132 849867 849872) (-502 "IDEAL.spad" 842037 842076 847049 847054) (-501 "ICDEN.spad" 841188 841204 842027 842032) (-500 "ICARD.spad" 840377 840385 841178 841183) (-499 "IBPTOOLS.spad" 838970 838987 840367 840372) (-498 "IBITS.spad" 838169 838182 838606 838633) (-497 "IBATOOL.spad" 835044 835063 838159 838164) (-496 "IBACHIN.spad" 833531 833546 835034 835039) (-495 "IARRAY2.spad" 832519 832545 833138 833165) (-494 "IARRAY1.spad" 831564 831579 831702 831729) (-493 "IAN.spad" 829777 829785 831380 831473) (-492 "IALGFACT.spad" 829378 829411 829767 829772) (-491 "HYPCAT.spad" 828802 828810 829368 829373) (-490 "HYPCAT.spad" 828224 828234 828792 828797) (-489 "HOSTNAME.spad" 828032 828040 828214 828219) (-488 "HOMOTOP.spad" 827775 827785 828022 828027) (-487 "HOAGG.spad" 825043 825053 827765 827770) (-486 "HOAGG.spad" 822086 822098 824810 824815) (-485 "HEXADEC.spad" 820188 820196 820553 820646) (-484 "HEUGCD.spad" 819203 819214 820178 820183) (-483 "HELLFDIV.spad" 818793 818817 819193 819198) (-482 "HEAP.spad" 818185 818195 818400 818427) (-481 "HEADAST.spad" 817716 817724 818175 818180) (-480 "HDP.spad" 807559 807575 807936 808067) (-479 "HDMP.spad" 804735 804750 805353 805480) (-478 "HB.spad" 802972 802980 804725 804730) (-477 "HASHTBL.spad" 801442 801473 801653 801680) (-476 "HASAST.spad" 801158 801166 801432 801437) (-475 "HACKPI.spad" 800641 800649 801060 801153) (-474 "GTSET.spad" 799580 799596 800287 800314) (-473 "GSTBL.spad" 798099 798134 798273 798288) (-472 "GSERIES.spad" 795266 795293 796231 796380) (-471 "GROUP.spad" 794535 794543 795246 795261) (-470 "GROUP.spad" 793812 793822 794525 794530) (-469 "GROEBSOL.spad" 792300 792321 793802 793807) (-468 "GRMOD.spad" 790871 790883 792290 792295) (-467 "GRMOD.spad" 789440 789454 790861 790866) (-466 "GRIMAGE.spad" 782045 782053 789430 789435) (-465 "GRDEF.spad" 780424 780432 782035 782040) (-464 "GRAY.spad" 778883 778891 780414 780419) (-463 "GRALG.spad" 777930 777942 778873 778878) (-462 "GRALG.spad" 776975 776989 777920 777925) (-461 "GPOLSET.spad" 776429 776452 776657 776684) (-460 "GOSPER.spad" 775694 775712 776419 776424) (-459 "GMODPOL.spad" 774832 774859 775662 775689) (-458 "GHENSEL.spad" 773901 773915 774822 774827) (-457 "GENUPS.spad" 770002 770015 773891 773896) (-456 "GENUFACT.spad" 769579 769589 769992 769997) (-455 "GENPGCD.spad" 769163 769180 769569 769574) (-454 "GENMFACT.spad" 768615 768634 769153 769158) (-453 "GENEEZ.spad" 766554 766567 768605 768610) (-452 "GDMP.spad" 763572 763589 764348 764475) (-451 "GCNAALG.spad" 757467 757494 763366 763433) (-450 "GCDDOM.spad" 756639 756647 757393 757462) (-449 "GCDDOM.spad" 755873 755883 756629 756634) (-448 "GB.spad" 753391 753429 755829 755834) (-447 "GBINTERN.spad" 749411 749449 753381 753386) (-446 "GBF.spad" 745168 745206 749401 749406) (-445 "GBEUCLID.spad" 743042 743080 745158 745163) (-444 "GAUSSFAC.spad" 742339 742347 743032 743037) (-443 "GALUTIL.spad" 740661 740671 742295 742300) (-442 "GALPOLYU.spad" 739107 739120 740651 740656) (-441 "GALFACTU.spad" 737272 737291 739097 739102) (-440 "GALFACT.spad" 727405 727416 737262 737267) (-439 "FVFUN.spad" 724428 724436 727395 727400) (-438 "FVC.spad" 723480 723488 724418 724423) (-437 "FUNCTION.spad" 723329 723341 723470 723475) (-436 "FT.spad" 721622 721630 723319 723324) (-435 "FTEM.spad" 720785 720793 721612 721617) (-434 "FSUPFACT.spad" 719685 719704 720721 720726) (-433 "FST.spad" 717771 717779 719675 719680) (-432 "FSRED.spad" 717249 717265 717761 717766) (-431 "FSPRMELT.spad" 716073 716089 717206 717211) (-430 "FSPECF.spad" 714150 714166 716063 716068) (-429 "FS.spad" 708212 708222 713925 714145) (-428 "FS.spad" 702052 702064 707767 707772) (-427 "FSINT.spad" 701710 701726 702042 702047) (-426 "FSERIES.spad" 700897 700909 701530 701629) (-425 "FSCINT.spad" 700210 700226 700887 700892) (-424 "FSAGG.spad" 699327 699337 700166 700205) (-423 "FSAGG.spad" 698406 698418 699247 699252) (-422 "FSAGG2.spad" 697105 697121 698396 698401) (-421 "FS2UPS.spad" 691588 691622 697095 697100) (-420 "FS2.spad" 691233 691249 691578 691583) (-419 "FS2EXPXP.spad" 690356 690379 691223 691228) (-418 "FRUTIL.spad" 689298 689308 690346 690351) (-417 "FR.spad" 682992 683002 688322 688391) (-416 "FRNAALG.spad" 678079 678089 682934 682987) (-415 "FRNAALG.spad" 673178 673190 678035 678040) (-414 "FRNAAF2.spad" 672632 672650 673168 673173) (-413 "FRMOD.spad" 672026 672056 672563 672568) (-412 "FRIDEAL.spad" 671221 671242 672006 672021) (-411 "FRIDEAL2.spad" 670823 670855 671211 671216) (-410 "FRETRCT.spad" 670334 670344 670813 670818) (-409 "FRETRCT.spad" 669711 669723 670192 670197) (-408 "FRAMALG.spad" 668039 668052 669667 669706) (-407 "FRAMALG.spad" 666399 666414 668029 668034) (-406 "FRAC.spad" 663498 663508 663901 664074) (-405 "FRAC2.spad" 663101 663113 663488 663493) (-404 "FR2.spad" 662435 662447 663091 663096) (-403 "FPS.spad" 659244 659252 662325 662430) (-402 "FPS.spad" 656081 656091 659164 659169) (-401 "FPC.spad" 655123 655131 655983 656076) (-400 "FPC.spad" 654251 654261 655113 655118) (-399 "FPATMAB.spad" 654013 654023 654241 654246) (-398 "FPARFRAC.spad" 652486 652503 654003 654008) (-397 "FORTRAN.spad" 650992 651035 652476 652481) (-396 "FORT.spad" 649921 649929 650982 650987) (-395 "FORTFN.spad" 647091 647099 649911 649916) (-394 "FORTCAT.spad" 646775 646783 647081 647086) (-393 "FORMULA.spad" 644239 644247 646765 646770) (-392 "FORMULA1.spad" 643718 643728 644229 644234) (-391 "FORDER.spad" 643409 643433 643708 643713) (-390 "FOP.spad" 642610 642618 643399 643404) (-389 "FNLA.spad" 642034 642056 642578 642605) (-388 "FNCAT.spad" 640621 640629 642024 642029) (-387 "FNAME.spad" 640513 640521 640611 640616) (-386 "FMTC.spad" 640311 640319 640439 640508) (-385 "FMONOID.spad" 637366 637376 640267 640272) (-384 "FM.spad" 637061 637073 637300 637327) (-383 "FMFUN.spad" 634091 634099 637051 637056) (-382 "FMC.spad" 633143 633151 634081 634086) (-381 "FMCAT.spad" 630797 630815 633111 633138) (-380 "FM1.spad" 630154 630166 630731 630758) (-379 "FLOATRP.spad" 627875 627889 630144 630149) (-378 "FLOAT.spad" 621163 621171 627741 627870) (-377 "FLOATCP.spad" 618580 618594 621153 621158) (-376 "FLINEXP.spad" 618292 618302 618560 618575) (-375 "FLINEXP.spad" 617958 617970 618228 618233) (-374 "FLASORT.spad" 617278 617290 617948 617953) (-373 "FLALG.spad" 614924 614943 617204 617273) (-372 "FLAGG.spad" 611942 611952 614904 614919) (-371 "FLAGG.spad" 608861 608873 611825 611830) (-370 "FLAGG2.spad" 607542 607558 608851 608856) (-369 "FINRALG.spad" 605571 605584 607498 607537) (-368 "FINRALG.spad" 603526 603541 605455 605460) (-367 "FINITE.spad" 602678 602686 603516 603521) (-366 "FINAALG.spad" 591659 591669 602620 602673) (-365 "FINAALG.spad" 580652 580664 591615 591620) (-364 "FILE.spad" 580235 580245 580642 580647) (-363 "FILECAT.spad" 578753 578770 580225 580230) (-362 "FIELD.spad" 578159 578167 578655 578748) (-361 "FIELD.spad" 577651 577661 578149 578154) (-360 "FGROUP.spad" 576260 576270 577631 577646) (-359 "FGLMICPK.spad" 575047 575062 576250 576255) (-358 "FFX.spad" 574422 574437 574763 574856) (-357 "FFSLPE.spad" 573911 573932 574412 574417) (-356 "FFPOLY.spad" 565163 565174 573901 573906) (-355 "FFPOLY2.spad" 564223 564240 565153 565158) (-354 "FFP.spad" 563620 563640 563939 564032) (-353 "FF.spad" 563068 563084 563301 563394) (-352 "FFNBX.spad" 561580 561600 562784 562877) (-351 "FFNBP.spad" 560093 560110 561296 561389) (-350 "FFNB.spad" 558558 558579 559774 559867) (-349 "FFINTBAS.spad" 555972 555991 558548 558553) (-348 "FFIELDC.spad" 553547 553555 555874 555967) (-347 "FFIELDC.spad" 551208 551218 553537 553542) (-346 "FFHOM.spad" 549956 549973 551198 551203) (-345 "FFF.spad" 547391 547402 549946 549951) (-344 "FFCGX.spad" 546238 546258 547107 547200) (-343 "FFCGP.spad" 545127 545147 545954 546047) (-342 "FFCG.spad" 543919 543940 544808 544901) (-341 "FFCAT.spad" 536946 536968 543758 543914) (-340 "FFCAT.spad" 530052 530076 536866 536871) (-339 "FFCAT2.spad" 529797 529837 530042 530047) (-338 "FEXPR.spad" 521506 521552 529553 529592) (-337 "FEVALAB.spad" 521212 521222 521496 521501) (-336 "FEVALAB.spad" 520703 520715 520989 520994) (-335 "FDIV.spad" 520145 520169 520693 520698) (-334 "FDIVCAT.spad" 518187 518211 520135 520140) (-333 "FDIVCAT.spad" 516227 516253 518177 518182) (-332 "FDIV2.spad" 515881 515921 516217 516222) (-331 "FCPAK1.spad" 514434 514442 515871 515876) (-330 "FCOMP.spad" 513813 513823 514424 514429) (-329 "FC.spad" 503728 503736 513803 513808) (-328 "FAXF.spad" 496663 496677 503630 503723) (-327 "FAXF.spad" 489650 489666 496619 496624) (-326 "FARRAY.spad" 487796 487806 488833 488860) (-325 "FAMR.spad" 485916 485928 487694 487791) (-324 "FAMR.spad" 484020 484034 485800 485805) (-323 "FAMONOID.spad" 483670 483680 483974 483979) (-322 "FAMONC.spad" 481892 481904 483660 483665) (-321 "FAGROUP.spad" 481498 481508 481788 481815) (-320 "FACUTIL.spad" 479694 479711 481488 481493) (-319 "FACTFUNC.spad" 478870 478880 479684 479689) (-318 "EXPUPXS.spad" 475703 475726 477002 477151) (-317 "EXPRTUBE.spad" 472931 472939 475693 475698) (-316 "EXPRODE.spad" 469803 469819 472921 472926) (-315 "EXPR.spad" 465078 465088 465792 466199) (-314 "EXPR2UPS.spad" 461170 461183 465068 465073) (-313 "EXPR2.spad" 460873 460885 461160 461165) (-312 "EXPEXPAN.spad" 457811 457836 458445 458538) (-311 "EXIT.spad" 457482 457490 457801 457806) (-310 "EXITAST.spad" 457218 457226 457472 457477) (-309 "EVALCYC.spad" 456676 456690 457208 457213) (-308 "EVALAB.spad" 456240 456250 456666 456671) (-307 "EVALAB.spad" 455802 455814 456230 456235) (-306 "EUCDOM.spad" 453344 453352 455728 455797) (-305 "EUCDOM.spad" 450948 450958 453334 453339) (-304 "ESTOOLS.spad" 442788 442796 450938 450943) (-303 "ESTOOLS2.spad" 442389 442403 442778 442783) (-302 "ESTOOLS1.spad" 442074 442085 442379 442384) (-301 "ES.spad" 434621 434629 442064 442069) (-300 "ES.spad" 427074 427084 434519 434524) (-299 "ESCONT.spad" 423847 423855 427064 427069) (-298 "ESCONT1.spad" 423596 423608 423837 423842) (-297 "ES2.spad" 423091 423107 423586 423591) (-296 "ES1.spad" 422657 422673 423081 423086) (-295 "ERROR.spad" 419978 419986 422647 422652) (-294 "EQTBL.spad" 418450 418472 418659 418686) (-293 "EQ.spad" 413324 413334 416123 416235) (-292 "EQ2.spad" 413040 413052 413314 413319) (-291 "EP.spad" 409354 409364 413030 413035) (-290 "ENV.spad" 408056 408064 409344 409349) (-289 "ENTIRER.spad" 407724 407732 408000 408051) (-288 "EMR.spad" 406925 406966 407650 407719) (-287 "ELTAGG.spad" 405165 405184 406915 406920) (-286 "ELTAGG.spad" 403369 403390 405121 405126) (-285 "ELTAB.spad" 402816 402834 403359 403364) (-284 "ELFUTS.spad" 402195 402214 402806 402811) (-283 "ELEMFUN.spad" 401884 401892 402185 402190) (-282 "ELEMFUN.spad" 401571 401581 401874 401879) (-281 "ELAGG.spad" 399514 399524 401551 401566) (-280 "ELAGG.spad" 397394 397406 399433 399438) (-279 "ELABEXPR.spad" 396325 396333 397384 397389) (-278 "EFUPXS.spad" 393101 393131 396281 396286) (-277 "EFULS.spad" 389937 389960 393057 393062) (-276 "EFSTRUC.spad" 387892 387908 389927 389932) (-275 "EF.spad" 382658 382674 387882 387887) (-274 "EAB.spad" 380934 380942 382648 382653) (-273 "E04UCFA.spad" 380470 380478 380924 380929) (-272 "E04NAFA.spad" 380047 380055 380460 380465) (-271 "E04MBFA.spad" 379627 379635 380037 380042) (-270 "E04JAFA.spad" 379163 379171 379617 379622) (-269 "E04GCFA.spad" 378699 378707 379153 379158) (-268 "E04FDFA.spad" 378235 378243 378689 378694) (-267 "E04DGFA.spad" 377771 377779 378225 378230) (-266 "E04AGNT.spad" 373613 373621 377761 377766) (-265 "DVARCAT.spad" 370298 370308 373603 373608) (-264 "DVARCAT.spad" 366981 366993 370288 370293) (-263 "DSMP.spad" 364412 364426 364717 364844) (-262 "DROPT.spad" 358357 358365 364402 364407) (-261 "DROPT1.spad" 358020 358030 358347 358352) (-260 "DROPT0.spad" 352847 352855 358010 358015) (-259 "DRAWPT.spad" 351002 351010 352837 352842) (-258 "DRAW.spad" 343602 343615 350992 350997) (-257 "DRAWHACK.spad" 342910 342920 343592 343597) (-256 "DRAWCX.spad" 340352 340360 342900 342905) (-255 "DRAWCURV.spad" 339889 339904 340342 340347) (-254 "DRAWCFUN.spad" 329061 329069 339879 339884) (-253 "DQAGG.spad" 327229 327239 329029 329056) (-252 "DPOLCAT.spad" 322570 322586 327097 327224) (-251 "DPOLCAT.spad" 317997 318015 322526 322531) (-250 "DPMO.spad" 310223 310239 310361 310662) (-249 "DPMM.spad" 302462 302480 302587 302888) (-248 "DOMCTOR.spad" 302354 302362 302452 302457) (-247 "DOMAIN.spad" 301485 301493 302344 302349) (-246 "DMP.spad" 298707 298722 299279 299406) (-245 "DLP.spad" 298055 298065 298697 298702) (-244 "DLIST.spad" 296634 296644 297238 297265) (-243 "DLAGG.spad" 295045 295055 296624 296629) (-242 "DIVRING.spad" 294587 294595 294989 295040) (-241 "DIVRING.spad" 294173 294183 294577 294582) (-240 "DISPLAY.spad" 292353 292361 294163 294168) (-239 "DIRPROD.spad" 281933 281949 282573 282704) (-238 "DIRPROD2.spad" 280741 280759 281923 281928) (-237 "DIRPCAT.spad" 279683 279699 280605 280736) (-236 "DIRPCAT.spad" 278354 278372 279278 279283) (-235 "DIOSP.spad" 277179 277187 278344 278349) (-234 "DIOPS.spad" 276163 276173 277159 277174) (-233 "DIOPS.spad" 275121 275133 276119 276124) (-232 "DIFRING.spad" 274413 274421 275101 275116) (-231 "DIFRING.spad" 273713 273723 274403 274408) (-230 "DIFEXT.spad" 272872 272882 273693 273708) (-229 "DIFEXT.spad" 271948 271960 272771 272776) (-228 "DIAGG.spad" 271578 271588 271928 271943) (-227 "DIAGG.spad" 271216 271228 271568 271573) (-226 "DHMATRIX.spad" 269520 269530 270673 270700) (-225 "DFSFUN.spad" 262928 262936 269510 269515) (-224 "DFLOAT.spad" 259649 259657 262818 262923) (-223 "DFINTTLS.spad" 257858 257874 259639 259644) (-222 "DERHAM.spad" 255768 255800 257838 257853) (-221 "DEQUEUE.spad" 255086 255096 255375 255402) (-220 "DEGRED.spad" 254701 254715 255076 255081) (-219 "DEFINTRF.spad" 252226 252236 254691 254696) (-218 "DEFINTEF.spad" 250722 250738 252216 252221) (-217 "DEFAST.spad" 250090 250098 250712 250717) (-216 "DECIMAL.spad" 248196 248204 248557 248650) (-215 "DDFACT.spad" 245995 246012 248186 248191) (-214 "DBLRESP.spad" 245593 245617 245985 245990) (-213 "DBASE.spad" 244247 244257 245583 245588) (-212 "DATAARY.spad" 243709 243722 244237 244242) (-211 "D03FAFA.spad" 243537 243545 243699 243704) (-210 "D03EEFA.spad" 243357 243365 243527 243532) (-209 "D03AGNT.spad" 242437 242445 243347 243352) (-208 "D02EJFA.spad" 241899 241907 242427 242432) (-207 "D02CJFA.spad" 241377 241385 241889 241894) (-206 "D02BHFA.spad" 240867 240875 241367 241372) (-205 "D02BBFA.spad" 240357 240365 240857 240862) (-204 "D02AGNT.spad" 235161 235169 240347 240352) (-203 "D01WGTS.spad" 233480 233488 235151 235156) (-202 "D01TRNS.spad" 233457 233465 233470 233475) (-201 "D01GBFA.spad" 232979 232987 233447 233452) (-200 "D01FCFA.spad" 232501 232509 232969 232974) (-199 "D01ASFA.spad" 231969 231977 232491 232496) (-198 "D01AQFA.spad" 231415 231423 231959 231964) (-197 "D01APFA.spad" 230839 230847 231405 231410) (-196 "D01ANFA.spad" 230333 230341 230829 230834) (-195 "D01AMFA.spad" 229843 229851 230323 230328) (-194 "D01ALFA.spad" 229383 229391 229833 229838) (-193 "D01AKFA.spad" 228909 228917 229373 229378) (-192 "D01AJFA.spad" 228432 228440 228899 228904) (-191 "D01AGNT.spad" 224491 224499 228422 228427) (-190 "CYCLOTOM.spad" 223997 224005 224481 224486) (-189 "CYCLES.spad" 220829 220837 223987 223992) (-188 "CVMP.spad" 220246 220256 220819 220824) (-187 "CTRIGMNP.spad" 218736 218752 220236 220241) (-186 "CTOR.spad" 218636 218644 218726 218731) (-185 "CTORKIND.spad" 218239 218247 218626 218631) (-184 "CTORCAT.spad" 217694 217702 218229 218234) (-183 "CTORCAT.spad" 217147 217157 217684 217689) (-182 "CTORCALL.spad" 216727 216735 217137 217142) (-181 "CSTTOOLS.spad" 215970 215983 216717 216722) (-180 "CRFP.spad" 209674 209687 215960 215965) (-179 "CRCEAST.spad" 209394 209402 209664 209669) (-178 "CRAPACK.spad" 208437 208447 209384 209389) (-177 "CPMATCH.spad" 207937 207952 208362 208367) (-176 "CPIMA.spad" 207642 207661 207927 207932) (-175 "COORDSYS.spad" 202535 202545 207632 207637) (-174 "CONTOUR.spad" 201937 201945 202525 202530) (-173 "CONTFRAC.spad" 197549 197559 201839 201932) (-172 "CONDUIT.spad" 197307 197315 197539 197544) (-171 "COMRING.spad" 196981 196989 197245 197302) (-170 "COMPPROP.spad" 196495 196503 196971 196976) (-169 "COMPLPAT.spad" 196262 196277 196485 196490) (-168 "COMPLEX.spad" 190298 190308 190542 190791) (-167 "COMPLEX2.spad" 190011 190023 190288 190293) (-166 "COMPFACT.spad" 189613 189627 190001 190006) (-165 "COMPCAT.spad" 187751 187761 189359 189608) (-164 "COMPCAT.spad" 185570 185582 187180 187185) (-163 "COMMUPC.spad" 185316 185334 185560 185565) (-162 "COMMONOP.spad" 184849 184857 185306 185311) (-161 "COMM.spad" 184658 184666 184839 184844) (-160 "COMMAAST.spad" 184421 184429 184648 184653) (-159 "COMBOPC.spad" 183326 183334 184411 184416) (-158 "COMBINAT.spad" 182071 182081 183316 183321) (-157 "COMBF.spad" 179439 179455 182061 182066) (-156 "COLOR.spad" 178276 178284 179429 179434) (-155 "COLONAST.spad" 177942 177950 178266 178271) (-154 "CMPLXRT.spad" 177651 177668 177932 177937) (-153 "CLLCTAST.spad" 177313 177321 177641 177646) (-152 "CLIP.spad" 173405 173413 177303 177308) (-151 "CLIF.spad" 172044 172060 173361 173400) (-150 "CLAGG.spad" 168529 168539 172034 172039) (-149 "CLAGG.spad" 164885 164897 168392 168397) (-148 "CINTSLPE.spad" 164210 164223 164875 164880) (-147 "CHVAR.spad" 162288 162310 164200 164205) (-146 "CHARZ.spad" 162203 162211 162268 162283) (-145 "CHARPOL.spad" 161711 161721 162193 162198) (-144 "CHARNZ.spad" 161464 161472 161691 161706) (-143 "CHAR.spad" 159332 159340 161454 161459) (-142 "CFCAT.spad" 158648 158656 159322 159327) (-141 "CDEN.spad" 157806 157820 158638 158643) (-140 "CCLASS.spad" 155955 155963 157217 157256) (-139 "CATEGORY.spad" 155045 155053 155945 155950) (-138 "CATCTOR.spad" 154936 154944 155035 155040) (-137 "CATAST.spad" 154563 154571 154926 154931) (-136 "CASEAST.spad" 154277 154285 154553 154558) (-135 "CARTEN.spad" 149380 149404 154267 154272) (-134 "CARTEN2.spad" 148766 148793 149370 149375) (-133 "CARD.spad" 146055 146063 148740 148761) (-132 "CAPSLAST.spad" 145829 145837 146045 146050) (-131 "CACHSET.spad" 145451 145459 145819 145824) (-130 "CABMON.spad" 145004 145012 145441 145446) (-129 "BYTE.spad" 144325 144333 144994 144999) (-128 "BYTEBUF.spad" 142157 142165 143494 143521) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2276369 2276374 2276379 2276384) (-2 NIL 2276349 2276354 2276359 2276364) (-1 NIL 2276329 2276334 2276339 2276344) (0 NIL 2276309 2276314 2276319 2276324) (-1274 "ZMOD.spad" 2276118 2276131 2276247 2276304) (-1273 "ZLINDEP.spad" 2275162 2275173 2276108 2276113) (-1272 "ZDSOLVE.spad" 2265011 2265033 2275152 2275157) (-1271 "YSTREAM.spad" 2264504 2264515 2265001 2265006) (-1270 "XRPOLY.spad" 2263724 2263744 2264360 2264429) (-1269 "XPR.spad" 2261515 2261528 2263442 2263541) (-1268 "XPOLY.spad" 2261070 2261081 2261371 2261440) (-1267 "XPOLYC.spad" 2260387 2260403 2260996 2261065) (-1266 "XPBWPOLY.spad" 2258824 2258844 2260167 2260236) (-1265 "XF.spad" 2257285 2257300 2258726 2258819) (-1264 "XF.spad" 2255726 2255743 2257169 2257174) (-1263 "XFALG.spad" 2252750 2252766 2255652 2255721) (-1262 "XEXPPKG.spad" 2252001 2252027 2252740 2252745) (-1261 "XDPOLY.spad" 2251615 2251631 2251857 2251926) (-1260 "XALG.spad" 2251275 2251286 2251571 2251610) (-1259 "WUTSET.spad" 2247114 2247131 2250921 2250948) (-1258 "WP.spad" 2246313 2246357 2246972 2247039) (-1257 "WHILEAST.spad" 2246111 2246120 2246303 2246308) (-1256 "WHEREAST.spad" 2245782 2245791 2246101 2246106) (-1255 "WFFINTBS.spad" 2243345 2243367 2245772 2245777) (-1254 "WEIER.spad" 2241559 2241570 2243335 2243340) (-1253 "VSPACE.spad" 2241232 2241243 2241527 2241554) (-1252 "VSPACE.spad" 2240925 2240938 2241222 2241227) (-1251 "VOID.spad" 2240602 2240611 2240915 2240920) (-1250 "VIEW.spad" 2238224 2238233 2240592 2240597) (-1249 "VIEWDEF.spad" 2233421 2233430 2238214 2238219) (-1248 "VIEW3D.spad" 2217256 2217265 2233411 2233416) (-1247 "VIEW2D.spad" 2204993 2205002 2217246 2217251) (-1246 "VECTOR.spad" 2203668 2203679 2203919 2203946) (-1245 "VECTOR2.spad" 2202295 2202308 2203658 2203663) (-1244 "VECTCAT.spad" 2200195 2200206 2202263 2202290) (-1243 "VECTCAT.spad" 2197903 2197916 2199973 2199978) (-1242 "VARIABLE.spad" 2197683 2197698 2197893 2197898) (-1241 "UTYPE.spad" 2197327 2197336 2197673 2197678) (-1240 "UTSODETL.spad" 2196620 2196644 2197283 2197288) (-1239 "UTSODE.spad" 2194808 2194828 2196610 2196615) (-1238 "UTS.spad" 2189597 2189625 2193275 2193372) (-1237 "UTSCAT.spad" 2187048 2187064 2189495 2189592) (-1236 "UTSCAT.spad" 2184143 2184161 2186592 2186597) (-1235 "UTS2.spad" 2183736 2183771 2184133 2184138) (-1234 "URAGG.spad" 2178368 2178379 2183726 2183731) (-1233 "URAGG.spad" 2172964 2172977 2178324 2178329) (-1232 "UPXSSING.spad" 2170607 2170633 2172045 2172178) (-1231 "UPXS.spad" 2167755 2167783 2168739 2168888) (-1230 "UPXSCONS.spad" 2165512 2165532 2165887 2166036) (-1229 "UPXSCCA.spad" 2164077 2164097 2165358 2165507) (-1228 "UPXSCCA.spad" 2162784 2162806 2164067 2164072) (-1227 "UPXSCAT.spad" 2161365 2161381 2162630 2162779) (-1226 "UPXS2.spad" 2160906 2160959 2161355 2161360) (-1225 "UPSQFREE.spad" 2159318 2159332 2160896 2160901) (-1224 "UPSCAT.spad" 2156911 2156935 2159216 2159313) (-1223 "UPSCAT.spad" 2154210 2154236 2156517 2156522) (-1222 "UPOLYC.spad" 2149188 2149199 2154052 2154205) (-1221 "UPOLYC.spad" 2144058 2144071 2148924 2148929) (-1220 "UPOLYC2.spad" 2143527 2143546 2144048 2144053) (-1219 "UP.spad" 2140684 2140699 2141077 2141230) (-1218 "UPMP.spad" 2139574 2139587 2140674 2140679) (-1217 "UPDIVP.spad" 2139137 2139151 2139564 2139569) (-1216 "UPDECOMP.spad" 2137374 2137388 2139127 2139132) (-1215 "UPCDEN.spad" 2136581 2136597 2137364 2137369) (-1214 "UP2.spad" 2135943 2135964 2136571 2136576) (-1213 "UNISEG.spad" 2135296 2135307 2135862 2135867) (-1212 "UNISEG2.spad" 2134789 2134802 2135252 2135257) (-1211 "UNIFACT.spad" 2133890 2133902 2134779 2134784) (-1210 "ULS.spad" 2124442 2124470 2125535 2125964) (-1209 "ULSCONS.spad" 2116836 2116856 2117208 2117357) (-1208 "ULSCCAT.spad" 2114565 2114585 2116682 2116831) (-1207 "ULSCCAT.spad" 2112402 2112424 2114521 2114526) (-1206 "ULSCAT.spad" 2110618 2110634 2112248 2112397) (-1205 "ULS2.spad" 2110130 2110183 2110608 2110613) (-1204 "UFD.spad" 2109195 2109204 2110056 2110125) (-1203 "UFD.spad" 2108322 2108333 2109185 2109190) (-1202 "UDVO.spad" 2107169 2107178 2108312 2108317) (-1201 "UDPO.spad" 2104596 2104607 2107125 2107130) (-1200 "TYPE.spad" 2104528 2104537 2104586 2104591) (-1199 "TYPEAST.spad" 2104447 2104456 2104518 2104523) (-1198 "TWOFACT.spad" 2103097 2103112 2104437 2104442) (-1197 "TUPLE.spad" 2102581 2102592 2102996 2103001) (-1196 "TUBETOOL.spad" 2099418 2099427 2102571 2102576) (-1195 "TUBE.spad" 2098059 2098076 2099408 2099413) (-1194 "TS.spad" 2096648 2096664 2097624 2097721) (-1193 "TSETCAT.spad" 2083775 2083792 2096616 2096643) (-1192 "TSETCAT.spad" 2070888 2070907 2083731 2083736) (-1191 "TRMANIP.spad" 2065254 2065271 2070594 2070599) (-1190 "TRIMAT.spad" 2064213 2064238 2065244 2065249) (-1189 "TRIGMNIP.spad" 2062730 2062747 2064203 2064208) (-1188 "TRIGCAT.spad" 2062242 2062251 2062720 2062725) (-1187 "TRIGCAT.spad" 2061752 2061763 2062232 2062237) (-1186 "TREE.spad" 2060323 2060334 2061359 2061386) (-1185 "TRANFUN.spad" 2060154 2060163 2060313 2060318) (-1184 "TRANFUN.spad" 2059983 2059994 2060144 2060149) (-1183 "TOPSP.spad" 2059657 2059666 2059973 2059978) (-1182 "TOOLSIGN.spad" 2059320 2059331 2059647 2059652) (-1181 "TEXTFILE.spad" 2057877 2057886 2059310 2059315) (-1180 "TEX.spad" 2055009 2055018 2057867 2057872) (-1179 "TEX1.spad" 2054565 2054576 2054999 2055004) (-1178 "TEMUTL.spad" 2054120 2054129 2054555 2054560) (-1177 "TBCMPPK.spad" 2052213 2052236 2054110 2054115) (-1176 "TBAGG.spad" 2051249 2051272 2052193 2052208) (-1175 "TBAGG.spad" 2050293 2050318 2051239 2051244) (-1174 "TANEXP.spad" 2049669 2049680 2050283 2050288) (-1173 "TABLE.spad" 2048080 2048103 2048350 2048377) (-1172 "TABLEAU.spad" 2047561 2047572 2048070 2048075) (-1171 "TABLBUMP.spad" 2044344 2044355 2047551 2047556) (-1170 "SYSTEM.spad" 2043618 2043627 2044334 2044339) (-1169 "SYSSOLP.spad" 2041091 2041102 2043608 2043613) (-1168 "SYNTAX.spad" 2037361 2037370 2041081 2041086) (-1167 "SYMTAB.spad" 2035417 2035426 2037351 2037356) (-1166 "SYMS.spad" 2031402 2031411 2035407 2035412) (-1165 "SYMPOLY.spad" 2030409 2030420 2030491 2030618) (-1164 "SYMFUNC.spad" 2029884 2029895 2030399 2030404) (-1163 "SYMBOL.spad" 2027311 2027320 2029874 2029879) (-1162 "SWITCH.spad" 2024068 2024077 2027301 2027306) (-1161 "SUTS.spad" 2020967 2020995 2022535 2022632) (-1160 "SUPXS.spad" 2018102 2018130 2019099 2019248) (-1159 "SUP.spad" 2014871 2014882 2015652 2015805) (-1158 "SUPFRACF.spad" 2013976 2013994 2014861 2014866) (-1157 "SUP2.spad" 2013366 2013379 2013966 2013971) (-1156 "SUMRF.spad" 2012332 2012343 2013356 2013361) (-1155 "SUMFS.spad" 2011965 2011982 2012322 2012327) (-1154 "SULS.spad" 2002504 2002532 2003610 2004039) (-1153 "SUCHTAST.spad" 2002273 2002282 2002494 2002499) (-1152 "SUCH.spad" 2001953 2001968 2002263 2002268) (-1151 "SUBSPACE.spad" 1993960 1993975 2001943 2001948) (-1150 "SUBRESP.spad" 1993120 1993134 1993916 1993921) (-1149 "STTF.spad" 1989219 1989235 1993110 1993115) (-1148 "STTFNC.spad" 1985687 1985703 1989209 1989214) (-1147 "STTAYLOR.spad" 1978085 1978096 1985568 1985573) (-1146 "STRTBL.spad" 1976590 1976607 1976739 1976766) (-1145 "STRING.spad" 1975999 1976008 1976013 1976040) (-1144 "STRICAT.spad" 1975787 1975796 1975967 1975994) (-1143 "STREAM.spad" 1972645 1972656 1975312 1975327) (-1142 "STREAM3.spad" 1972190 1972205 1972635 1972640) (-1141 "STREAM2.spad" 1971258 1971271 1972180 1972185) (-1140 "STREAM1.spad" 1970962 1970973 1971248 1971253) (-1139 "STINPROD.spad" 1969868 1969884 1970952 1970957) (-1138 "STEP.spad" 1969069 1969078 1969858 1969863) (-1137 "STBL.spad" 1967595 1967623 1967762 1967777) (-1136 "STAGG.spad" 1966670 1966681 1967585 1967590) (-1135 "STAGG.spad" 1965743 1965756 1966660 1966665) (-1134 "STACK.spad" 1965094 1965105 1965350 1965377) (-1133 "SREGSET.spad" 1962798 1962815 1964740 1964767) (-1132 "SRDCMPK.spad" 1961343 1961363 1962788 1962793) (-1131 "SRAGG.spad" 1956440 1956449 1961311 1961338) (-1130 "SRAGG.spad" 1951557 1951568 1956430 1956435) (-1129 "SQMATRIX.spad" 1949173 1949191 1950089 1950176) (-1128 "SPLTREE.spad" 1943725 1943738 1948609 1948636) (-1127 "SPLNODE.spad" 1940313 1940326 1943715 1943720) (-1126 "SPFCAT.spad" 1939090 1939099 1940303 1940308) (-1125 "SPECOUT.spad" 1937640 1937649 1939080 1939085) (-1124 "SPADXPT.spad" 1929779 1929788 1937630 1937635) (-1123 "spad-parser.spad" 1929244 1929253 1929769 1929774) (-1122 "SPADAST.spad" 1928945 1928954 1929234 1929239) (-1121 "SPACEC.spad" 1912958 1912969 1928935 1928940) (-1120 "SPACE3.spad" 1912734 1912745 1912948 1912953) (-1119 "SORTPAK.spad" 1912279 1912292 1912690 1912695) (-1118 "SOLVETRA.spad" 1910036 1910047 1912269 1912274) (-1117 "SOLVESER.spad" 1908556 1908567 1910026 1910031) (-1116 "SOLVERAD.spad" 1904566 1904577 1908546 1908551) (-1115 "SOLVEFOR.spad" 1902986 1903004 1904556 1904561) (-1114 "SNTSCAT.spad" 1902586 1902603 1902954 1902981) (-1113 "SMTS.spad" 1900846 1900872 1902151 1902248) (-1112 "SMP.spad" 1898285 1898305 1898675 1898802) (-1111 "SMITH.spad" 1897128 1897153 1898275 1898280) (-1110 "SMATCAT.spad" 1895238 1895268 1897072 1897123) (-1109 "SMATCAT.spad" 1893280 1893312 1895116 1895121) (-1108 "SKAGG.spad" 1892241 1892252 1893248 1893275) (-1107 "SINT.spad" 1891067 1891076 1892107 1892236) (-1106 "SIMPAN.spad" 1890795 1890804 1891057 1891062) (-1105 "SIG.spad" 1890123 1890132 1890785 1890790) (-1104 "SIGNRF.spad" 1889231 1889242 1890113 1890118) (-1103 "SIGNEF.spad" 1888500 1888517 1889221 1889226) (-1102 "SIGAST.spad" 1887881 1887890 1888490 1888495) (-1101 "SHP.spad" 1885799 1885814 1887837 1887842) (-1100 "SHDP.spad" 1875510 1875537 1876019 1876150) (-1099 "SGROUP.spad" 1875118 1875127 1875500 1875505) (-1098 "SGROUP.spad" 1874724 1874735 1875108 1875113) (-1097 "SGCF.spad" 1867605 1867614 1874714 1874719) (-1096 "SFRTCAT.spad" 1866533 1866550 1867573 1867600) (-1095 "SFRGCD.spad" 1865596 1865616 1866523 1866528) (-1094 "SFQCMPK.spad" 1860233 1860253 1865586 1865591) (-1093 "SFORT.spad" 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(-1074 "SDPOL.spad" 1837824 1837835 1838115 1838242) (-1073 "SCPKG.spad" 1835903 1835914 1837814 1837819) (-1072 "SCOPE.spad" 1835048 1835057 1835893 1835898) (-1071 "SCACHE.spad" 1833730 1833741 1835038 1835043) (-1070 "SASTCAT.spad" 1833639 1833648 1833720 1833725) (-1069 "SAOS.spad" 1833511 1833520 1833629 1833634) (-1068 "SAERFFC.spad" 1833224 1833244 1833501 1833506) (-1067 "SAE.spad" 1831399 1831415 1832010 1832145) (-1066 "SAEFACT.spad" 1831100 1831120 1831389 1831394) (-1065 "RURPK.spad" 1828741 1828757 1831090 1831095) (-1064 "RULESET.spad" 1828182 1828206 1828731 1828736) (-1063 "RULE.spad" 1826386 1826410 1828172 1828177) (-1062 "RULECOLD.spad" 1826238 1826251 1826376 1826381) (-1061 "RSTRCAST.spad" 1825955 1825964 1826228 1826233) (-1060 "RSETGCD.spad" 1822333 1822353 1825945 1825950) (-1059 "RSETCAT.spad" 1812117 1812134 1822301 1822328) (-1058 "RSETCAT.spad" 1801921 1801940 1812107 1812112) (-1057 "RSDCMPK.spad" 1800373 1800393 1801911 1801916) (-1056 "RRCC.spad" 1798757 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"RIDIST.spad" 1734219 1734228 1734825 1734830) (-1036 "RGCHAIN.spad" 1732798 1732814 1733704 1733731) (-1035 "RGBCSPC.spad" 1732579 1732591 1732788 1732793) (-1034 "RGBCMDL.spad" 1732109 1732121 1732569 1732574) (-1033 "RF.spad" 1729723 1729734 1732099 1732104) (-1032 "RFFACTOR.spad" 1729185 1729196 1729713 1729718) (-1031 "RFFACT.spad" 1728920 1728932 1729175 1729180) (-1030 "RFDIST.spad" 1727908 1727917 1728910 1728915) (-1029 "RETSOL.spad" 1727325 1727338 1727898 1727903) (-1028 "RETRACT.spad" 1726753 1726764 1727315 1727320) (-1027 "RETRACT.spad" 1726179 1726192 1726743 1726748) (-1026 "RETAST.spad" 1725991 1726000 1726169 1726174) (-1025 "RESULT.spad" 1724051 1724060 1724638 1724665) (-1024 "RESRING.spad" 1723398 1723445 1723989 1724046) (-1023 "RESLATC.spad" 1722722 1722733 1723388 1723393) (-1022 "REPSQ.spad" 1722451 1722462 1722712 1722717) (-1021 "REP.spad" 1720003 1720012 1722441 1722446) (-1020 "REPDB.spad" 1719708 1719719 1719993 1719998) (-1019 "REP2.spad" 1709280 1709291 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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 5ee57dc2..eae8086c 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(161873 . 3439752261) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) #0#) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) -((((-558)) . T) (($) -3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-1028 (-406 (-558))))) ((|#1|) . T)) +(161890 . 3440274389) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) #0#) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) +((((-558)) . 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T)) @@ -797,7 +797,7 @@ ((((-635 |#1|)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#2|) |has| |#2| (-308 |#2|))) (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -807,7 +807,7 @@ (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) ((($) . T) (((-558)) . T) (((-406 (-558))) . T)) (|has| |#2| (-367)) -(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) @@ -821,8 +821,8 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -((($) . T) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-112)) . T)) @@ -846,26 +846,26 @@ ((((-853)) . T)) ((((-1168)) . T)) (|has| |#1| (-811)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#1| (-841)) -(-3986 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-171)) (|has| |#1| (-550))) (|has| |#1| (-550)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((|#1|) . T) (((-558)) . T)) (|has| |#1| (-899)) (((|#1|) . T)) (|has| |#1| (-1087)) ((((-853)) . 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T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#) ((|#2|) . T) (((-558)) . T)) (((|#1| |#2| |#3|) . T)) -(-3986 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) +(-3996 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) (|has| $ (-146)) (|has| $ (-146)) ((((-1168)) . T)) @@ -938,14 +938,14 @@ ((((-853)) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) ((($ $) |has| |#1| (-285 $ $)) ((|#1| $) |has| |#1| (-285 |#1| |#1|))) (((|#1| (-406 (-558))) . T)) (((|#1|) . T)) ((((-1163)) . T)) (|has| |#1| (-550)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-550)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) @@ -956,7 +956,7 @@ (|has| |#1| (-146)) (|has| |#1| (-144)) (|has| |#4| (-839)) -(((|#2| (-239 (-1427 |#1|) (-762)) (-855 |#1|)) . T)) +(((|#2| (-239 (-1450 |#1|) (-762)) (-855 |#1|)) . T)) (|has| |#3| (-839)) (((|#1| (-529 |#3|) |#3|) . T)) (|has| |#1| (-146)) @@ -970,20 +970,20 @@ (|has| |#1| (-144)) ((((-406 (-558))) |has| |#2| (-362)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3986 (|has| |#1| (-348)) (|has| |#1| (-367))) +(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3996 (|has| |#1| (-348)) (|has| |#1| (-367))) ((((-1129 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-171)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-232)) (|has| |#2| (-1039))) -(((|#2|) . T) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) -(-3986 (|has| |#3| (-784)) (|has| |#3| (-839))) -(-3986 (|has| |#3| (-784)) (|has| |#3| (-839))) +(((|#2|) . T) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +(-3996 (|has| |#3| (-784)) (|has| |#3| (-839))) +(-3996 (|has| |#3| (-784)) (|has| |#3| (-839))) ((((-853)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-689)) . T)) -(-3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (|has| |#1| (-550)) (((|#1|) . T)) (((|#1|) . T)) @@ -1007,11 +1007,11 @@ (((|#1| (-406 (-558))) . T)) (((|#3|) . T) (((-604 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) -((((-558)) -3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-1039))) ((|#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-1087))) (((-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-558)) -3996 (|has| |#2| (-171)) (|has| |#2| (-839)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-1039))) ((|#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-1087))) (((-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1019,8 +1019,8 @@ ((((-853)) . T)) ((((-853)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) |has| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (-308 (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) |has| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (-308 (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))))) ((((-853)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1031,10 +1031,10 @@ ((($ $) . T) ((#0=(-855 |#1|) $) . T) ((#0# |#2|) . 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T)) -((($) -3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) -3996 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((((-558) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -1080,39 +1080,39 @@ (-12 (|has| |#1| (-367)) (|has| |#2| (-367))) ((((-853)) . T)) ((((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-308 |#1|))) @@ -1122,11 +1122,11 @@ (|has| |#1| (-367)) ((((-1163) $) |has| |#1| (-512 (-1163) $)) (($ $) |has| |#1| (-308 $)) ((|#1| |#1|) |has| |#1| (-308 |#1|)) (((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|))) ((((-1163)) |has| |#1| (-890 (-1163)))) -(-3986 (-12 (|has| |#1| (-232)) (|has| |#1| (-362))) (|has| |#1| (-348))) +(-3996 (-12 (|has| |#1| (-232)) (|has| |#1| (-362))) (|has| |#1| (-348))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-387) |#1|) . T)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-1087)) (((|#2|) . T) (((-853)) . T)) ((((-853)) . T)) @@ -1134,8 +1134,8 @@ ((((-900 |#1|)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-1168)) . T)) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) -((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) -3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) -3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1144,16 +1144,16 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) (((|#1| |#1|) . T)) (((#0=(-860 |#1|)) |has| #0# (-308 #0#))) -((((-558)) . 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T)) (|has| |#1| (-1185)) (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) ((((-406 (-558))) . T) (($) . T)) @@ -1164,8 +1164,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-406 (-558)) #0#) . T)) (|has| |#1| (-362)) ((((-558)) . T) (((-406 (-558))) . T) (($) . T)) -((($ $) . T) ((#0=(-406 (-558)) #0#) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((($ $) . T) ((#0=(-406 (-558)) #0#) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1|) . T) (($) . T) (((-406 (-558))) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -1180,14 +1180,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-839)) (|has| |#1| (-839)) -((($) . T) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) -(-3986 (|has| |#1| (-171)) (|has| |#1| (-550))) +((($) . T) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +(-3996 (|has| |#1| (-171)) (|has| |#1| (-550))) ((($) . T)) -(((#0=(-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) #0#) |has| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))))) +(((#0=(-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) #0#) |has| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))))) (|has| |#2| (-841)) ((($) . T)) (((|#2|) |has| |#2| (-1087))) -((((-853)) -3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) +((((-853)) -3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) (|has| |#1| (-841)) (|has| |#1| (-841)) ((((-1145) (-52)) . T)) @@ -1196,10 +1196,10 @@ ((((-558)) |has| #0=(-406 |#2|) (-631 (-558))) ((#0#) . T)) ((($) . T) (((-558)) . T)) ((((-558) (-143)) . T)) -((((-558) (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T) ((|#1| |#2|) . T)) +((((-558) (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T) ((|#1| |#2|) . T)) ((((-406 (-558))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-853)) . T)) ((((-900 |#1|)) . T)) (|has| |#1| (-362)) @@ -1226,21 +1226,21 @@ ((((-853)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-558) (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T) ((|#1| |#2|) . 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T)) @@ -1248,39 +1248,39 @@ (|has| |#1| (-550)) ((((-1145) |#1|) . T)) (|has| |#1| (-1138)) -(-3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-948 |#1|)) . T)) -(((#0=(-406 (-558)) #0#) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($ $) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) ((|#1| |#1|) . T)) +(((#0=(-406 (-558)) #0#) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($ $) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) ((|#1| |#1|) . T)) ((((-406 (-558))) |has| |#1| (-1028 (-558))) (((-558)) |has| |#1| (-1028 (-558))) (((-1163)) |has| |#1| (-1028 (-1163))) ((|#1|) . T)) ((((-558) |#2|) . T)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) |has| |#1| (-1028 (-558))) ((|#1|) . 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T)) +((((-853)) -3996 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-605 (-853))) (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-367)) (|has| |#3| (-717)) (|has| |#3| (-784)) (|has| |#3| (-839)) (|has| |#3| (-1039)) (|has| |#3| (-1087))) (((-1246 |#3|)) . T)) ((((-558) |#2|) . T)) -(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) -(((|#2| |#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($ $) |has| |#2| (-171))) +(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(((|#2| |#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($ $) |has| |#2| (-171))) (((|#2|) . T) (((-558)) . T)) ((((-853)) . T)) ((((-853)) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T) ((|#2|) . T)) ((((-853)) . T)) ((((-853)) . T)) ((((-1145) (-1163) (-558) (-224) (-853)) . T)) @@ -1315,8 +1315,8 @@ (|has| |#1| (-38 (-406 (-558)))) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -(((|#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($) |has| |#2| (-171))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +(((|#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($) |has| |#2| (-171))) (|has| $ (-146)) ((((-406 |#2|)) . T)) ((((-883 |#1|)) . T) ((|#2|) . T) (((-558)) . T) (((-810 |#1|)) . T)) @@ -1328,11 +1328,11 @@ (((|#3|) |has| |#3| (-171))) (|has| |#1| (-146)) (|has| |#1| (-144)) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) (((|#1|) . T)) (|has| |#2| (-232)) @@ -1369,7 +1369,7 @@ ((((-989 |#1|)) . T) ((|#1|) . T)) ((((-853)) . T)) ((((-853)) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-406 (-558))) . T) (((-406 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1159 |#1|)) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1377,9 +1377,9 @@ (|has| |#1| (-841)) (((|#2|) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) -((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) +((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) ((((-558) |#2|) . T)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#2|) . T)) ((((-558) |#3|) . T)) (((|#2|) . T)) @@ -1394,7 +1394,7 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (((|#2|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) #0#) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) #0#) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) (((|#2| |#2|) . T)) (((|#1|) . T)) (|has| |#2| (-362)) @@ -1427,19 +1427,19 @@ (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1| |#2|) . T)) ((((-558) (-143)) . T)) -(((#0=(-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) #0#) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) -((($) -3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +(((#0=(-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) #0#) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) +((($) -3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (|has| |#1| (-841)) (((|#2| (-762) (-1069)) . T)) (((|#1| |#2|) . T)) -(-3986 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-171)) (|has| |#1| (-550))) (|has| |#1| (-782)) (((|#1|) |has| |#1| (-171))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3986 (|has| |#1| (-146)) (-12 (|has| |#1| (-362)) (|has| |#2| (-146)))) -(-3986 (|has| |#1| (-144)) (-12 (|has| |#1| (-362)) (|has| |#2| (-144)))) +(-3996 (|has| |#1| (-146)) (-12 (|has| |#1| (-362)) (|has| |#2| (-146)))) +(-3996 (|has| |#1| (-144)) (-12 (|has| |#1| (-362)) (|has| |#2| (-144)))) (((|#4|) . T)) (|has| |#1| (-144)) ((((-1145) |#1|) . T)) @@ -1453,10 +1453,10 @@ (((|#3|) . T)) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-853)) . T)) -(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#1|) . T)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087))) (((-948 |#1|)) . T)) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087))) (((-948 |#1|)) . 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T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) @@ -1479,7 +1479,7 @@ (|has| |#2| (-144)) (|has| |#2| (-146)) (|has| |#1| (-471)) -(-3986 (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +(-3996 (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) (|has| |#1| (-362)) ((((-853)) . T)) (|has| |#1| (-38 (-406 (-558)))) @@ -1490,8 +1490,8 @@ (|has| |#1| (-839)) ((((-853)) . T)) (((|#2|) . T)) -((((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-1238 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) -(((|#1|) |has| |#1| (-171)) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550)))) +((((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-1238 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) +(((|#1|) |has| |#1| (-171)) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550)))) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#2|) . T) (((-558)) . T) (((-810 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1500,7 +1500,7 @@ ((((-853)) . T)) ((((-853)) . T)) (|has| |#1| (-1087)) -(((|#2| (-480 (-1427 |#1|) (-762)) (-855 |#1|)) . T)) +(((|#2| (-480 (-1450 |#1|) (-762)) (-855 |#1|)) . T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#)) (((|#1| (-529 (-1163)) (-1163)) . T)) (((|#1|) . T)) @@ -1520,16 +1520,16 @@ (|has| |#1| (-146)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) -((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-1163) (-52)) . T)) ((($ $) . T)) (((|#1| (-558)) . T)) ((((-900 |#1|)) . T)) -(((|#1|) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039))) (($) -3986 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) +(((|#1|) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039))) (($) -3996 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) (((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) (|has| |#1| (-841)) (|has| |#1| (-841)) @@ -1547,11 +1547,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) (|has| |#2| (-841)) (|has| |#1| (-841)) -(((|#3|) -3986 (|has| |#3| (-171)) (|has| |#3| (-362)))) -(-3986 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-899))) +(((|#3|) -3996 (|has| |#3| (-171)) (|has| |#3| (-362)))) +(-3996 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-899))) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) ((((-558) |#2|) . T)) -(((|#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)))) +(((|#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-362)))) (|has| |#1| (-348)) (((|#3| |#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1087)))) (((|#2|) . T) (((-558)) . T)) @@ -1560,7 +1560,7 @@ (|has| |#1| (-811)) (|has| |#1| (-811)) (((|#1|) . T)) -(-3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-839)) (|has| |#1| (-839)) (|has| |#1| (-839)) @@ -1569,13 +1569,13 @@ ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-558)))) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-1163)) |has| |#1| (-890 (-1163))) (((-1069)) . T)) (((|#1|) . T)) (|has| |#1| (-839)) -(((#0=(-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) #0#) |has| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))))) +(((#0=(-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) #0#) |has| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (|has| |#1| (-1087)) ((((-853)) . T) (((-1168)) . T)) @@ -1590,15 +1590,15 @@ (((|#1|) . T)) (((|#1| (-529 |#2|) |#2|) . T)) ((((-853)) . T)) -((((-143)) . T) (((-762)) . T) (((-853)) . T)) +((((-143)) . T) (((-853)) . T)) (((|#1| (-762) (-1069)) . T)) (((|#3|) . T)) ((((-143)) . T)) -((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3986 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) +((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3996 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) (((|#1|) . T)) ((((-143)) . T)) (((|#2|) |has| |#2| (-171))) -(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((|#1|) . T)) (|has| |#1| (-144)) (|has| |#1| (-146)) @@ -1621,32 +1621,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) (|has| |#1| (-1185)) (|has| |#1| (-1185)) -(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (|has| |#1| (-1185)) (|has| |#1| (-1185)) (((|#3| |#3|) . T)) @@ -1681,16 +1681,16 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((((-1145) (-52)) . T)) (|has| |#1| (-1087)) -(-3986 (|has| |#2| (-811)) (|has| |#2| (-841))) +(-3996 (|has| |#2| (-811)) (|has| |#2| (-841))) (((|#1|) . T)) (((|#1|) |has| |#1| (-171)) (($) . T)) -((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((($) . T)) ((((-1161 |#1| |#2| |#3|)) -12 (|has| (-1161 |#1| |#2| |#3|) (-308 (-1161 |#1| |#2| |#3|))) (|has| |#1| (-362)))) ((((-853)) . T)) ((((-558)) . T) (($) . T)) ((((-762)) . T)) -(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-853)) . T)) ((($) . T) (((-558)) . T)) @@ -1698,29 +1698,29 @@ (|has| |#2| (-899)) (|has| |#1| (-362)) (((|#2|) |has| |#2| (-1087))) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((((-534)) . T) (((-406 (-1159 (-558)))) . T) (((-224)) . T) (((-378)) . T)) ((((-378)) . T) (((-224)) . T) (((-853)) . T)) (|has| |#1| (-899)) (|has| |#1| (-899)) (|has| |#1| (-899)) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-899))) ((($) . T) ((|#2|) . T)) -(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) ((($ $) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((($ $) . T)) ((((-558) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-558)) . T)) ((((-112)) . T)) -(-3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-38 (-406 (-558)))) (((|#1| (-558)) . T)) ((($) . T)) @@ -1742,7 +1742,7 @@ (((|#1| (-1210 |#1| |#2| |#3|)) . T)) (((|#1| (-762)) . T)) (((|#1|) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-853)) . T)) (|has| |#1| (-1087)) ((((-1145) |#1|) . T)) @@ -1762,18 +1762,18 @@ (((|#1|) . T)) ((((-558)) . T)) ((((-853)) . T)) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-348))) (|has| |#1| (-146)) ((((-853)) . T)) (((|#3|) . T)) -(-3986 (|has| |#3| (-171)) (|has| |#3| (-839)) (|has| |#3| (-1039))) +(-3996 (|has| |#3| (-171)) (|has| |#3| (-839)) (|has| |#3| (-1039))) ((((-853)) . T)) ((((-1231 |#2| |#3| |#4|)) . T) (((-1232 |#1| |#2| |#3| |#4|)) . T)) ((((-853)) . T)) -((((-48)) -12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (((-604 $)) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) -3986 (-12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) +((((-48)) -12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (((-604 $)) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) -3996 (-12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-762)) . T)) -((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) +((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) (((|#1|) |has| |#1| (-308 |#1|))) ((((-1232 |#1| |#2| |#3| |#4|)) . T)) ((((-558)) |has| |#1| (-876 (-558))) (((-378)) |has| |#1| (-876 (-378)))) @@ -1781,7 +1781,7 @@ (|has| |#1| (-550)) (((|#1|) . T)) ((((-853)) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) (((|#1|) |has| |#1| (-171))) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) @@ -1789,7 +1789,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1087))) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) -(((|#2|) -3986 (|has| |#2| (-171)) (|has| |#2| (-362)))) +(((|#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-362)))) ((((-1231 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-811)) @@ -1799,8 +1799,8 @@ (|has| |#1| (-839)) (|has| |#1| (-839)) (((|#1| (-558) (-1069)) . T)) -(-3986 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +(-3996 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) (((|#1| (-406 (-558)) (-1069)) . T)) (((|#1| (-762) (-1069)) . T)) (|has| |#1| (-841)) @@ -1813,33 +1813,33 @@ (|has| |#1| (-1087)) ((((-900 |#1|)) . T) (($) . T) (((-406 (-558))) . T)) (|has| |#1| (-1087)) -((((-558)) -3986 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) +((((-558)) -3996 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) (((|#1|) . T)) (|has| |#1| (-1087)) ((((-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-631 (-558)))) ((|#2|) |has| |#1| (-362))) -(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) -((((-679 (-338 (-2551) (-2551 (QUOTE X) (QUOTE HESS)) (-689)))) . T)) +(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +((((-679 (-338 (-3870) (-3870 (QUOTE X) (QUOTE HESS)) (-689)))) . T)) (((|#2|) |has| |#2| (-171))) (((|#1|) |has| |#1| (-171))) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) -((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) ((((-853)) . T)) (|has| |#3| (-839)) ((((-853)) . T)) ((((-1231 |#2| |#3| |#4|) (-318 |#2| |#3| |#4|)) . T)) ((((-853)) . T)) -(((|#1| |#1|) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) +(((|#1| |#1|) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) (((|#1|) . T)) ((((-558)) . T)) ((((-558)) . T)) -(((|#1|) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) +(((|#1|) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) (((|#2|) |has| |#2| (-362))) ((($) . T) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-362))) (|has| |#1| (-841)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) |has| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))))) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-899))) +((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) |has| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-899))) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) ((((-853)) . T)) ((((-853)) . T)) @@ -1870,25 +1870,25 @@ (|has| |#1| (-144)) ((((-558)) . T) ((|#1|) . T) (($) . T) (((-406 (-558))) . T) (((-1163)) |has| |#1| (-1028 (-1163)))) (((|#1| |#2|) . T)) -((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3986 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) +((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3996 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) ((((-143)) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (((|#1|) . T)) -(-3986 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-558)) . T)) ((((-853)) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| (-406 |#2|) (-232)) ((((-635 |#1|)) . T)) (|has| |#1| (-899)) (((|#2|) |has| |#2| (-1039))) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) (|has| |#1| (-362)) (((|#1|) |has| |#1| (-171))) (((|#1| |#1|) . T)) @@ -1915,7 +1915,7 @@ (((|#1| (-406 (-558)) (-1069)) . T)) (((|#1| (-762) (-1069)) . T)) (((#0=(-406 |#2|) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-558)) -3986 (|has| (-406 (-558)) (-1028 (-558))) (|has| |#1| (-1028 (-558)))) (((-406 (-558))) . T)) +(((|#1|) . T) (((-558)) -3996 (|has| (-406 (-558)) (-1028 (-558))) (|has| |#1| (-1028 (-558)))) (((-406 (-558))) . T)) (((|#1| (-594 |#1| |#3|) (-594 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) @@ -1936,25 +1936,26 @@ (((|#2|) |has| |#2| (-171))) (|has| |#2| (-839)) ((((-558)) . T) ((|#2|) . T) (((-406 (-558))) |has| |#2| (-1028 (-406 (-558))))) -((((-112)) |has| |#1| (-1087)) (((-853)) -3986 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087)))) +((((-112)) |has| |#1| (-1087)) (((-853)) -3996 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))) . T)) +((((-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))) . T)) ((((-853)) . T)) ((((-558) |#1|) . T)) ((((-853)) . T)) ((((-689)) . T) (((-406 (-558))) . T) (((-558)) . T)) (((|#1| |#1|) |has| |#1| (-171))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) ((((-378)) . T)) ((((-689)) . T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#)) (((|#1|) |has| |#1| (-171))) ((((-406 (-942 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-841)) (|has| |#2| (-899)) @@ -1964,14 +1965,14 @@ (((|#3|) |has| |#3| (-1039))) ((((-1163)) |has| |#2| (-890 (-1163)))) ((((-853)) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-406 (-558))) . T) (($) . T)) (|has| |#1| (-471)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-362)) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) (|has| |#1| (-38 (-406 (-558)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -1992,11 +1993,11 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-841)) -((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) +((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) |has| (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)) (-308 (-2 (|:| -2045 |#1|) (|:| -2957 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2014,11 +2015,11 @@ ((((-534)) |has| |#1| (-606 (-534))) (((-882 (-558))) |has| |#1| (-606 (-882 (-558)))) (((-882 (-378))) |has| |#1| (-606 (-882 (-378)))) (((-378)) . #0=(|has| |#1| (-1012))) (((-224)) . #0#)) (((|#1|) |has| |#1| (-362))) ((((-853)) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((($ $) . T) (((-604 $) $) . T)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) ((($) . T) (((-1232 |#1| |#2| |#3| |#4|)) . T) (((-406 (-558))) . T)) -((($) -3986 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-550))) +((($) -3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| |#1| (-362)) @@ -2029,11 +2030,11 @@ ((((-378)) . T)) (((|#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1087)))) ((((-853)) . T)) -(-3986 (|has| |#2| (-450)) (|has| |#2| (-899))) +(-3996 (|has| |#2| (-450)) (|has| |#2| (-899))) (((|#1|) . T)) (|has| |#1| (-841)) (|has| |#1| (-841)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-534)) |has| |#1| (-606 (-534)))) (((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) ((((-762)) . 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T) (($ $) -3986 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-558)) #0#) |has| |#1| (-362))) -((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -3996 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-558)) #0#) |has| |#1| (-362))) +((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) ((((-942 |#1|)) . T)) ((($) . T)) ((((-558) |#1|) . T)) ((((-1163)) |has| (-406 |#2|) (-890 (-1163)))) -(((|#1|) . T) (($) -3986 (|has| |#1| (-289)) (|has| |#1| (-362))) (((-406 (-558))) |has| |#1| (-362))) +(((|#1|) . T) (($) -3996 (|has| |#1| (-289)) (|has| |#1| (-362))) (((-406 (-558))) |has| |#1| (-362))) ((((-534)) |has| |#2| (-606 (-534)))) ((((-679 |#2|)) . T) (((-853)) . T)) (((|#1|) . T)) @@ -2089,8 +2090,8 @@ (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) ((((-860 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3986 (|has| |#4| (-784)) (|has| |#4| (-839))) -(-3986 (|has| |#3| (-784)) (|has| |#3| (-839))) +(-3996 (|has| |#4| (-784)) (|has| |#4| (-839))) +(-3996 (|has| |#3| (-784)) (|has| |#3| (-839))) ((((-853)) . T)) ((((-853)) . T)) (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) @@ -2106,17 +2107,17 @@ ((((-406 (-558))) . T) (($) . T)) ((((-406 (-558))) . T) (($) . T)) ((((-406 (-558))) . T) (($) . T)) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-1204))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-1204))) ((($) . T)) ((((-406 (-558))) |has| #0=(-406 |#2|) (-1028 (-406 (-558)))) (((-558)) |has| #0# (-1028 (-558))) ((#0#) . T)) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) (((|#1| (-762)) . T)) (|has| |#1| (-841)) (((|#1|) . T) (((-558)) |has| |#1| (-631 (-558)))) -((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3986 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((((-558)) . T)) (|has| |#1| (-38 (-406 (-558)))) -((((-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))) |has| (-2 (|:| -2045 (-1145)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))))) +((((-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))) |has| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (|has| |#1| (-839)) (|has| |#1| (-38 (-406 (-558)))) @@ -2139,29 +2140,29 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) ((((-1145)) . T) (((-1163)) . T) (((-224)) . T) (((-558)) . T)) -(((|#2|) . T) (((-558)) . T) (($) -3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((-1069)) . T) ((|#1|) . 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T)) (|has| |#1| (-839)) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) |has| (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|)) (-308 (-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) |has| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (-308 (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))))) (|has| |#1| (-1087)) (|has| |#1| (-362)) (|has| |#1| (-841)) @@ -2170,16 +2171,16 @@ (((|#1|) . T)) ((((-662 |#1|)) . T)) ((($) . T) (((-406 (-558))) . T)) -((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) +((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) (|has| |#1| (-144)) (|has| |#1| (-146)) -(-3986 (-12 (|has| (-1161 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) -(-3986 (-12 (|has| (-1161 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) +(-3996 (-12 (|has| (-1161 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) +(-3996 (-12 (|has| (-1161 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) (|has| |#1| (-839)) (((|#1| |#2|) . T)) @@ -2203,9 +2204,9 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -(((|#1|) -3986 (|has| |#1| (-171)) (|has| |#1| (-362)))) +(((|#1|) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)))) ((((-315 |#1|)) . T)) (((|#2|) |has| |#2| (-362))) (((|#2|) . T)) @@ -2227,13 +2228,13 @@ (|has| |#1| (-144)) (|has| |#1| (-146)) ((($ $) . 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T) (($) |has| |#1| (-550)) (((-406 (-558))) -3996 (|has| |#1| (-550)) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) ((((-406 (-558))) |has| |#2| (-1028 (-406 (-558)))) (((-558)) |has| |#2| (-1028 (-558))) ((|#2|) . T) (((-855 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-406 (-558))) . T)) ((((-1112 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) @@ -2262,12 +2263,12 @@ (((|#1| |#2|) . T)) ((((-1163) |#1|) . T)) (((|#4|) . T)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((((-1163) (-52)) . T)) ((((-1231 |#2| |#3| |#4|) (-318 |#2| |#3| |#4|)) . T)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) |has| |#1| (-1028 (-558))) ((|#1|) . T)) ((((-853)) . T)) -(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((#0=(-1232 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-171)) ((#0=(-406 (-558)) #0#) |has| |#1| (-550)) (($ $) |has| |#1| (-550))) (((|#1|) . T) (($) . T) (((-406 (-558))) . T)) @@ -2287,14 +2288,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) (((|#2| |#3|) . T)) -(-3986 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3996 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((|#1| (-529 |#2|)) . T)) (((|#1| (-762)) . T)) (((|#1| (-529 (-1075 (-1163)))) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (|has| |#2| (-899)) -(-3986 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3996 (|has| |#2| (-784)) (|has| |#2| (-839))) ((((-853)) . T)) ((($ $) . T) ((#0=(-1231 |#2| |#3| |#4|) #0#) . T) ((#1=(-406 (-558)) #1#) |has| #0# (-38 (-406 (-558))))) ((((-900 |#1|)) . T)) @@ -2303,14 +2304,14 @@ ((((-853)) . T)) ((($) . T)) ((($) . T)) -(-3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-362)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1231 |#2| |#3| |#4|)) . T) (((-406 (-558))) |has| #0# (-38 (-406 (-558))))) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -(-3986 (-12 (|has| |#1| (-306)) (|has| |#1| (-899))) (|has| |#1| (-362)) (|has| |#1| (-348))) -(-3986 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +(-3996 (-12 (|has| |#1| (-306)) (|has| |#1| (-899))) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) ((((-558)) |has| |#1| (-631 (-558))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-853)) . T)) @@ -2343,27 +2344,27 @@ (((|#1|) |has| |#1| (-171))) ((((-853)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) -(((|#2|) -3986 (|has| |#2| (-6 (-4384 "*"))) (|has| |#2| (-171)))) -(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(((|#2|) -3996 (|has| |#2| (-6 (-4385 "*"))) (|has| |#2| (-171)))) +(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#2| (-841)) (|has| |#2| (-899)) (|has| |#1| (-899)) (((|#2|) |has| |#2| (-171))) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-853)) . T)) ((((-853)) . T)) ((((-534)) . T) (((-558)) . T) (((-882 (-558))) . T) (((-378)) . T) (((-224)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) -((((-2 (|:| -2045 (-1145)) (|:| -2957 (-52)))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))) . T)) (((|#1|) . T)) ((((-853)) . T)) (((|#1| |#2|) . T)) (((|#1| (-406 (-558))) . T)) (((|#1|) . T)) -(-3986 (|has| |#1| (-289)) (|has| |#1| (-362))) +(-3996 (|has| |#1| (-289)) (|has| |#1| (-362))) ((((-143)) . T)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T)) (|has| |#1| (-839)) @@ -2379,7 +2380,7 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-186)) . T) (((-853)) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -2392,7 +2393,7 @@ ((((-853)) . T)) ((((-1145)) . T)) ((((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) +((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) (|has| |#1| (-841)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) @@ -2404,16 +2405,16 @@ (((|#2|) . T)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T)) ((($) . T) (((-558)) . T) (((-406 (-558))) . T) (((-604 $)) . T)) -(-3986 (|has| |#4| (-171)) (|has| |#4| (-717)) (|has| |#4| (-839)) (|has| |#4| (-1039))) -(-3986 (|has| |#3| (-171)) (|has| |#3| (-717)) (|has| |#3| (-839)) (|has| |#3| (-1039))) +(-3996 (|has| |#4| (-171)) (|has| |#4| (-717)) (|has| |#4| (-839)) (|has| |#4| (-1039))) +(-3996 (|has| |#3| (-171)) (|has| |#3| (-717)) (|has| |#3| (-839)) (|has| |#3| (-1039))) ((((-1163) (-52)) . T)) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3986 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) -(-3986 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (|has| |#1| (-899)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) (|has| |#1| (-899)) @@ -2430,12 +2431,12 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#1| (-811)) (((#0=(-900 |#1|) #0#) . T) (($ $) . T) ((#1=(-406 (-558)) #1#) . T)) ((((-406 |#2|)) . T)) (|has| |#1| (-839)) -((((-1186 |#1|)) . T) (((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-1186 |#1|)) . T) (((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) . T) ((#1=(-558) #1#) . T) (($ $) . T)) ((((-900 |#1|)) . T) (($) . T) (((-406 (-558))) . T)) (((|#2|) |has| |#2| (-1039)) (((-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039)))) @@ -2446,25 +2447,26 @@ (((|#2|) . T)) ((((-853)) . T)) ((((-406 (-558))) . T) (((-689)) . T) (($) . T) (((-558)) . T)) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) -((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2045 (-1163)) (|:| -2957 #0#))) . T)) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2055 (-1163)) (|:| -3528 #0#))) . T)) (|has| |#1| (-348)) ((((-558)) . T)) ((((-853)) . T)) +(((|#1|) . T)) (((#0=(-1232 |#1| |#2| |#3| |#4|) $) |has| #0# (-285 #0# #0#))) (|has| |#1| (-362)) (((#0=(-1069) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) (((#0=(-406 (-558)) #0#) . T) ((#1=(-689) #1#) . T) (($ $) . T)) ((((-315 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) |has| |#1| (-362))) (|has| |#1| (-1087)) (((|#1|) . T)) -(((|#1|) -3986 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) -(((|#1|) -3986 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) +(((|#1|) -3996 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) +(((|#1|) -3996 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) (((|#2|) . T)) ((((-406 (-558))) . T) (((-689)) . T) (($) . T)) ((((-573)) . T)) @@ -2487,7 +2489,7 @@ (((|#1|) . T)) ((((-558)) . T)) (((|#2|) . T) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((|#1|) . T) (($) . T) (((-558)) . T)) -(-3986 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2525,7 +2527,7 @@ (|has| |#2| (-1012)) ((($) . T)) (|has| |#1| (-899)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2533,9 +2535,9 @@ ((($) . T)) (|has| |#1| (-362)) ((((-900 |#1|)) . T)) -((($) -3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) -(-3986 (|has| |#1| (-367)) (|has| |#1| (-841))) +(-3996 (|has| |#1| (-367)) (|has| |#1| (-841))) (((|#1|) . T)) ((((-762)) . T)) ((((-853)) . T)) @@ -2546,16 +2548,16 @@ ((((-558)) . T) (($) . T)) ((((-558)) . T) (($) . T)) ((((-762) |#1|) . T)) -(((|#2| (-239 (-1427 |#1|) (-762))) . T)) +(((|#2| (-239 (-1450 |#1|) (-762))) . T)) (((|#1| (-529 |#3|)) . T)) ((((-406 (-558))) . T)) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((((-1145)) . T) (((-853)) . T)) -(((#0=(-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) #0#) |has| (-2 (|:| -2045 (-1163)) (|:| -2957 (-52))) (-308 (-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))))) +(((#0=(-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) #0#) |has| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))))) ((((-1145)) . T)) (|has| |#1| (-899)) (|has| |#2| (-362)) -(-3986 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-168 (-378))) . T) (((-224)) . T) (((-378)) . T)) ((((-853)) . T)) (((|#1|) . T)) @@ -2572,11 +2574,11 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3986 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-558)))) (-12 (|has| |#1| (-543)) (|has| |#1| (-819))) ((((-853)) . T)) -((((-1163)) -3986 (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-890 (-1163)))) (-12 (|has| |#1| (-362)) (|has| |#2| (-890 (-1163)))))) +((((-1163)) -3996 (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-890 (-1163)))) (-12 (|has| |#1| (-362)) (|has| |#2| (-890 (-1163)))))) (|has| |#1| (-362)) ((((-1163)) -12 (|has| |#1| (-15 * (|#1| (-406 (-558)) |#1|))) (|has| |#1| (-890 (-1163))))) (|has| |#1| (-362)) @@ -2587,7 +2589,7 @@ (((|#2|) |has| |#1| (-362))) (((|#2|) |has| |#1| (-362))) ((((-558)) . T) (($) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) @@ -2612,9 +2614,9 @@ ((((-378)) -12 (|has| |#1| (-362)) (|has| |#2| (-876 (-378)))) (((-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-876 (-558))))) (|has| |#1| (-362)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-362)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-550)) (((|#1|) . T)) @@ -2623,22 +2625,22 @@ ((((-1145)) . T) (((-1163)) . T) (((-224)) . T) (((-558)) . T)) (((|#1|) . T)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) -(-3986 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (((|#2|) . T)) (((|#2|) . T)) -(-3986 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) -((((-2 (|:| -2045 (-1145)) (|:| -2957 |#1|))) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +(-3996 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) (|has| |#1| (-38 (-406 (-558)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-406 (-558)))) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) ((((-1145) |#1|) . T)) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) ((((-575 |#1|)) . T)) ((($) . T)) @@ -2646,7 +2648,7 @@ (|has| |#1| (-550)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3986 (|has| |#1| (-144)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-348))) (|has| |#1| (-146)) ((((-853)) . T)) ((($) . T)) @@ -2673,7 +2675,7 @@ ((((-853)) . T)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2695,7 +2697,7 @@ ((((-558)) . T)) ((((-853)) . T)) ((((-558)) . T)) -(-3986 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3996 (|has| |#2| (-784)) (|has| |#2| (-839))) ((((-168 (-378))) . T) (((-224)) . T) (((-378)) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -2707,9 +2709,9 @@ (((|#1|) . T) (($) . T) (((-406 (-558))) . 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T)) +((((-1159 |#1|)) . T) (((-558)) . T) (($) -3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((-1069)) . T) ((|#1|) . T) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558)))))) +(-3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) +((((-1112 |#1| (-1163))) . T) (((-558)) . T) (((-1075 (-1163))) . T) (($) -3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-1163)) . T)) (((#0=(-575 |#1|) #0#) . T) (($ $) . T) ((#1=(-406 (-558)) #1#) . T)) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) (((|#1|) |has| |#1| (-171))) @@ -2780,13 +2782,13 @@ ((((-575 |#1|)) . T) (($) . T) (((-406 (-558))) . T)) ((($) . T) (((-406 (-558))) . T)) ((($) . T) (((-406 (-558))) . T)) -(((|#2|) |has| |#2| (-6 (-4384 "*")))) +(((|#2|) |has| |#2| (-6 (-4385 "*")))) (((|#1|) . T)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((|#1|) . T) (((-558)) . T)) (((|#1|) . T)) ((((-853)) . T)) ((((-293 |#3|)) . T)) -(((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558)))) ((|#2| |#2|) . T) (($ $) -3986 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +(((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558)))) ((|#2| |#2|) . T) (($ $) -3996 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) . T)) @@ -2794,21 +2796,21 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) -((($ $) -3986 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . 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T) (((-406 (-558))) -3986 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) . T)) +((((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#2|) |has| |#1| (-362)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) ((((-558)) |has| |#1| (-876 (-558))) (((-378)) |has| |#1| (-876 (-378)))) @@ -2894,12 +2896,12 @@ (((|#2| (-762)) . T)) ((((-1163)) . T)) ((((-860 |#1|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-406 (-558)) #0#) . T) (($ $) . T)) ((((-558)) . T)) @@ -3243,17 +3245,17 @@ ((((-129)) . T)) ((((-853)) . T)) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) . T)) (|has| |#1| (-362)) -((($) -3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((((-1091)) . T)) ((((-853)) . 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T)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-1168)) . T)) (((|#1|) |has| |#1| (-171))) ((((-1168)) . T)) @@ -3275,13 +3277,13 @@ ((((-1168)) . T)) ((((-1168)) . T)) ((((-1168)) . T)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((((-1168)) . T)) ((((-1168)) . T)) (|has| |#1| (-362)) (|has| |#1| (-362)) -(-3986 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-171)) (|has| |#1| (-550))) (((|#1| (-558)) . T)) (((|#1| (-406 (-558))) . T)) (((|#1| (-762)) . T)) @@ -3296,16 +3298,16 @@ ((((-882 (-378))) . T) (((-882 (-558))) . T) (((-1163)) . T) (((-534)) . T)) (((|#1|) . T)) ((((-853)) . T)) -(-3986 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) -(-3986 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-130)) (|has| |#2| (-130))) (-12 (|has| |#1| (-784)) (|has| |#2| (-784)))) +(-3996 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-130)) (|has| |#2| (-130))) (-12 (|has| |#1| (-784)) (|has| |#2| (-784)))) ((((-558)) . T)) ((((-558)) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3986 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3996 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039)))) -(-3986 (-12 (|has| |#1| (-471)) (|has| |#2| (-471))) (-12 (|has| |#1| (-717)) (|has| |#2| (-717)))) +(-3996 (-12 (|has| |#1| (-471)) (|has| |#2| (-471))) (-12 (|has| |#1| (-717)) (|has| |#2| (-717)))) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-362)) @@ -3331,7 +3333,7 @@ (((|#1| |#2|) . T)) ((((-558)) . T) ((|#2|) |has| |#2| (-171))) ((((-114)) . T) ((|#1|) . T) (((-558)) . T)) -(-3986 (|has| |#1| (-348)) (|has| |#1| (-367))) +(-3996 (|has| |#1| (-348)) (|has| |#1| (-367))) (((|#1| |#2|) . T)) ((((-224)) . T)) ((((-406 (-558))) . T) (($) . T) (((-558)) . T)) @@ -3343,7 +3345,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) ((($) . T) (((-406 (-558))) . T)) (|has| |#1| (-899)) (|has| |#1| (-899)) @@ -3354,14 +3356,14 @@ (((|#1| |#1|) |has| |#1| (-171))) (((|#1|) . T) (((-558)) . T)) ((((-1168)) . T)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3986 (|has| |#1| (-21)) (|has| |#1| (-839))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3996 (|has| |#1| (-21)) (|has| |#1| (-839))) (((|#2|) . T)) -(-3986 (|has| |#1| (-21)) (|has| |#1| (-839))) +(-3996 (|has| |#1| (-21)) (|has| |#1| (-839))) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (((|#1|) . 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T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -(((|#2|) . T) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) -((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1012)) -(((|#2|) . T) (((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) ((((-853)) . T)) ((((-534)) |has| |#2| (-606 (-534))) (((-882 (-558))) |has| |#2| (-606 (-882 (-558)))) (((-882 (-378))) |has| |#2| (-606 (-882 (-378)))) (((-378)) . #0=(|has| |#2| (-1012))) (((-224)) . #0#)) ((((-293 |#3|)) . T)) @@ -3419,15 +3421,15 @@ ((((-1161 |#1| |#2| |#3|)) . T)) ((((-1161 |#1| |#2| |#3|)) . T) (((-1154 |#1| |#2| |#3|)) . T)) ((((-853)) . T)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-558) |#1|) . 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T)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-129)) . T) (((-853)) . T)) ((((-558) |#1|) . T)) ((((-129)) . T)) @@ -3451,13 +3453,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-362)) (|has| |#2| (-285 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3986 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) -(-3986 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) ((((-853)) . T)) ((((-853)) . T)) ((((-853)) . T)) (((|#1| (-529 |#2|)) . T)) -((((-2 (|:| -2045 (-1163)) (|:| -2957 (-52)))) . T)) +((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) ((((-558) (-129)) . T)) (((|#1| (-558)) . T)) (((|#1| (-406 (-558))) . T)) @@ -3471,8 +3473,8 @@ ((((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) -(-3986 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3986 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((($) . T)) (((|#2| (-529 (-855 |#1|))) . T)) ((((-1168)) . T)) @@ -3487,13 +3489,13 @@ ((((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-1168)) . T)) -((((-853)) -3986 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1|) . T)) (((|#2| (-762)) . T)) (((|#1| |#2|) . T)) ((((-1145) |#1|) . T)) ((((-406 |#2|)) . T)) -((((-2 (|:| -2045 |#1|) (|:| -2957 |#2|))) . T)) +((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) (|has| |#1| (-550)) (|has| |#1| (-550)) ((($) . T) ((|#2|) . T)) @@ -3502,14 +3504,14 @@ ((((-558)) . T) (($) . 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. -605) 155542) ((-50 . -1046) T) ((-250 . -717) 155452) ((-249 . -717) 155362) ((-1194 . -1087) T) ((-660 . -23) T) ((-575 . -1046) T) ((-516 . -1046) T) ((-378 . -1045) 155327) ((-321 . -111) 155302) ((-73 . -382) T) ((-73 . -394) T) ((-1014 . -38) 155239) ((-684 . -399) 155221) ((-99 . -102) T) ((-702 . -1087) T) ((-993 . -144) 155193) ((-993 . -146) 155165) ((-378 . -111) 155121) ((-318 . -1204) 155100) ((-472 . -992) 155066) ((-353 . -38) 155031) ((-40 . -369) 155003) ((-863 . -605) 154875) ((-127 . -125) 154859) ((-121 . -125) 154843) ((-827 . -1045) 154813) ((-824 . -21) 154765) ((-818 . -1045) 154749) ((-824 . -25) 154701) ((-318 . -550) 154652) ((-515 . -608) 154633) ((-558 . -819) T) ((-239 . -1200) T) ((-1024 . -608) 154602) ((-827 . -111) 154567) ((-818 . -111) 154546) ((-1230 . -605) 154528) ((-1209 . -605) 154510) ((-1209 . -606) 154181) ((-1159 . -899) 154160) ((-1112 . -899) 154139) ((-48 . -38) 154104) ((-1268 . -1099) T) ((-594 . -605) 154016) ((-594 . -606) 153977) 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141081) ((-1081 . -605) 141048) ((-108 . -130) T) ((-944 . -1087) T) ((-911 . -1087) T) ((-762 . -1087) T) ((-662 . -1087) T) ((-691 . -146) T) ((-116 . -146) T) ((-1268 . -21) T) ((-1268 . -25) T) ((-1266 . -21) T) ((-1266 . -25) T) ((-654 . -1045) 141032) ((-529 . -841) T) ((-498 . -841) T) ((-354 . -1045) 140984) ((-351 . -1045) 140936) ((-343 . -1045) 140888) ((-250 . -1200) T) ((-249 . -1200) T) ((-263 . -1045) 140731) ((-246 . -1045) 140574) ((-654 . -111) 140553) ((-354 . -111) 140491) ((-351 . -111) 140429) ((-343 . -111) 140367) ((-263 . -111) 140196) ((-246 . -111) 140025) ((-808 . -1204) 140004) ((-615 . -410) 139988) ((-44 . -21) T) ((-44 . -25) T) ((-806 . -631) 139894) ((-808 . -550) 139873) ((-250 . -1028) 139700) ((-249 . -1028) 139527) ((-126 . -119) 139511) ((-900 . -1045) 139476) ((-703 . -102) T) ((-689 . -1046) T) ((-534 . -610) 139379) ((-342 . -171) T) ((-151 . -21) T) ((-151 . -25) T) ((-88 . -605) 139361) ((-900 . -111) 139317) ((-40 . -708) 139262) ((-860 . 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137112) ((-1143 . -150) 137096) ((-250 . -890) 137028) ((-249 . -890) 136960) ((-1069 . -841) T) ((-413 . -1099) T) ((-1043 . -23) T) ((-900 . -1039) T) ((-321 . -638) 136942) ((-1014 . -839) T) ((-1194 . -992) 136908) ((-1160 . -910) 136887) ((-1154 . -910) 136866) ((-1154 . -811) NIL) ((-900 . -242) T) ((-808 . -362) 136845) ((-384 . -23) T) ((-127 . -1087) 136823) ((-121 . -1087) 136801) ((-900 . -232) T) ((-128 . -34) T) ((-378 . -638) 136766) ((-860 . -708) 136753) ((-1036 . -150) 136718) ((-40 . -171) T) ((-684 . -410) 136700) ((-703 . -308) 136687) ((-827 . -638) 136647) ((-818 . -638) 136621) ((-318 . -25) T) ((-318 . -21) T) ((-648 . -285) 136600) ((-574 . -1087) T) ((-558 . -1087) T) ((-493 . -1087) T) ((-244 . -287) 136577) ((-312 . -230) 136538) ((-1159 . -876) NIL) ((-55 . -1087) T) ((-1112 . -876) 136397) ((-129 . -841) T) ((-1159 . -1028) 136277) ((-1112 . -1028) 136160) ((-182 . -605) 136142) ((-845 . -1028) 136038) ((-773 . -285) 135965) ((-808 . -1099) T) ((-1024 . -717) T) ((-594 . -641) 135949) ((-1036 . -966) 135878) ((-989 . -102) T) ((-808 . -23) T) ((-703 . -1138) 135856) ((-684 . -1046) T) ((-594 . -372) 135840) ((-350 . -450) T) ((-342 . -289) T) ((-1247 . -1087) T) ((-247 . -1087) T) ((-398 . -102) T) ((-288 . -21) T) ((-288 . -25) T) ((-360 . -717) T) ((-701 . -1087) T) ((-689 . -1087) T) ((-360 . -471) T) ((-1194 . -605) 135822) ((-1159 . -376) 135806) ((-1112 . -376) 135790) ((-1014 . -410) 135752) ((-140 . -228) 135734) ((-378 . -785) T) ((-378 . -782) T) ((-860 . -171) T) ((-378 . -717) T) ((-702 . -605) 135716) ((-703 . -38) 135545) ((-1246 . -1244) 135529) ((-350 . -401) T) ((-1246 . -1087) 135479) ((-574 . -708) 135466) ((-558 . -708) 135453) ((-493 . -708) 135418) ((-315 . -621) 135397) ((-827 . -717) T) ((-818 . -717) T) ((-635 . -1200) T) ((-1067 . -631) 135345) ((-1159 . -890) 135288) ((-1112 . -890) 135272) ((-652 . -1045) 135256) ((-108 . -631) 135238) ((-480 . -130) 135108) ((-1165 . -1099) T) ((-942 . -47) 135077) ((-615 . -1087) T) ((-652 . -111) 135056) ((-489 . -605) 135022) ((-326 . -287) 134999) ((-479 . -47) 134956) ((-1165 . -23) T) ((-117 . -1087) T) ((-103 . -102) 134934) ((-1258 . -1099) T) ((-1043 . -130) T) ((-1014 . -1046) T) ((-810 . -1028) 134918) ((-993 . -715) 134890) ((-1258 . -23) T) ((-689 . -708) 134855) ((-579 . -605) 134837) ((-385 . -1028) 134821) ((-353 . -1046) T) ((-384 . -130) T) ((-323 . -1028) 134805) ((-224 . -876) 134787) ((-994 . -910) T) ((-91 . -34) T) ((-994 . -811) T) ((-904 . -910) T) ((-1180 . -605) 134769) ((-1107 . -819) T) ((-485 . -1204) T) ((-1092 . -1087) T) ((-1067 . -21) T) ((-1067 . -25) T) ((-216 . -1204) T) ((-989 . -308) 134734) ((-224 . -1028) 134694) ((-40 . -289) T) ((-705 . -638) 134654) ((-671 . -608) 134635) ((-666 . -608) 134616) ((-485 . -550) T) ((-476 . -608) 134597) ((-358 . -25) T) ((-358 . -21) T) ((-352 . -25) T) ((-216 . -550) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-244 . -608) 134574) ((-137 . -608) 134555) ((-136 . -608) 134536) ((-132 . -608) 134517) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1046) T) ((-574 . -171) T) ((-558 . -171) T) ((-493 . -171) T) ((-648 . -605) 134499) ((-728 . -727) 134483) ((-335 . -605) 134465) ((-68 . -382) T) ((-68 . -394) T) ((-1089 . -107) 134449) ((-1050 . -876) 134431) ((-942 . -876) 134356) ((-643 . -1099) T) ((-615 . -708) 134343) ((-479 . -876) NIL) ((-1133 . -102) T) ((-1081 . -610) 134327) ((-1050 . -1028) 134309) ((-97 . -605) 134291) ((-475 . -146) T) ((-942 . -1028) 134171) ((-117 . -708) 134116) ((-643 . -23) T) ((-479 . -1028) 133992) ((-1074 . -606) NIL) ((-1074 . -605) 133974) ((-773 . -606) NIL) ((-773 . -605) 133935) ((-771 . -606) 133569) ((-771 . -605) 133483) ((-1100 . -631) 133389) ((-459 . -605) 133371) ((-452 . -605) 133353) ((-452 . -606) 133214) ((-1025 . -228) 133160) ((-862 . -899) 133139) ((-126 . -34) T) ((-808 . -130) T) ((-639 . -605) 133121) ((-572 . -102) T) ((-354 . -1265) 133105) ((-351 . -1265) 133089) ((-343 . -1265) 133073) 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. -394) T) ((-216 . -23) T) ((-1270 . -1263) 130923) ((-574 . -289) T) ((-558 . -289) T) ((-667 . -1028) 130907) ((-493 . -289) T) ((-135 . -468) 130862) ((-48 . -1087) T) ((-703 . -230) 130846) ((-861 . -890) NIL) ((-1219 . -876) NIL) ((-879 . -102) T) ((-875 . -102) T) ((-387 . -1087) T) ((-168 . -376) 130830) ((-168 . -337) 130814) ((-1219 . -1028) 130694) ((-846 . -1028) 130590) ((-1129 . -102) T) ((-643 . -130) T) ((-117 . -512) 130498) ((-652 . -783) 130477) ((-652 . -786) 130456) ((-565 . -1028) 130438) ((-293 . -1253) 130408) ((-856 . -102) T) ((-953 . -550) 130387) ((-1194 . -1045) 130270) ((-480 . -631) 130176) ((-894 . -1087) T) ((-1014 . -708) 130113) ((-702 . -1045) 130078) ((-609 . -102) T) ((-594 . -34) T) ((-1134 . -1200) T) ((-1194 . -111) 129947) ((-472 . -638) 129844) ((-353 . -708) 129789) ((-168 . -890) 129748) ((-689 . -289) T) ((-684 . -171) T) ((-702 . -111) 129704) ((-1274 . -1046) T) ((-1219 . -376) 129688) ((-417 . -1204) 129666) ((-1105 . -605) 129648) 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. -1046) T) ((-684 . -992) NIL) ((-3 . |UnionCategory|) T) ((-1230 . -47) 121181) ((-1209 . -47) 121158) ((-1128 . -1000) 121129) ((-224 . -910) T) ((-40 . -111) 121058) ((-862 . -1028) 120922) ((-1107 . -708) 120909) ((-1092 . -605) 120891) ((-1067 . -146) 120870) ((-1067 . -144) 120821) ((-994 . -362) T) ((-318 . -1188) 120787) ((-378 . -306) T) ((-318 . -1185) 120753) ((-315 . -171) 120732) ((-312 . -171) T) ((-993 . -230) 120709) ((-904 . -362) T) ((-575 . -1265) 120696) ((-516 . -1265) 120673) ((-358 . -146) 120652) ((-358 . -144) 120603) ((-352 . -146) 120582) ((-352 . -144) 120533) ((-600 . -1176) 120509) ((-344 . -146) 120488) ((-344 . -144) 120439) ((-318 . -35) 120405) ((-473 . -1176) 120384) ((0 . |EnumerationCategory|) T) ((-318 . -95) 120350) ((-378 . -1012) T) ((-108 . -146) T) ((-108 . -144) NIL) ((-45 . -234) 120300) ((-644 . -1087) T) ((-600 . -107) 120247) ((-483 . -130) T) ((-473 . -107) 120197) ((-239 . -1099) 120107) ((-862 . -376) 120091) ((-862 . -337) 120075) 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-144) 100950) ((-406 . -289) T) ((-1154 . -146) 100857) ((-1113 . -146) 100836) ((-1113 . -144) 100815) ((-318 . -38) 100656) ((-168 . -130) T) ((-312 . -786) NIL) ((-312 . -783) NIL) ((-644 . -1039) T) ((-48 . -638) 100621) ((-883 . -608) 100598) ((-1153 . -102) T) ((-984 . -102) T) ((-983 . -21) T) ((-127 . -1000) 100582) ((-121 . -1000) 100566) ((-983 . -25) T) ((-891 . -119) 100550) ((-1145 . -102) T) ((-807 . -841) 100529) ((-1219 . -130) T) ((-1159 . -25) T) ((-1159 . -21) T) ((-846 . -130) T) ((-1112 . -25) T) ((-1112 . -21) T) ((-845 . -25) T) ((-845 . -21) T) ((-773 . -306) 100508) ((-637 . -102) 100486) ((-624 . -102) T) ((-1146 . -308) 100281) ((-565 . -130) T) ((-613 . -839) 100260) ((-1143 . -487) 100244) ((-1137 . -150) 100194) ((-1133 . -605) 100156) ((-1133 . -606) 100117) ((-1014 . -782) T) ((-1014 . -785) T) ((-1014 . -717) T) ((-703 . -1045) 99940) ((-482 . -308) 99878) ((-451 . -416) 99848) ((-350 . -171) T) ((-288 . -38) 99835) ((-273 . -102) T) ((-272 . -102) T) 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92304) ((-1210 . -95) 92270) ((-1209 . -1099) T) ((-586 . -150) 92252) ((-1067 . -348) 92231) ((-173 . -289) T) ((-117 . -376) 92208) ((-117 . -337) 92185) ((-1210 . -35) 92151) ((-860 . -306) T) ((-312 . -785) NIL) ((-312 . -782) NIL) ((-315 . -717) 92000) ((-312 . -717) T) ((-472 . -362) 91979) ((-358 . -348) 91958) ((-352 . -348) 91937) ((-344 . -348) 91916) ((-315 . -471) 91895) ((-1230 . -23) T) ((-1209 . -23) T) ((-709 . -1099) T) ((-705 . -130) T) ((-643 . -102) T) ((-475 . -708) 91860) ((-45 . -281) 91810) ((-105 . -1087) T) ((-68 . -605) 91792) ((-960 . -102) T) ((-855 . -102) T) ((-615 . -890) 91751) ((-1270 . -1087) T) ((-380 . -1087) T) ((-1199 . -1087) T) ((-1100 . -230) 91720) ((-82 . -1200) T) ((-1050 . -841) T) ((-942 . -841) 91699) ((-117 . -890) NIL) ((-773 . -910) 91678) ((-704 . -841) T) ((-529 . -1087) T) ((-498 . -1087) T) ((-354 . -1204) T) ((-351 . -1204) T) ((-343 . -1204) T) ((-263 . -1204) 91657) ((-246 . -1204) 91636) ((-531 . -851) T) ((-479 . -841) 91615) 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-1039) T) ((-703 . -899) 88715) ((-1143 . -608) 88692) ((-993 . -232) 88664) ((-993 . -242) T) ((-117 . -1012) NIL) ((-900 . -1099) T) ((-1231 . -450) 88643) ((-1210 . -450) 88622) ((-521 . -605) 88554) ((-703 . -638) 88479) ((-406 . -1045) 88431) ((-502 . -605) 88413) ((-900 . -23) T) ((-485 . -308) NIL) ((-1269 . -608) 88369) ((-472 . -130) T) ((-216 . -308) NIL) ((-406 . -111) 88307) ((-806 . -1046) 88237) ((-728 . -1085) 88221) ((-1230 . -491) 88187) ((-1209 . -491) 88153) ((-140 . -1085) 88135) ((-475 . -289) T) ((-1269 . -1039) T) ((-1051 . -102) T) ((-834 . -608) 88003) ((-498 . -512) NIL) ((-693 . -102) T) ((-480 . -237) 87982) ((-406 . -608) 87880) ((-1159 . -144) 87859) ((-1159 . -146) 87838) ((-1112 . -146) 87817) ((-1112 . -144) 87796) ((-627 . -1045) 87780) ((-599 . -1045) 87764) ((-660 . -1087) T) ((-660 . -1042) 87704) ((-1161 . -1237) 87688) ((-1161 . -1224) 87665) ((-485 . -1138) T) ((-1160 . -1229) 87626) ((-1160 . -1224) 87596) ((-1160 . -1227) 87580) ((-216 . -1138) 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85612) ((-1050 . -146) T) ((-942 . -146) 85591) ((-942 . -144) 85570) ((-790 . -102) T) ((-151 . -708) 85554) ((-479 . -146) 85533) ((-479 . -144) 85512) ((-350 . -111) 85441) ((-1067 . -1046) T) ((-321 . -841) 85420) ((-1238 . -963) 85389) ((-619 . -1087) T) ((-1231 . -963) 85351) ((-509 . -130) T) ((-505 . -130) T) ((-294 . -228) 85301) ((-358 . -1046) T) ((-352 . -1046) T) ((-344 . -1046) T) ((-293 . -1039) 85243) ((-1210 . -963) 85212) ((-378 . -841) T) ((-108 . -1046) T) ((-989 . -717) T) ((-860 . -910) T) ((-834 . -786) 85191) ((-834 . -783) 85170) ((-417 . -308) 85109) ((-466 . -102) T) ((-588 . -963) 85078) ((-318 . -1087) T) ((-406 . -786) 85057) ((-406 . -783) 85036) ((-498 . -487) 85018) ((-1232 . -1028) 84984) ((-1230 . -21) T) ((-1230 . -25) T) ((-1209 . -21) T) ((-1209 . -25) T) ((-806 . -708) 84926) ((-350 . -608) 84856) ((-689 . -403) T) ((-1259 . -1200) T) ((-598 . -102) T) ((-1100 . -410) 84825) ((-993 . -367) NIL) ((-661 . -102) T) ((-179 . -102) T) ((-160 . -102) T) 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-605) 83480) ((-1100 . -1046) 83410) ((-574 . -910) T) ((-558 . -811) T) ((-558 . -910) T) ((-493 . -910) T) ((-135 . -1028) 83394) ((-224 . -95) T) ((-75 . -439) T) ((-75 . -394) T) ((0 . -605) 83376) ((-168 . -146) 83355) ((-168 . -144) 83306) ((-224 . -35) T) ((-49 . -605) 83288) ((-475 . -1046) T) ((-485 . -230) 83270) ((-482 . -958) 83254) ((-480 . -839) 83233) ((-216 . -230) 83215) ((-81 . -439) T) ((-81 . -394) T) ((-1133 . -34) T) ((-806 . -171) 83194) ((-722 . -102) T) ((-1016 . -605) 83161) ((-498 . -285) 83136) ((-315 . -376) 83105) ((-312 . -376) 83066) ((-312 . -337) 83027) ((-1072 . -605) 83009) ((-807 . -939) 82956) ((-652 . -130) T) ((-1219 . -144) 82935) ((-1219 . -146) 82914) ((-1161 . -102) T) ((-1160 . -102) T) ((-1154 . -102) T) ((-1146 . -1087) T) ((-1113 . -102) T) ((-221 . -34) T) ((-288 . -708) 82901) ((-1146 . -602) 82877) ((-586 . -308) NIL) ((-482 . -1087) 82855) ((-389 . -605) 82837) ((-508 . -841) T) ((-1137 . -228) 82787) ((-1238 . -1237) 82771) ((-1238 . -1224) 82748) ((-1231 . -1229) 82709) ((-1231 . -1224) 82679) ((-1231 . -1227) 82663) ((-1210 . -1208) 82624) ((-1210 . -1224) 82601) ((-613 . -605) 82583) ((-1210 . -1206) 82567) ((-689 . -910) T) ((-1161 . -283) 82533) ((-1160 . -283) 82499) ((-1154 . -283) 82465) ((-1067 . -1087) T) ((-1049 . -1087) T) ((-48 . -301) T) ((-315 . -890) 82431) ((-312 . -890) NIL) ((-1049 . -1056) 82410) ((-1107 . -876) 82392) ((-790 . -38) 82376) ((-263 . -631) 82324) ((-246 . -631) 82272) ((-691 . -1045) 82259) ((-588 . -1224) 82236) ((-1113 . -283) 82202) ((-318 . -171) 82133) ((-358 . -1087) T) ((-352 . -1087) T) ((-344 . -1087) T) ((-498 . -19) 82115) ((-1107 . -1028) 82097) ((-1089 . -150) 82081) ((-108 . -1087) T) ((-116 . -1045) 82068) ((-702 . -362) T) ((-498 . -596) 82043) ((-691 . -111) 82028) ((-435 . -102) T) ((-45 . -1136) 81978) ((-116 . -111) 81963) ((-627 . -711) T) ((-599 . -711) T) ((-806 . -512) 81896) ((-1025 . -1200) T) ((-933 . -150) 81880) ((-1159 . -450) 81811) ((-1153 . -1087) T) ((-1145 . -1087) T) ((-523 . -102) T) ((-518 . -102) 81761) ((-1129 . -638) 81735) ((-1112 . -450) 81686) ((-1074 . -1204) 81665) ((-773 . -1204) 81644) ((-771 . -1204) 81623) ((-62 . -1200) T) ((-475 . -605) 81575) ((-475 . -606) 81497) ((-1074 . -550) 81428) ((-984 . -1087) T) ((-773 . -550) 81339) ((-771 . -550) 81270) ((-480 . -410) 81239) ((-615 . -910) 81218) ((-452 . -1204) 81197) ((-722 . -308) 81184) ((-691 . -608) 81156) ((-397 . -605) 81138) ((-665 . -512) 81071) ((-654 . -25) T) ((-654 . -21) T) ((-452 . -550) 81002) ((-354 . -25) T) ((-354 . -21) T) ((-117 . -910) T) ((-117 . -811) NIL) ((-351 . -25) T) ((-351 . -21) T) ((-343 . -25) T) ((-343 . -21) T) ((-263 . -25) T) ((-263 . -21) T) ((-246 . -25) T) ((-246 . -21) T) ((-83 . -383) T) ((-83 . -394) T) ((-133 . -608) 80984) ((-116 . -608) 80956) ((-1248 . -605) 80938) ((-1194 . -1099) T) ((-1194 . -23) T) ((-1154 . -308) 80823) ((-1113 . -308) 80810) ((-1067 . -708) 80678) ((-856 . -638) 80638) ((-933 . -970) 80622) 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66109) ((-993 . -1028) 65997) ((-1154 . -839) NIL) ((-684 . -1204) T) ((-790 . -1046) T) ((-689 . -1099) T) ((-1268 . -1039) T) ((-1266 . -608) 65926) ((-1266 . -1039) T) ((-1143 . -1200) T) ((-993 . -376) 65903) ((-900 . -144) T) ((-900 . -146) 65885) ((-860 . -130) T) ((-806 . -1045) 65782) ((-684 . -550) T) ((-689 . -23) T) ((-637 . -605) 65714) ((-637 . -606) 65675) ((-624 . -606) NIL) ((-624 . -605) 65657) ((-485 . -171) T) ((-222 . -21) T) ((-216 . -171) T) ((-222 . -25) T) ((-472 . -1188) 65623) ((-472 . -1185) 65589) ((-273 . -605) 65571) ((-272 . -605) 65553) ((-271 . -605) 65535) ((-270 . -605) 65517) ((-269 . -605) 65499) ((-498 . -641) 65481) ((-268 . -605) 65463) ((-338 . -717) T) ((-267 . -605) 65445) ((-110 . -19) 65427) ((-173 . -717) T) ((-498 . -372) 65409) ((-211 . -605) 65391) ((-518 . -1136) 65375) ((-498 . -123) T) ((-110 . -596) 65350) ((-210 . -605) 65332) ((-472 . -35) 65298) ((-472 . -95) 65264) ((-208 . -605) 65246) ((-207 . -605) 65228) ((-206 . -605) 65210) 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. -372) 23136) ((-342 . -1253) 23113) ((-1017 . -1200) T) ((-861 . -289) T) ((-1219 . -512) 23060) ((-474 . -1200) T) ((-461 . -1200) T) ((-579 . -102) T) ((-1159 . -285) 22987) ((-615 . -450) 22966) ((-990 . -985) 22950) ((-1261 . -381) 22922) ((-515 . -1087) T) ((-117 . -450) T) ((-1180 . -102) T) ((-1079 . -1087) 22900) ((-1024 . -1087) T) ((-1102 . -93) T) ((-883 . -841) T) ((-350 . -1204) T) ((-1238 . -1045) 22783) ((-1100 . -376) 22752) ((-1231 . -1045) 22587) ((-1210 . -1045) 22377) ((-1238 . -111) 22246) ((-1231 . -111) 22067) ((-1210 . -111) 21836) ((-1194 . -308) 21823) ((-350 . -550) T) ((-364 . -605) 21805) ((-288 . -306) T) ((-589 . -1045) 21778) ((-588 . -1045) 21661) ((-360 . -1087) T) ((-321 . -1087) T) ((-250 . -605) 21622) ((-249 . -605) 21583) ((-993 . -130) T) ((-627 . -23) T) ((-684 . -408) 21550) ((-599 . -23) T) ((-648 . -102) T) ((-589 . -111) 21521) ((-588 . -111) 21390) ((-378 . -1087) T) ((-335 . -102) T) ((-168 . -289) 21301) ((-1209 . -839) 21254) ((-705 . 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152869) ((-494 . -285) 152846) ((-378 . -242) T) ((-378 . -232) T) ((-827 . -1039) T) ((-818 . -1039) T) ((-703 . -939) 152815) ((-691 . -841) T) ((-472 . -605) 152797) ((-818 . -232) 152776) ((-133 . -841) T) ((-648 . -1087) T) ((-1173 . -596) 152755) ((-544 . -1176) 152734) ((-335 . -1087) T) ((-318 . -362) 152713) ((-406 . -146) 152692) ((-406 . -144) 152671) ((-954 . -1099) 152570) ((-239 . -890) 152502) ((-806 . -1099) 152412) ((-644 . -843) 152396) ((-477 . -596) 152375) ((-544 . -107) 152325) ((-994 . -376) 152307) ((-994 . -337) 152289) ((-97 . -1087) T) ((-954 . -23) 152100) ((-475 . -21) T) ((-475 . -25) T) ((-806 . -23) 151970) ((-1163 . -605) 151952) ((-59 . -19) 151936) ((-1163 . -606) 151858) ((-1159 . -717) T) ((-1112 . -717) T) ((-514 . -19) 151842) ((-494 . -19) 151826) ((-59 . -596) 151803) ((-1074 . -1087) T) ((-891 . -102) 151781) ((-845 . -717) T) ((-773 . -1087) T) ((-514 . -596) 151758) ((-494 . -596) 151735) ((-771 . -1087) T) ((-771 . -1053) 151702) ((-459 . -1087) T) ((-452 . -1087) T) ((-579 . -708) 151677) ((-639 . -1087) T) ((-1238 . -47) 151654) ((-1232 . -102) T) ((-1231 . -47) 151624) ((-1210 . -47) 151601) ((-1194 . -171) 151552) ((-1160 . -306) 151531) ((-994 . -890) NIL) ((-1154 . -306) 151510) ((-619 . -1099) T) ((-660 . -130) T) ((-1083 . -608) 151491) ((-1077 . -608) 151472) ((-1067 . -550) 151423) ((-1067 . -1204) 151374) ((-1061 . -608) 151355) ((-274 . -1087) T) ((-85 . -439) T) ((-85 . -394) T) ((-1054 . -608) 151336) ((-1026 . -608) 151317) ((-50 . -1087) T) ((-1009 . -608) 151298) ((-702 . -171) T) ((-588 . -47) 151275) ((-224 . -638) 151240) ((-575 . -1087) T) ((-516 . -1087) T) ((-358 . -1204) T) ((-352 . -1204) T) ((-344 . -1204) T) ((-485 . -811) T) ((-485 . -910) T) ((-318 . -1099) T) ((-108 . -1204) T) ((-705 . -1045) 151210) ((-338 . -841) T) ((-216 . -910) T) ((-216 . -811) T) ((-618 . -608) 151191) ((-358 . -550) T) ((-352 . -550) T) ((-344 . -550) T) ((-481 . -608) 151172) ((-108 . -550) T) ((-648 . -708) 151142) ((-1154 . -1012) NIL) ((-217 . -608) 151123) ((-318 . -23) T) ((-67 . -1200) T) ((-990 . -605) 151055) ((-684 . -230) 151037) ((-705 . -111) 151002) ((-635 . -34) T) ((-244 . -487) 150986) ((-1089 . -1085) 150970) ((-170 . -1087) T) ((-942 . -899) 150949) ((-513 . -608) 150933) ((-1274 . -1138) T) ((-1270 . -21) T) ((-479 . -899) 150912) ((-1270 . -25) T) ((-1268 . -130) T) ((-1266 . -130) T) ((-1259 . -102) T) ((-1242 . -605) 150878) ((-1231 . -1028) 150813) ((-1074 . -708) 150662) ((-1050 . -638) 150649) ((-942 . -638) 150574) ((-773 . -708) 150403) ((-534 . -605) 150385) ((-534 . -606) 150366) ((-771 . -708) 150215) ((-1210 . -1200) 150194) ((-1064 . -102) T) ((-380 . -25) T) ((-380 . -21) T) ((-479 . -638) 150119) ((-459 . -708) 150090) ((-452 . -708) 149939) ((-977 . -102) T) ((-1210 . -876) NIL) ((-1210 . -874) 149891) ((-1173 . -606) NIL) ((-728 . -102) T) ((-1173 . -605) 149873) ((-597 . -608) 149855) ((-1129 . -1110) 149800) ((-1036 . -1193) 149729) ((-529 . -25) T) 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. -786) T) ((-222 . -1087) T) ((-378 . -783) T) ((-224 . -785) T) ((-224 . -782) T) ((-59 . -606) 148571) ((-59 . -605) 148483) ((-224 . -717) T) ((-514 . -606) 148444) ((-514 . -605) 148356) ((-495 . -605) 148288) ((-494 . -606) 148249) ((-494 . -605) 148161) ((-1067 . -362) 148112) ((-40 . -410) 148089) ((-77 . -1200) T) ((-861 . -899) NIL) ((-358 . -328) 148073) ((-358 . -362) T) ((-352 . -328) 148057) ((-352 . -362) T) ((-344 . -328) 148041) ((-344 . -362) T) ((-315 . -283) 148020) ((-108 . -362) T) ((-70 . -1200) T) ((-1210 . -337) 147972) ((-861 . -638) 147917) ((-1210 . -376) 147869) ((-954 . -130) 147724) ((-806 . -130) 147594) ((-948 . -641) 147578) ((-1074 . -171) 147489) ((-948 . -372) 147473) ((-1050 . -785) T) ((-1050 . -782) T) ((-862 . -608) 147371) ((-773 . -171) 147262) ((-771 . -171) 147173) ((-807 . -47) 147135) ((-1050 . -717) T) ((-326 . -487) 147119) ((-942 . -717) T) ((-452 . -171) 147030) ((-244 . -285) 147007) ((-479 . -717) T) ((-1259 . -308) 146945) ((-1238 . -890) 146858) ((-1231 . -890) 146764) ((-1230 . -1045) 146599) ((-1210 . -890) 146432) ((-1209 . -1045) 146240) ((-1194 . -289) 146219) ((-1133 . -150) 146203) ((-1107 . -102) T) ((-1105 . -1087) T) ((-1067 . -23) T) ((-1062 . -102) T) ((-917 . -945) T) ((-728 . -308) 146141) ((-75 . -1200) T) ((-30 . -945) T) ((-168 . -899) 146094) ((-654 . -381) 146066) ((-112 . -835) T) ((-1 . -605) 146048) ((-1067 . -1099) T) ((-128 . -641) 146030) ((-50 . -612) 146014) ((-993 . -408) 145986) ((-588 . -890) 145899) ((-437 . -102) T) ((-140 . -308) NIL) ((-128 . -372) 145881) ((-862 . -1039) T) ((-824 . -841) 145860) ((-81 . -1200) T) ((-702 . -289) T) ((-40 . -1046) T) ((-575 . -171) T) ((-516 . -171) T) ((-509 . -605) 145842) ((-168 . -638) 145752) ((-505 . -605) 145734) ((-350 . -146) 145716) ((-350 . -144) T) ((-358 . -1099) T) ((-352 . -1099) T) ((-344 . -1099) T) ((-994 . -306) T) ((-904 . -306) T) ((-862 . -242) T) ((-108 . -1099) T) ((-862 . -232) 145695) ((-1230 . -111) 145516) ((-1209 . -111) 145305) ((-244 . -1234) 145289) ((-558 . -839) T) ((-358 . -23) T) ((-353 . -348) T) ((-315 . -308) 145276) ((-312 . -308) 145217) ((-352 . -23) T) ((-318 . -130) T) ((-344 . -23) T) ((-994 . -1012) T) ((-31 . -608) 145198) ((-108 . -23) T) ((-244 . -596) 145175) ((-1232 . -38) 145067) ((-1219 . -899) 145046) ((-112 . -1087) T) ((-1025 . -102) T) ((-1219 . -638) 144971) ((-861 . -785) NIL) ((-846 . -638) 144945) ((-861 . -782) NIL) ((-807 . -876) NIL) ((-861 . -717) T) ((-1074 . -512) 144818) ((-773 . -512) 144765) ((-771 . -512) 144717) ((-565 . -638) 144704) ((-807 . -1028) 144532) ((-452 . -512) 144475) ((-387 . -388) T) ((-1230 . -608) 144288) ((-1209 . -608) 144036) ((-60 . -1200) T) ((-613 . -841) 144015) ((-498 . -651) T) ((-1133 . -966) 143984) ((-993 . -450) T) ((-689 . -839) T) ((-508 . -783) T) ((-472 . -1045) 143819) ((-342 . -1087) T) ((-312 . -1138) NIL) ((-288 . -130) T) ((-393 . -1087) T) ((-684 . -369) 143786) ((-860 . -1046) T) ((-222 . -612) 143763) ((-326 . -285) 143740) ((-472 . -111) 143561) ((-1230 . -1039) T) ((-1209 . -1039) T) ((-807 . -376) 143545) ((-168 . -717) T) ((-644 . -102) T) ((-1230 . -242) 143524) ((-1230 . -232) 143476) ((-1209 . -232) 143381) ((-1209 . -242) 143360) ((-993 . -401) NIL) ((-660 . -631) 143308) ((-315 . -38) 143218) ((-312 . -38) 143147) ((-69 . -605) 143129) ((-318 . -491) 143095) ((-1173 . -287) 143074) ((-1100 . -1099) 142984) ((-83 . -1200) T) ((-61 . -605) 142966) ((-477 . -287) 142945) ((-1261 . -1028) 142922) ((-1151 . -1087) T) ((-1100 . -23) 142792) ((-807 . -890) 142728) ((-1219 . -717) T) ((-1089 . -1200) T) ((-472 . -608) 142554) ((-1074 . -289) 142485) ((-956 . -1087) T) ((-883 . -102) T) ((-773 . -289) 142396) ((-326 . -19) 142380) ((-59 . -287) 142357) ((-771 . -289) 142288) ((-846 . -717) T) ((-117 . -839) NIL) ((-514 . -287) 142265) ((-326 . -596) 142242) ((-494 . -287) 142219) ((-452 . -289) 142150) ((-1025 . -308) 142001) ((-671 . -488) 141982) ((-565 . -717) T) ((-666 . -488) 141963) 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139334) ((-40 . -708) 139279) ((-860 . -1087) T) ((-654 . -608) 139256) ((-636 . -608) 139237) ((-354 . -608) 139174) ((-351 . -608) 139111) ((-343 . -608) 139048) ((-326 . -606) 139009) ((-326 . -605) 138921) ((-263 . -608) 138674) ((-246 . -608) 138459) ((-1209 . -783) 138412) ((-1209 . -786) 138365) ((-250 . -376) 138334) ((-249 . -376) 138303) ((-644 . -38) 138273) ((-600 . -34) T) ((-480 . -1099) 138183) ((-473 . -34) T) ((-1100 . -130) 138053) ((-954 . -25) 137864) ((-900 . -608) 137814) ((-864 . -605) 137796) ((-954 . -21) 137751) ((-806 . -21) 137661) ((-806 . -25) 137512) ((-615 . -1046) T) ((-1165 . -550) 137491) ((-1159 . -47) 137468) ((-354 . -1039) T) ((-351 . -1039) T) ((-480 . -23) 137338) ((-343 . -1039) T) ((-246 . -1039) T) ((-263 . -1039) T) ((-1112 . -47) 137310) ((-117 . -1046) T) ((-1024 . -638) 137284) ((-948 . -34) T) ((-354 . -232) 137263) ((-354 . -242) T) ((-351 . -232) 137242) ((-351 . -242) T) ((-343 . -232) 137221) ((-343 . -242) T) ((-246 . -325) 137178) 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135982) ((-808 . -1099) T) ((-1024 . -717) T) ((-594 . -641) 135966) ((-1036 . -966) 135895) ((-989 . -102) T) ((-808 . -23) T) ((-703 . -1138) 135873) ((-684 . -1046) T) ((-594 . -372) 135857) ((-350 . -450) T) ((-342 . -289) T) ((-1247 . -1087) T) ((-247 . -1087) T) ((-398 . -102) T) ((-288 . -21) T) ((-288 . -25) T) ((-360 . -717) T) ((-701 . -1087) T) ((-689 . -1087) T) ((-360 . -471) T) ((-1194 . -605) 135839) ((-1159 . -376) 135823) ((-1112 . -376) 135807) ((-1014 . -410) 135769) ((-140 . -228) 135751) ((-378 . -785) T) ((-378 . -782) T) ((-860 . -171) T) ((-378 . -717) T) ((-702 . -605) 135733) ((-703 . -38) 135562) ((-1246 . -1244) 135546) ((-350 . -401) T) ((-1246 . -1087) 135496) ((-574 . -708) 135483) ((-558 . -708) 135470) ((-493 . -708) 135435) ((-315 . -621) 135414) ((-827 . -717) T) ((-818 . -717) T) ((-635 . -1200) T) ((-1067 . -631) 135362) ((-1159 . -890) 135305) ((-1112 . -890) 135289) ((-652 . -1045) 135273) ((-108 . -631) 135255) ((-480 . -130) 135125) ((-1165 . -1099) T) ((-942 . -47) 135094) ((-615 . -1087) T) ((-652 . -111) 135073) ((-489 . -605) 135039) ((-326 . -287) 135016) ((-479 . -47) 134973) ((-1165 . -23) T) ((-117 . -1087) T) ((-103 . -102) 134951) ((-1258 . -1099) T) ((-1043 . -130) T) ((-1014 . -1046) T) ((-810 . -1028) 134935) ((-993 . -715) 134907) ((-1258 . -23) T) ((-689 . -708) 134872) ((-579 . -605) 134854) ((-385 . -1028) 134838) ((-353 . -1046) T) ((-384 . -130) T) ((-323 . -1028) 134822) ((-224 . -876) 134804) ((-994 . -910) T) ((-91 . -34) T) ((-994 . -811) T) ((-904 . -910) T) ((-1180 . -605) 134786) ((-1107 . -819) T) ((-485 . -1204) T) ((-1092 . -1087) T) ((-1067 . -21) T) ((-1067 . -25) T) ((-216 . -1204) T) ((-989 . -308) 134751) ((-224 . -1028) 134711) ((-40 . -289) T) ((-705 . -638) 134671) ((-671 . -608) 134652) ((-666 . -608) 134633) ((-485 . -550) T) ((-476 . -608) 134614) ((-358 . -25) T) ((-358 . -21) T) ((-352 . -25) T) ((-216 . -550) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-244 . -608) 134591) ((-137 . -608) 134572) ((-136 . -608) 134553) ((-132 . -608) 134534) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1046) T) ((-574 . -171) T) ((-558 . -171) T) ((-493 . -171) T) ((-648 . -605) 134516) ((-728 . -727) 134500) ((-335 . -605) 134482) ((-68 . -382) T) ((-68 . -394) T) ((-1089 . -107) 134466) ((-1050 . -876) 134448) ((-942 . -876) 134373) ((-643 . -1099) T) ((-615 . -708) 134360) ((-479 . -876) NIL) ((-1133 . -102) T) ((-1081 . -610) 134344) ((-1050 . -1028) 134326) ((-97 . -605) 134308) ((-475 . -146) T) ((-942 . -1028) 134188) ((-117 . -708) 134133) ((-643 . -23) T) ((-479 . -1028) 134009) ((-1074 . -606) NIL) ((-1074 . -605) 133991) ((-773 . -606) NIL) ((-773 . -605) 133952) ((-771 . -606) 133586) ((-771 . -605) 133500) ((-1100 . -631) 133406) ((-459 . -605) 133388) ((-452 . -605) 133370) ((-452 . -606) 133231) ((-1025 . -228) 133177) ((-862 . -899) 133156) ((-126 . -34) T) ((-808 . -130) T) ((-639 . -605) 133138) ((-572 . -102) T) ((-354 . -1265) 133122) ((-351 . -1265) 133106) ((-343 . -1265) 133090) ((-127 . -512) 133023) ((-121 . -512) 132956) ((-509 . -783) T) ((-509 . -786) T) ((-508 . -785) T) ((-103 . -308) 132894) ((-221 . -102) 132872) ((-684 . -1087) T) ((-689 . -171) T) ((-862 . -638) 132824) ((-65 . -383) T) ((-274 . -605) 132806) ((-65 . -394) T) ((-942 . -376) 132790) ((-860 . -289) T) ((-50 . -605) 132772) ((-989 . -38) 132720) ((-575 . -605) 132702) ((-479 . -376) 132686) ((-575 . -606) 132668) ((-516 . -605) 132650) ((-900 . -1265) 132637) ((-861 . -1200) T) ((-691 . -450) T) ((-493 . -512) 132603) ((-485 . -362) T) ((-354 . -367) 132582) ((-351 . -367) 132561) ((-343 . -367) 132540) ((-705 . -717) T) ((-216 . -362) T) ((-116 . -450) T) ((-1269 . -1260) 132524) ((-861 . -874) 132501) ((-861 . -876) NIL) ((-954 . -841) 132400) ((-806 . -841) 132351) ((-644 . -646) 132335) ((-1186 . -34) T) ((-170 . -605) 132317) ((-1100 . -21) 132227) ((-1100 . -25) 132078) ((-861 . -1028) 132055) ((-942 . -890) 132036) ((-1219 . -47) 132013) 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. -1204) 129683) ((-1105 . -605) 129665) ((-312 . -839) NIL) ((-417 . -550) T) ((-224 . -306) T) ((-1209 . -782) 129618) ((-1209 . -785) 129571) ((-1230 . -717) T) ((-1209 . -717) T) ((-48 . -708) 129536) ((-224 . -1012) T) ((-350 . -1253) 129513) ((-1232 . -410) 129479) ((-709 . -717) T) ((-1219 . -890) 129422) ((-1194 . -608) 129304) ((-112 . -605) 129286) ((-112 . -606) 129268) ((-709 . -471) T) ((-702 . -608) 129218) ((-480 . -21) 129128) ((-127 . -487) 129112) ((-121 . -487) 129096) ((-480 . -25) 128947) ((-615 . -289) T) ((-579 . -1045) 128922) ((-436 . -1087) T) ((-1050 . -306) T) ((-117 . -289) T) ((-1091 . -102) T) ((-993 . -102) T) ((-579 . -111) 128890) ((-1129 . -308) 128828) ((-1194 . -1039) T) ((-1050 . -1012) T) ((-66 . -1200) T) ((-1043 . -25) T) ((-1043 . -21) T) ((-702 . -1039) T) ((-384 . -21) T) ((-384 . -25) T) ((-684 . -512) NIL) ((-1014 . -171) T) ((-702 . -242) T) ((-1050 . -543) T) ((-504 . -102) T) ((-500 . -102) T) ((-353 . -171) T) ((-342 . -605) 128810) ((-393 . -605) 128792) ((-472 . -717) T) ((-1107 . -839) T) ((-882 . -1028) 128760) ((-108 . -841) T) ((-648 . -1045) 128744) ((-485 . -130) T) ((-1232 . -1046) T) ((-216 . -130) T) ((-1143 . -102) 128722) ((-99 . -1087) T) ((-244 . -656) 128706) ((-244 . -641) 128690) ((-648 . -111) 128669) ((-579 . -608) 128653) ((-315 . -410) 128637) ((-244 . -372) 128621) ((-1146 . -234) 128568) ((-989 . -230) 128552) ((-74 . -1200) T) ((-48 . -171) T) ((-691 . -386) T) ((-691 . -142) T) ((-1269 . -102) T) ((-1180 . -608) 128534) ((-1074 . -1045) 128377) ((-263 . -899) 128356) ((-246 . -899) 128335) ((-773 . -1045) 128158) ((-771 . -1045) 128001) ((-600 . -1200) T) ((-1151 . -605) 127983) ((-1074 . -111) 127812) ((-1036 . -102) T) ((-473 . -1200) T) ((-459 . -1045) 127783) ((-452 . -1045) 127626) ((-654 . -638) 127610) ((-861 . -306) T) ((-773 . -111) 127419) ((-771 . -111) 127248) ((-354 . -638) 127200) ((-351 . -638) 127152) ((-343 . -638) 127104) ((-263 . -638) 127029) ((-246 . -638) 126954) 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-717) T) ((-351 . -717) T) ((-343 . -717) T) ((-263 . -717) T) ((-246 . -717) T) ((-1036 . -308) 124123) ((-891 . -1087) 124101) ((-50 . -1039) T) ((-1258 . -21) T) ((-1258 . -25) T) ((-1161 . -550) 124080) ((-1160 . -1204) 124059) ((-575 . -1039) T) ((-516 . -1039) T) ((-1154 . -1204) 124038) ((-360 . -1028) 124022) ((-321 . -1028) 124006) ((-1014 . -289) T) ((-378 . -876) 123988) ((-1160 . -550) 123939) ((-1154 . -550) 123890) ((-993 . -38) 123835) ((-790 . -1099) T) ((-900 . -717) T) ((-575 . -242) T) ((-575 . -232) T) ((-516 . -232) T) ((-516 . -242) T) ((-1113 . -550) 123814) ((-353 . -289) T) ((-637 . -685) 123798) ((-378 . -1028) 123758) ((-1107 . -1046) T) ((-103 . -125) 123742) ((-790 . -23) T) ((-1246 . -285) 123719) ((-406 . -308) 123684) ((-1268 . -1263) 123660) ((-1266 . -1263) 123639) ((-1232 . -1087) T) ((-860 . -605) 123621) ((-827 . -1028) 123590) ((-202 . -778) T) ((-201 . -778) T) ((-200 . -778) T) ((-199 . -778) T) ((-198 . -778) T) ((-197 . -778) T) ((-196 . -778) T) ((-195 . -778) T) ((-194 . -778) T) ((-193 . -778) T) ((-493 . -992) T) ((-273 . -830) T) ((-272 . -830) T) ((-271 . -830) T) ((-270 . -830) T) ((-48 . -289) T) ((-269 . -830) T) ((-268 . -830) T) ((-267 . -830) T) ((-192 . -778) T) ((-604 . -841) T) ((-644 . -410) 123574) ((-222 . -608) 123536) ((-110 . -841) T) ((-643 . -21) T) ((-643 . -25) T) ((-1269 . -38) 123506) ((-117 . -285) 123457) ((-1246 . -19) 123441) ((-1246 . -596) 123418) ((-1259 . -1087) T) ((-1064 . -1087) T) ((-977 . -1087) T) ((-953 . -130) T) ((-728 . -1087) T) ((-726 . -130) T) ((-706 . -130) T) ((-509 . -784) T) ((-406 . -1138) 123396) ((-451 . -130) T) ((-509 . -785) T) ((-222 . -1039) T) ((-293 . -102) 123178) ((-140 . -1087) T) ((-689 . -992) T) ((-91 . -1200) T) ((-127 . -605) 123110) ((-121 . -605) 123042) ((-1274 . -171) T) ((-1160 . -362) 123021) ((-1154 . -362) 123000) ((-315 . -1087) T) ((-417 . -130) T) ((-312 . -1087) T) ((-406 . -38) 122952) ((-1120 . -102) T) ((-1232 . -708) 122844) ((-644 . 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-874) 121303) ((-862 . -876) 121228) ((-703 . -1046) T) ((-684 . -992) NIL) ((-3 . |UnionCategory|) T) ((-1230 . -47) 121198) ((-1209 . -47) 121175) ((-1128 . -1000) 121146) ((-224 . -910) T) ((-40 . -111) 121075) ((-862 . -1028) 120939) ((-1107 . -708) 120926) ((-1092 . -605) 120908) ((-1067 . -146) 120887) ((-1067 . -144) 120838) ((-994 . -362) T) ((-318 . -1188) 120804) ((-378 . -306) T) ((-318 . -1185) 120770) ((-315 . -171) 120749) ((-312 . -171) T) ((-993 . -230) 120726) ((-904 . -362) T) ((-575 . -1265) 120713) ((-516 . -1265) 120690) ((-358 . -146) 120669) ((-358 . -144) 120620) ((-352 . -146) 120599) ((-352 . -144) 120550) ((-600 . -1176) 120526) ((-344 . -146) 120505) ((-344 . -144) 120456) ((-318 . -35) 120422) ((-473 . -1176) 120401) ((0 . |EnumerationCategory|) T) ((-318 . -95) 120367) ((-378 . -1012) T) ((-108 . -146) T) ((-108 . -144) NIL) ((-45 . -234) 120317) ((-644 . -1087) T) ((-600 . -107) 120264) ((-483 . -130) T) ((-473 . -107) 120214) ((-239 . -1099) 120124) 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. -1200) T) ((-586 . -841) T) ((-1129 . -1087) T) ((-1129 . -1042) 109564) ((-103 . -512) 109497) ((-917 . -605) 109479) ((-342 . -717) T) ((-30 . -605) 109461) ((-856 . -1087) T) ((-834 . -1046) 109440) ((-40 . -638) 109385) ((-224 . -1204) T) ((-406 . -1046) T) ((-1145 . -150) 109367) ((-989 . -289) 109318) ((-609 . -1087) T) ((-224 . -550) T) ((-318 . -1227) 109302) ((-318 . -1224) 109272) ((-1173 . -1176) 109251) ((-1062 . -605) 109233) ((-637 . -150) 109217) ((-624 . -150) 109163) ((-1173 . -107) 109113) ((-477 . -1176) 109092) ((-485 . -146) T) ((-485 . -144) NIL) ((-1107 . -606) 109007) ((-437 . -605) 108989) ((-216 . -146) T) ((-216 . -144) NIL) ((-1107 . -605) 108971) ((-129 . -102) T) ((-52 . -102) T) ((-1210 . -631) 108923) ((-477 . -107) 108873) ((-983 . -23) T) ((-1270 . -38) 108843) ((-1159 . -1099) T) ((-1112 . -1099) T) ((-1050 . -1204) T) ((-310 . -102) T) ((-845 . -1099) T) ((-942 . -1204) 108822) ((-479 . -1204) 108801) ((-722 . -841) 108780) ((-1050 . -550) T) 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108138) ((-861 . -1204) T) ((-644 . -605) 108120) ((-861 . -550) T) ((-684 . -367) NIL) ((-1274 . -608) 108102) ((-358 . -1253) 108086) ((-660 . -102) T) ((-352 . -1253) 108070) ((-344 . -1253) 108054) ((-1269 . -1087) T) ((-518 . -841) 108033) ((-808 . -450) 108012) ((-1036 . -1087) T) ((-1036 . -1059) 107941) ((-1017 . -966) 107910) ((-810 . -1099) T) ((-993 . -708) 107855) ((-385 . -1099) T) ((-474 . -966) 107824) ((-461 . -966) 107793) ((-110 . -150) 107775) ((-73 . -605) 107757) ((-883 . -605) 107739) ((-1067 . -715) 107718) ((-1274 . -1039) T) ((-807 . -631) 107666) ((-293 . -1046) 107608) ((-168 . -1204) 107513) ((-224 . -1099) T) ((-323 . -23) T) ((-1154 . -982) 107465) ((-834 . -1087) T) ((-1232 . -1045) 107370) ((-1113 . -731) 107349) ((-1230 . -910) 107328) ((-1209 . -910) 107307) ((-860 . -717) T) ((-168 . -550) 107218) ((-574 . -638) 107205) ((-558 . -638) 107192) ((-406 . -1087) T) ((-262 . -1087) T) ((-212 . -605) 107174) ((-493 . -638) 107139) ((-224 . -23) T) ((-1209 . 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. -608) 103932) ((-312 . -608) 103815) ((-639 . -1028) 103799) ((-619 . -102) T) ((-221 . -487) 103783) ((-1246 . -34) T) ((-135 . -608) 103767) ((-627 . -708) 103751) ((-599 . -708) 103735) ((-660 . -38) 103695) ((-318 . -102) T) ((-85 . -605) 103677) ((-50 . -1028) 103661) ((-1107 . -1045) 103648) ((-1074 . -376) 103632) ((-773 . -376) 103616) ((-60 . -57) 103578) ((-689 . -785) T) ((-689 . -782) T) ((-575 . -1028) 103565) ((-516 . -1028) 103542) ((-689 . -717) T) ((-323 . -130) T) ((-315 . -1039) 103432) ((-312 . -1039) T) ((-168 . -1099) T) ((-771 . -376) 103416) ((-45 . -150) 103366) ((-994 . -982) 103348) ((-452 . -376) 103332) ((-406 . -171) T) ((-315 . -242) 103311) ((-312 . -242) T) ((-312 . -232) NIL) ((-293 . -1087) 103093) ((-224 . -130) T) ((-1107 . -111) 103078) ((-168 . -23) T) ((-790 . -146) 103057) ((-790 . -144) 103036) ((-250 . -631) 102942) ((-249 . -631) 102848) ((-318 . -283) 102814) ((-1143 . -512) 102747) ((-1120 . -1087) T) ((-224 . -1048) T) ((-806 . -308) 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-102) T) ((-1143 . -606) 94624) ((-1143 . -605) 94556) ((-1159 . -841) 94535) ((-45 . -102) T) ((-1112 . -841) 94514) ((-808 . -102) T) ((-1219 . -25) T) ((-1219 . -21) T) ((-846 . -25) T) ((-44 . -366) 94498) ((-846 . -21) T) ((-722 . -450) 94449) ((-1269 . -605) 94431) ((-1043 . -308) 94369) ((-661 . -1070) T) ((-598 . -1070) T) ((-389 . -1087) T) ((-565 . -25) T) ((-565 . -21) T) ((-179 . -1070) T) ((-160 . -1070) T) ((-155 . -1070) T) ((-153 . -1070) T) ((-613 . -1087) T) ((-689 . -876) 94351) ((-1246 . -1200) T) ((-226 . -308) 94289) ((-143 . -367) T) ((-1036 . -606) 94231) ((-1036 . -605) 94174) ((-312 . -899) NIL) ((-689 . -1028) 94119) ((-702 . -910) T) ((-472 . -1204) 94098) ((-1160 . -450) 94077) ((-1154 . -450) 94056) ((-329 . -102) T) ((-862 . -1099) T) ((-315 . -638) 93877) ((-312 . -638) 93806) ((-472 . -550) 93757) ((-338 . -512) 93723) ((-544 . -150) 93673) ((-40 . -306) T) ((-834 . -605) 93655) ((-691 . -289) T) ((-862 . -23) T) ((-378 . -491) T) ((-1067 . -230) 93625) 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. -95) 92352) ((-1231 . -35) 92318) ((-1230 . -1099) T) ((-1107 . -638) 92305) ((-1210 . -95) 92271) ((-1209 . -1099) T) ((-586 . -150) 92253) ((-1067 . -348) 92232) ((-173 . -289) T) ((-117 . -376) 92209) ((-117 . -337) 92186) ((-1210 . -35) 92152) ((-860 . -306) T) ((-312 . -785) NIL) ((-312 . -782) NIL) ((-315 . -717) 92001) ((-312 . -717) T) ((-472 . -362) 91980) ((-358 . -348) 91959) ((-352 . -348) 91938) ((-344 . -348) 91917) ((-315 . -471) 91896) ((-1230 . -23) T) ((-1209 . -23) T) ((-709 . -1099) T) ((-705 . -130) T) ((-643 . -102) T) ((-475 . -708) 91861) ((-45 . -281) 91811) ((-105 . -1087) T) ((-68 . -605) 91793) ((-960 . -102) T) ((-855 . -102) T) ((-615 . -890) 91752) ((-1270 . -1087) T) ((-380 . -1087) T) ((-1199 . -1087) T) ((-1100 . -230) 91721) ((-82 . -1200) T) ((-1050 . -841) T) ((-942 . -841) 91700) ((-117 . -890) NIL) ((-773 . -910) 91679) ((-704 . -841) T) ((-529 . -1087) T) ((-498 . -1087) T) ((-354 . -1204) T) ((-351 . -1204) T) ((-343 . -1204) T) ((-263 . -1204) 91658) ((-246 . -1204) 91637) ((-531 . -851) T) ((-479 . -841) 91616) ((-1145 . -819) T) ((-1129 . -1045) 91600) ((-389 . -752) T) ((-684 . -1200) T) ((-681 . -1028) 91584) ((-354 . -550) T) ((-351 . -550) T) ((-343 . -550) T) ((-263 . -550) 91515) ((-246 . -550) 91446) ((-523 . -1070) T) ((-1129 . -111) 91425) ((-451 . -735) 91395) ((-856 . -1045) 91365) ((-808 . -38) 91307) ((-684 . -874) 91289) ((-684 . -876) 91271) ((-294 . -308) 91075) ((-900 . -1204) T) ((-660 . -410) 91059) ((-856 . -111) 91024) ((-684 . -1028) 90969) ((-994 . -450) T) ((-900 . -550) T) ((-531 . -605) 90951) ((-575 . -910) T) ((-472 . -1099) T) ((-516 . -910) T) ((-1143 . -287) 90928) ((-904 . -450) T) ((-65 . -605) 90910) ((-624 . -228) 90856) ((-472 . -23) T) ((-1107 . -785) T) ((-862 . -130) T) ((-1107 . -782) T) ((-1261 . -1263) 90835) ((-1107 . -717) T) ((-644 . -638) 90809) ((-293 . -605) 90550) ((-1129 . -608) 90468) ((-1025 . -34) T) ((-806 . -839) 90447) ((-574 . -306) T) ((-558 . -306) T) ((-493 . -306) T) ((-1270 . -708) 90417) ((-684 . -376) 90399) ((-684 . -337) 90381) ((-475 . -171) T) ((-380 . -708) 90351) ((-856 . -608) 90286) ((-861 . -841) NIL) ((-558 . -1012) T) ((-493 . -1012) T) ((-1120 . -605) 90268) ((-1100 . -237) 90247) ((-213 . -102) T) ((-1137 . -102) T) ((-71 . -605) 90229) ((-1129 . -1039) T) ((-1165 . -38) 90126) ((-849 . -605) 90108) ((-558 . -543) T) ((-660 . -1046) T) ((-722 . -939) 90061) ((-1129 . -232) 90040) ((-1069 . -1087) T) ((-1024 . -25) T) ((-1024 . -21) T) ((-993 . -1045) 89985) ((-895 . -102) T) ((-856 . -1039) T) ((-684 . -890) NIL) ((-354 . -328) 89969) ((-354 . -362) T) ((-351 . -328) 89953) ((-351 . -362) T) ((-343 . -328) 89937) ((-343 . -362) T) ((-485 . -102) T) ((-1258 . -38) 89907) ((-521 . -677) 89857) ((-216 . -102) T) ((-1014 . -1028) 89737) ((-993 . -111) 89666) ((-1161 . -963) 89635) ((-1160 . -963) 89597) ((-518 . -150) 89581) ((-1067 . -369) 89560) ((-350 . -605) 89542) ((-321 . -21) T) ((-353 . -1028) 89519) ((-321 . -25) T) 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-1138) T) ((-1160 . -1229) 87611) ((-1160 . -1224) 87581) ((-1160 . -1227) 87565) ((-216 . -1138) T) ((-342 . -910) T) ((-809 . -265) 87549) ((-627 . -111) 87528) ((-599 . -111) 87507) ((-1154 . -1208) 87468) ((-834 . -1039) 87447) ((-1154 . -1224) 87424) ((-513 . -25) T) ((-493 . -301) T) ((-509 . -23) T) ((-508 . -25) T) ((-506 . -25) T) ((-505 . -23) T) ((-1154 . -1206) 87408) ((-406 . -1039) T) ((-318 . -1046) T) ((-684 . -306) T) ((-108 . -839) T) ((-703 . -717) T) ((-406 . -242) T) ((-406 . -232) 87387) ((-485 . -38) 87337) ((-216 . -38) 87287) ((-472 . -491) 87253) ((-1145 . -1131) T) ((-1088 . -102) T) ((-691 . -605) 87235) ((-691 . -606) 87150) ((-705 . -21) T) ((-705 . -25) T) ((-1122 . -102) T) ((-133 . -605) 87132) ((-116 . -605) 87114) ((-156 . -25) T) ((-1268 . -1087) T) ((-862 . -631) 87062) ((-1266 . -1087) T) ((-953 . -102) T) ((-726 . -102) T) ((-706 . -102) T) ((-451 . -102) T) ((-807 . -450) 87013) ((-44 . -1087) T) ((-1075 . -841) T) ((-654 . -130) T) ((-1051 . 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82840) ((-389 . -605) 82822) ((-508 . -841) T) ((-1137 . -228) 82772) ((-1238 . -1237) 82756) ((-1238 . -1224) 82733) ((-1231 . -1229) 82694) ((-1231 . -1224) 82664) ((-1231 . -1227) 82648) ((-1210 . -1208) 82609) ((-1210 . -1224) 82586) ((-613 . -605) 82568) ((-1210 . -1206) 82552) ((-689 . -910) T) ((-1161 . -283) 82518) ((-1160 . -283) 82484) ((-1154 . -283) 82450) ((-1067 . -1087) T) ((-1049 . -1087) T) ((-48 . -301) T) ((-315 . -890) 82416) ((-312 . -890) NIL) ((-1049 . -1056) 82395) ((-1107 . -876) 82377) ((-790 . -38) 82361) ((-263 . -631) 82309) ((-246 . -631) 82257) ((-691 . -1045) 82244) ((-588 . -1224) 82221) ((-1113 . -283) 82187) ((-318 . -171) 82118) ((-358 . -1087) T) ((-352 . -1087) T) ((-344 . -1087) T) ((-498 . -19) 82100) ((-1107 . -1028) 82082) ((-1089 . -150) 82066) ((-108 . -1087) T) ((-116 . -1045) 82053) ((-702 . -362) T) ((-498 . -596) 82028) ((-691 . -111) 82013) ((-435 . -102) T) ((-45 . -1136) 81963) ((-116 . -111) 81948) ((-627 . -711) T) ((-599 . -711) T) 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-841) T) ((-1100 . -171) 76681) ((-1107 . -1012) T) ((-1036 . -34) T) ((-827 . -146) 76660) ((-827 . -144) 76639) ((-728 . -107) 76623) ((-604 . -131) T) ((-480 . -1087) 76413) ((-1165 . -1046) T) ((-861 . -450) T) ((-85 . -1200) T) ((-239 . -38) 76383) ((-140 . -107) 76365) ((-703 . -376) 76349) ((-824 . -608) 76217) ((-1107 . -543) T) ((-573 . -102) T) ((-129 . -488) 76199) ((-389 . -1045) 76183) ((-1269 . -717) T) ((-1159 . -939) 76152) ((-129 . -605) 76119) ((-52 . -605) 76101) ((-1112 . -939) 76068) ((-643 . -410) 76052) ((-1258 . -1046) T) ((-613 . -1045) 76036) ((-652 . -25) T) ((-652 . -21) T) ((-1145 . -512) NIL) ((-1238 . -102) T) ((-1231 . -102) T) ((-389 . -111) 76015) ((-221 . -253) 75999) ((-1210 . -102) T) ((-1043 . -1087) T) ((-994 . -1138) T) ((-1043 . -1042) 75939) ((-809 . -1087) T) ((-342 . -1204) T) ((-627 . -638) 75923) ((-613 . -111) 75902) ((-599 . -638) 75886) ((-589 . -102) T) ((-310 . -488) 75867) ((-579 . -130) T) ((-588 . -102) T) ((-413 . -1087) T) ((-384 . -1087) T) ((-310 . -605) 75833) ((-226 . -1087) 75811) ((-637 . -512) 75744) ((-624 . -512) 75588) ((-824 . -1039) 75567) ((-635 . -150) 75551) ((-342 . -550) T) ((-703 . -890) 75494) ((-544 . -228) 75444) ((-1238 . -283) 75410) ((-1067 . -289) 75361) ((-485 . -839) T) ((-222 . -1099) T) ((-1231 . -283) 75327) ((-1210 . -283) 75293) ((-994 . -38) 75243) ((-216 . -839) T) ((-1194 . -491) 75209) ((-904 . -38) 75161) ((-834 . -785) 75140) ((-834 . -782) 75119) ((-834 . -717) 75098) ((-358 . -289) T) ((-352 . -289) T) ((-344 . -289) T) ((-168 . -450) 75029) ((-426 . -38) 75013) ((-108 . -289) T) ((-222 . -23) T) ((-406 . -785) 74992) ((-406 . -782) 74971) ((-406 . -717) T) ((-498 . -287) 74946) ((-475 . -1045) 74911) ((-648 . -130) T) ((-613 . -608) 74880) ((-1100 . -512) 74813) ((-335 . -130) T) ((-168 . -401) 74792) ((-480 . -708) 74734) ((-806 . -285) 74711) ((-475 . -111) 74667) ((-643 . -1046) T) ((-1219 . -450) 74598) ((-1257 . -1070) T) ((-1256 . -1070) T) ((-1074 . -130) T) 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. -102) T) ((-330 . -605) 23345) ((-1100 . -1028) 23172) ((-586 . -641) 23154) ((-128 . -1087) T) ((-586 . -372) 23136) ((-342 . -1253) 23113) ((-1017 . -1200) T) ((-861 . -289) T) ((-1219 . -512) 23060) ((-474 . -1200) T) ((-461 . -1200) T) ((-579 . -102) T) ((-1159 . -285) 22987) ((-615 . -450) 22966) ((-990 . -985) 22950) ((-1261 . -381) 22922) ((-515 . -1087) T) ((-117 . -450) T) ((-1180 . -102) T) ((-1079 . -1087) 22900) ((-1024 . -1087) T) ((-1102 . -93) T) ((-883 . -841) T) ((-350 . -1204) T) ((-1238 . -1045) 22783) ((-1100 . -376) 22752) ((-1231 . -1045) 22587) ((-1210 . -1045) 22377) ((-1238 . -111) 22246) ((-1231 . -111) 22067) ((-1210 . -111) 21836) ((-1194 . -308) 21823) ((-350 . -550) T) ((-364 . -605) 21805) ((-288 . -306) T) ((-589 . -1045) 21778) ((-588 . -1045) 21661) ((-360 . -1087) T) ((-321 . -1087) T) ((-250 . -605) 21622) ((-249 . -605) 21583) ((-993 . -130) T) ((-627 . -23) T) ((-684 . -408) 21550) ((-599 . -23) T) ((-648 . -102) T) ((-589 . -111) 21521) ((-588 . 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. -38) 16029) ((-807 . -232) 16008) ((-773 . -38) 15837) ((-771 . -38) 15686) ((-1102 . -488) 15667) ((-452 . -38) 15516) ((-1102 . -605) 15482) ((-1105 . -102) T) ((-635 . -606) 15443) ((-635 . -605) 15355) ((-575 . -1138) T) ((-516 . -1138) T) ((-1134 . -487) 15339) ((-1186 . -1087) 15317) ((-1129 . -25) T) ((-1129 . -21) T) ((-1261 . -608) 15266) ((-472 . -1046) T) ((-1210 . -783) NIL) ((-1210 . -786) NIL) ((-989 . -841) 15245) ((-829 . -1087) T) ((-810 . -605) 15227) ((-856 . -21) T) ((-856 . -25) T) ((-790 . -717) T) ((-173 . -1204) T) ((-575 . -38) 15192) ((-516 . -38) 15157) ((-385 . -605) 15139) ((-323 . -605) 15121) ((-168 . -285) 15079) ((-63 . -1200) T) ((-112 . -102) T) ((-862 . -1087) T) ((-173 . -550) T) ((-705 . -708) 15049) ((-293 . -130) 14932) ((-224 . -605) 14914) ((-224 . -606) 14844) ((-993 . -631) 14783) ((-1261 . -1039) T) ((-1107 . -146) T) ((-624 . -1176) 14758) ((-722 . -899) 14737) ((-586 . -34) T) ((-637 . -107) 14721) ((-624 . -107) 14667) ((-1219 . -285) 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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 1b7e849c..f5a3efbe 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3439752253) -(4385 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3440274379) +(4386 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -474,655 +474,659 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |duplicates?| |exactQuotient!| |nextSublist| - |tanh2trigh| |patternVariable| |hi| |decreasePrecision| - |solveLinearPolynomialEquation| |intersect| - |removeRoughlyRedundantFactorsInContents| |coefficients| |associates?| - |prod| |indicialEquations| |pToDmp| |countable?| |permutation| |prime| - |s13adf| |moduloP| |asechIfCan| |atom?| |push!| |selectFiniteRoutines| - |maxdeg| |rightRecip| |readByteIfCan!| |pToHdmp| |karatsubaDivide| - |setColumn!| |constantRight| |delta| |cycle| |ParCond| |meatAxe| - |second| |capacity| |toroidal| |stopTable!| |f04adf| |fortran| - |validExponential| |OMgetEndError| |iCompose| |OMread| |OMgetApp| - |third| |rightTrace| |coerceImages| |components| |definingPolynomial| - |coord| |solveLinearPolynomialEquationByFractions| |tValues| - |roughBase?| |sample| |datalist| |lcm| |doublyTransitive?| |extract!| - |fibonacci| |recolor| |cap| |stop| |block| |enterInCache| - |factorAndSplit| |linearAssociatedLog| |interReduce| |saturate| - |internalLastSubResultant| |normalElement| |dioSolve| |physicalLength| - |degreeSubResultant| |clikeUniv| |inc| |denomLODE| |append| |red| - |generalizedContinuumHypothesisAssumed| |findBinding| |df2ef| - |rootProduct| |unitNormalize| |degreePartition| |computePowers| - |redPol| |nil| |gcd| |expressIdealMember| |repeatUntilLoop| |expint| - |iidsum| |left| |presuper| |initiallyReduce| |getGraph| |eigenvectors| - |s17ahf| |false| |resultant| |lastSubResultantEuclidean| - |leftFactorIfCan| |fixedDivisor| |completeEchelonBasis| |isobaric?| - |formula| |lambda| |createGenericMatrix| |symmetric?| |right| - |subResultantsChain| |buildSyntax| |mantissa| |genericRightTrace| - |f01brf| |besselY| |represents| |largest| |approximate| - |rightQuotient| |totalDegree| |readLineIfCan!| |setPredicates| |bat1| - |mdeg| |UnVectorise| |halfExtendedResultant2| |s21bdf| |complex| - |laplacian| |tanAn| |mainVariable| |squareFree| |depth| |addPoint2| - |sayLength| |precision| |rewriteSetWithReduction| |quasiRegular?| - |cubic| |BumInSepFFE| |mkIntegral| |stoseLastSubResultant| - |addPointLast| |drawCurves| |curve| |#| |e01bff| |figureUnits| - |ScanRoman| |pointSizeDefault| |nrows| |conjugates| - |exprHasAlgebraicWeight| |internalIntegrate| |s17akf| |generators| - |OMencodingXML| |measure2Result| |close| |antiCommutator| - |solveLinearlyOverQ| |packageCall| |ncols| |contractSolve| - |approximants| |OMputVariable| |getSyntaxFormsFromFile| |surface| |mr| - |associatedSystem| |digit| |integralMatrix| |primitiveElement| - |showSummary| |script| |host| |constantIfCan| |showClipRegion| - |topFortranOutputStack| |expintfldpoly| |remove| |display| - |OMgetFloat| |safetyMargin| |roughUnitIdeal?| |cSec| BY |exponent| - |critMTonD1| |ratDsolve| |enqueue!| |possiblyInfinite?| |f07adf| - |chvar| |power!| |npcoef| |showAttributes| |headReduced?| - |reciprocalPolynomial| |musserTrials| |monomialIntegrate| - |pseudoRemainder| |last| |listConjugateBases| |pointPlot| - |defineProperty| |product| |tex| |xn| |minPoly| |oddlambert| - |leftPower| |sylvesterSequence| |assoc| |gcdPrimitive| - |computeCycleLength| |trailingCoefficient| |ellipticCylindrical| - |mkAnswer| |critpOrder| |quoted?| |e02aef| |initials| - |viewThetaDefault| |singRicDE| |subresultantSequence| |empty?| - |mapMatrixIfCan| |sech2cosh| |getMatch| |symbol| |representationType| - |rationalApproximation| |expPot| |input| |eigenvector| - |branchPointAtInfinity?| |iicot| |expenseOfEvaluationIF| - |FormatArabic| |notOperand| |expression| |medialSet| |complement| - |selectSumOfSquaresRoutines| |digit?| |library| |internalInfRittWu?| - |printInfo| |conditionsForIdempotents| |preprocess| |iisinh| - |pointColorPalette| |doubleComplex?| |cCosh| |mainCoefficients| - |integer| |solid| |e02zaf| |cAcot| |hasoln| |quasiMonic?| |romberg| - |sin?| |binding| |leftRankPolynomial| |relerror| |taylorIfCan| - |printInfo!| |mainKernel| |extractSplittingLeaf| |or?| |substring?| - |ReduceOrder| |factorSFBRlcUnit| |univariate?| |lifting| - |splitDenominator| |label| |any| |laurentRep| |iiasinh| |isPlus| - |setStatus| |minPoints| |logGamma| |bumprow| |close!| |removeZeroes| - |set| |bubbleSort!| |OMputObject| |wordInGenerators| |getProperties| - |genericLeftDiscriminant| |d02cjf| |node?| |rule| |blankSeparate| - |normalForm| |comp| |debug3D| |leftRank| |associator| - |algebraicDecompose| |iteratedInitials| |children| |unmakeSUP| - |divideIfCan!| |lazyPseudoQuotient| |iiexp| |changeThreshhold| - |extensionDegree| |nextSubsetGray| |numericalIntegration| - |realElementary| |groebSolve| |rightRegularRepresentation| - |changeBase| |f02bbf| |headAst| |nodes| |singularitiesOf| |expIfCan| - |ip4Address| |minPoints3D| |cyclePartition| |relativeApprox| |coth| - |extractTop!| |euclideanSize| |internal?| |palgRDE0| |basisOfCenter| - |euclideanGroebner| |bit?| |noKaratsuba| |meshPar1Var| |list| |sech| - |froot| |morphism| |commutativeEquality| |numberOfDivisors| |say| - |constructor| |ideal| |plenaryPower| |polyred| |mathieu11| - |graphCurves| |car| |csch| |pushup| |primextintfrac| - |numberOfFractionalTerms| |getDatabase| |unary?| |e04naf| |move| - |genericRightMinimalPolynomial| |cdr| |asinh| |subscriptedVariables| - |s14baf| |void| |makeViewport3D| |numeric| |addiag| |imports| - |setDifference| |showAll?| |ptFunc| |listYoungTableaus| |acosh| - |option| |ffactor| |df2fi| |notelem| |radical| |monicRightDivide| - |nullary?| |setIntersection| |pair?| |const| |lazyPrem| |atanh| - |identitySquareMatrix| |palglimint| |hash| |findCycle| - |nextNormalPrimitivePoly| |vedf2vef| |beauzamyBound| |setUnion| - |OMUnknownSymbol?| |algebraicVariables| |acoth| |count| |show| - |e02bef| |compound?| |tanintegrate| |getMultiplicationTable| |s21baf| - |clearTheIFTable| |OMUnknownCD?| |apply| |asech| |factorList| = - |inrootof| |callForm?| |rdregime| |OMgetEndApp| - |semiIndiceSubResultantEuclidean| |unravel| |explicitlyFinite?| - |partialFraction| |trace| |transpose| |cross| |commutative?| - |readable?| |size| |subSet| |stopTableGcd!| |lineColorDefault| - |multiple| < |head| |reducedContinuedFraction| |s17dhf| - |symmetricPower| |imaginary| |mergeDifference| |applyQuote| |repSq| > - |shallowExpand| |cExp| |triangular?| |rootRadius| |frobenius| - |rightTrim| |LazardQuotient| |toseSquareFreePart| <= |cyclicCopy| - |write!| |permutationRepresentation| |trivialIdeal?| |completeEval| - |removeZero| |modTree| |leftTrim| |symmetricGroup| |first| >= - |pushdown| |length| |changeNameToObjf| |irreducibleFactors| - |LowTriBddDenomInv| |e01daf| |schema| |iflist2Result| - |subResultantChain| |rest| |ruleset| |initTable!| |scripts| - |choosemon| |antisymmetric?| |deriv| |lepol| |substitute| - |setAdaptive3D| |laurentIfCan| |virtualDegree| |mappingAst| - |composites| |stoseIntegralLastSubResultant| |readIfCan!| - |removeDuplicates| |iisin| |diagonals| |pleskenSplit| + - |removeRedundantFactorsInPols| |mainMonomial| |coth2tanh| |generate| - |quasiMonicPolynomials| |expandLog| |reopen!| |f02fjf| |suchThat| - - |unvectorise| |s14abf| |FormatRoman| |matrixConcat3D| - |mapUnivariateIfCan| |nativeModuleExtension| |pattern| |zero| / - |plotPolar| |e02bdf| |updateStatus!| |squareFreeFactors| |incrementBy| - |finiteBasis| |characteristicSet| |OMputEndAtp| |dequeue!| |f02axf| - |iicsch| |tanQ| |s13aaf| |expand| |convergents| |divideIfCan| - |bezoutMatrix| |OMputSymbol| |And| |viewPhiDefault| |squareMatrix| - |empty| |showScalarValues| |filterWhile| |prinb| |positiveRemainder| - |algDsolve| |cyclicParents| |e01bef| |Or| |distance| |changeMeasure| - |filterUntil| |testDim| |mainMonomials| |cPower| |squareFreePart| - |message| |Not| |qroot| |traverse| |birth| |GospersMethod| - |getGoodPrime| |select| |antiAssociative?| |getRef| |universe| - |primintfldpoly| |leftExtendedGcd| |sqfree| |tensorProduct| |s21bcf| - |controlPanel| |nthFactor| |removeSuperfluousQuasiComponents| - |internalAugment| |nil?| |intermediateResultsIF| |extendedEuclidean| - |padicallyExpand| |digits| |palglimint0| |OMwrite| |edf2ef| |makeFR| - |compiledFunction| |badValues| |varList| |iitanh| |double?| |omError| - |subspace| |f02xef| |infiniteProduct| |getMultiplicationMatrix| - |evenlambert| |getOperator| |loopPoints| |zeroSquareMatrix| |elem?| - |nullity| |negative?| |style| |atrapezoidal| |rangePascalTriangle| - |cons| |OMgetObject| |outputBinaryFile| |bumptab1| |graphImage| - |polygon?| |delay| |prevPrime| |cAcoth| |removeSuperfluousCases| - |retract| |rischNormalize| |fglmIfCan| |selectNonFiniteRoutines| - |lazyPquo| |s19adf| |socf2socdf| |stoseInvertibleSetsqfreg| - |expintegrate| |compdegd| |coerceP| |setMinPoints3D| |jacobiIdentity?| - |modifyPoint| |matrix| |iisqrt3| |basisOfRightAnnihilator| - |numberOfIrreduciblePoly| |definingEquations| |rur| - |genericLeftMinimalPolynomial| |doubleDisc| |useEisensteinCriterion| - |rotate!| |sort| |completeSmith| |palgextint| |limitedIntegrate| - |matrixDimensions| |parent| |indiceSubResultantEuclidean| |resize| - |iomode| |shiftRoots| |rk4a| |outputFixed| |extension| |sumOfSquares| - |wrregime| |cAsinh| |imagI| |createLowComplexityNormalBasis| - |removeIrreducibleRedundantFactors| |internalSubPolSet?| |magnitude| - |graphState| |f01rcf| |setScreenResolution3D| |linSolve| |status| - |source| |scripted?| |createLowComplexityTable| |normDeriv2| |subst| - |sinh2csch| |s17dgf| |optpair| |leftUnit| |listBranches| - |checkForZero| |box| |slex| |bindings| |terms| |backOldPos| |random| - |quadratic?| |cLog| |quadratic| |endOfFile?| |d02bhf| |monomRDE| - |log2| |lazyPremWithDefault| |c06fuf| |increase| |f02aef| |dequeue| - |numberOfComposites| |gcdcofact| |permanent| |localAbs| |extendIfCan| - |LyndonCoordinates| |ptree| |noncommutativeJordanAlgebra?| - |interpretString| |coshIfCan| |compose| |linearMatrix| |limitedint| - |scan| |outlineRender| |subNode?| |hyperelliptic| |color| |escape| - |monicLeftDivide| |plus| |f02aaf| |OMputInteger| |e02adf| |isOpen?| - |obj| |iiasin| |f2st| |generateIrredPoly| - |rewriteIdealWithQuasiMonicGenerators| |purelyTranscendental?| - |associatorDependence| |constantCoefficientRicDE| |basisOfNucleus| - |recur| |cache| |objects| |setLabelValue| |showTheFTable| |module| - |lyndonIfCan| |keys| |poisson| |dihedralGroup| |rCoord| |OMReadError?| - |toseInvertibleSet| |parents| |base| |extractBottom!| |mainVariables| - |linear?| |symmetricRemainder| |s01eaf| |fracPart| |iiGamma| - |basisOfMiddleNucleus| |testModulus| |oddintegers| |summation| - |partialNumerators| |interval| |setValue!| |polarCoordinates| |paren| - |sechIfCan| |times| |drawStyle| |deleteProperty!| |iiacsc| - |separateFactors| |binaryFunction| |isQuotient| |signatureAst| |node| - |generalizedInverse| |normal01| |rootSplit| |myDegree| |bernoulli| - |key| |outputAsTex| |karatsuba| |processTemplate| |OMputApp| |root| - |list?| |minGbasis| |meshFun2Var| |high| |lflimitedint| - |quadraticForm| |antiCommutative?| |curryRight| |e02akf| |adaptive?| - |maxColIndex| |coHeight| |filename| |mainForm| |nand| |diagonal| - |reduceBasisAtInfinity| |binary| |unitCanonical| |symbolTable| |row| - |selectAndPolynomials| |setEpilogue!| |monom| |char| |inspect| |not?| - |subMatrix| |concat!| |finite?| |cot2tan| |minordet| |hostPlatform| - |upperCase?| |setTex!| |setButtonValue| |entry?| |parse| |Ei| - |OMlistSymbols| |height| |cfirst| |constantLeft| |showTheIFTable| - |matrixGcd| |numberOfCycles| |pdct| |cCoth| |cscIfCan| |OMgetType| - |characteristicSerie| |common| |OMreadFile| |shallowCopy| |members| - |multiset| |flexible?| |dec| |pushucoef| |OMgetEndAttr| - |indiceSubResultant| |llprop| |coerceS| |reverseLex| |weight| - |toseInvertible?| |approxNthRoot| |vspace| |exponential| |zerosOf| - |region| |extractIfCan| |showTypeInOutput| |null| |collectQuasiMonic| - |innerEigenvectors| |youngGroup| |previous| |float| |intcompBasis| - |compBound| |increment| |exponentialOrder| |zag| |nonSingularModel| - |c05pbf| |not| |lazyVariations| |makeVariable| |LazardQuotient2| - |groebnerFactorize| |mainContent| |lazyResidueClass| - |chainSubResultants| |typeLists| |and| |less?| |realSolve| |updatD| - |gcdPolynomial| |tail| |yellow| |alternating| |integralAtInfinity?| - |copy!| |d02bbf| |setleft!| |s18adf| |or| |mapDown!| |mapUp!| - |normalizedAssociate| |highCommonTerms| |legendreP| |orOperands| - |minRowIndex| |raisePolynomial| |pushFortranOutputStack| |xor| - |stoseInternalLastSubResultant| |binaryTree| |fortranCarriageReturn| - |messagePrint| |ratPoly| |Lazard| |critM| |expandPower| - |sizeMultiplication| |popFortranOutputStack| |case| - |resultantReduitEuclidean| |numFunEvals3D| |startTableGcd!| |dihedral| - |createZechTable| |fortranDouble| |characteristic| |changeName| - |usingTable?| |equation| |Zero| |OMgetError| |diagonal?| |lowerCase?| - |iiasech| |prefixRagits| |OMbindTCP| |operator| |nonQsign| - |localReal?| |split!| |One| |extractClosed| |readLine!| |invertible?| - |invertibleElseSplit?| |index| |randnum| |isOp| |acoshIfCan| - |numerators| |divisor| |prinpolINFO| |cosh2sech| |bitTruth| |equiv?| - |elRow1!| |applyRules| |lastSubResultant| |doubleRank| - |leadingCoefficientRicDE| |RittWuCompare| |currentCategoryFrame| - |f04mbf| |viewport2D| |union| |cosIfCan| |tableau| |unitVector| - |getStream| |symmetricProduct| |leftZero| |weierstrass| |contains?| - |squareFreePolynomial| |deref| |pair| |option?| |mathieu24| |factors| - |getCurve| |li| |numericIfCan| |polygamma| |scalarTypeOf| |f01qcf| - |wordsForStrongGenerators| |selectfirst| |perspective| |arity| - |string?| GF2FG |hasSolution?| |elt| |d01fcf| |cycleEntry| |upperCase| - |hex| |linearlyDependent?| |recoverAfterFail| |generalLambert| - |overlap| |lex| |s20adf| |invmultisect| |explogs2trigs| - |expandTrigProducts| |pascalTriangle| |factorByRecursion| |printCode| - |stopMusserTrials| |curveColor| |numberOfOperations| |bounds| - |decimal| |lexico| |comparison| |mapUnivariate| |leadingTerm| - |lambert| |iiacoth| |pmComplexintegrate| |doubleFloatFormat| |suffix?| - |useSingleFactorBound?| |d01apf| |fortranCharacter| |extendedint| - |radPoly| |value| |mix| |tubePointsDefault| |tubeRadiusDefault| - |bfKeys| |pastel| |integrate| |genericLeftTrace| |lexTriangular| - |imagk| |semiSubResultantGcdEuclidean1| |iicsc| |prefix?| |rightGcd| - |extend| |showArrayValues| |deepCopy| - |setLegalFortranSourceExtensions| |elColumn2!| |totalDifferential| - |countRealRoots| |PollardSmallFactor| |exprToXXP| |newReduc| - |leftTraceMatrix| |imagJ| |cAcosh| |pile| |derivative| |d01bbf| |init| - |e01baf| |viewWriteAvailable| |localIntegralBasis| |nilFactor| - |subscript| |insertRoot!| |iibinom| |predicate| |float?| |setEmpty!| - |integers| |computeInt| |UpTriBddDenomInv| |thenBranch| |outputArgs| - |cyclotomicFactorization| |rangeIsFinite| |test| |permutationGroup| - |domainOf| |ddFact| |mpsode| |univariateSolve| |e02ajf| |pade| - |splitConstant| |checkRur| |numberOfHues| |selectsecond| |maxrow| - |e04gcf| |listRepresentation| |s18acf| |OMputEndObject| |powmod| - |possiblyNewVariety?| |connectTo| |infix?| |leftUnits| |limit| - |distdfact| |maxPoints3D| |nthFlag| |OMgetBVar| |mask| - |mainDefiningPolynomial| |laguerreL| |primPartElseUnitCanonical| - |d01ajf| |selectOrPolynomials| |prefix| |realRoots| |e01bhf| - |numberOfMonomials| |rotate| |getZechTable| |lintgcd| |primaryDecomp| - |setright!| |polyRDE| |constDsolve| |assign| |swap!| |coefChoose| - |maxIndex| |ran| |d01anf| |loadNativeModule| |optional?| |cyclicGroup| - |coerceL| |refine| |solve1| |OMcloseConn| |semiResultantEuclideannaif| - |light| |divide| |cothIfCan| |reduceByQuasiMonic| |meshPar2Var| - |d03edf| |parameters| |alternative?| |sequences| |rectangularMatrix| - |has?| |jacobian| |rootKerSimp| |lowerCase| |numFunEvals| |quoByVar| - |subPolSet?| |isList| |sign| |semiResultantEuclidean1| |clearTable!| - |sturmVariationsOf| |rquo| |normalizeAtInfinity| |coefficient| - |e02def| |bringDown| |tube| |tubePlot| |principal?| |transform| - |getOrder| |balancedFactorisation| |e01sff| |upperCase!| |asinhIfCan| - |viewWriteDefault| |problemPoints| |semiDiscriminantEuclidean| - |setAdaptive| |stosePrepareSubResAlgo| |binaryTournament| - |OMgetEndBVar| |e04mbf| |sh| |simpsono| |mathieu23| |key?| - |maxRowIndex| |subQuasiComponent?| |rootDirectory| |groebgen| - |factorFraction| |integralCoordinates| |generalSqFr| - |mainPrimitivePart| |integralBasis| |newTypeLists| |triangSolve| - |tubeRadius| |tab| |ode1| |search| |e01sef| |makingStats?| |weighted| - |unparse| |reverse!| |eigenMatrix| |eyeDistance| |output| - |simplifyLog| |rowEch| |totalLex| |f04maf| |invertibleSet| - |rationalPoints| |any?| |OMconnectTCP| |screenResolution| - |removeSinhSq| |moduleSum| |invertIfCan| |byteBuffer| - |extractProperty| |dictionary| |toseLastSubResultant| |biRank| |radix| - F2FG |hdmpToDmp| |critT| |infieldint| |nextIrreduciblePoly| - |fprindINFO| |equivOperands| |algebraicSort| |btwFact| |vector| - |differentialVariables| |hclf| |enumerate| |doubleResultant| - |denomRicDE| |parabolic| |supRittWu?| |pack!| |nextsubResultant2| - |exportedOperators| |squareTop| |modularFactor| |resetVariableOrder| - |anfactor| |selectPDERoutines| |rightZero| |digamma| |branchIfCan| - |Beta| |innerSolve| |true| |delete!| |commonDenominator| - |univariatePolynomial| |iExquo| |groebner| |lowerPolynomial| |eulerE| - |arbitrary| |sPol| UTS2UP ~= |stoseSquareFreePart| |rightExtendedGcd| - |vectorise| |irreducibleFactor| |variationOfParameters| - |resultantReduit| |radicalEigenvectors| |external?| |tanSum| - |fortranComplex| |wreath| |createNormalPoly| |sparsityIF| |coerce| - |noLinearFactor?| |factor1| |setprevious!| |df2mf| |bitCoef| - |cycleLength| |numberOfImproperPartitions| |polar| |isMult| |c06ebf| - |construct| |rational?| |revert| |insertTop!| - |factorsOfCyclicGroupSize| |midpoints| |radicalRoots| |minPol| - |standardBasisOfCyclicSubmodule| |setClipValue| |var2Steps| - |factorsOfDegree| |implies?| |makeCos| |cos2sec| |f01mcf| |odd?| - |setrest!| |erf| |super| |f04axf| |mapdiv| |setMaxPoints3D| |roman| - |sncndn| |getCode| |leaves| |alphanumeric?| - |semiSubResultantGcdEuclidean2| |belong?| |inRadical?| - |currentSubProgram| |s18aff| |is?| |selectPolynomials| |stack| - |explicitlyEmpty?| |extendedSubResultantGcd| |binarySearchTree| - |var2StepsDefault| |integerBound| |perfectNthRoot| |redPo| - |fractRadix| |solveLinearPolynomialEquationByRecursion| |merge| - |leadingIndex| |badNum| |pol| |imagE| |PDESolve| |dilog| |ceiling| - |realEigenvectors| |argumentListOf| |c06gsf| |connect| - |ramifiedAtInfinity?| |viewpoint| |expenseOfEvaluation| - |makeViewport2D| |traceMatrix| |systemCommand| |sin| |eq?| |rotatey| - |quasiRegular| |rootSimp| |baseRDE| |bits| |inputOutputBinaryFile| - |makeSeries| |bfEntry| |systemSizeIF| |f04asf| |cos| |vark| - |bipolarCylindrical| |d02gbf| |derivationCoordinates| |imagK| - |getExplanations| |nthExpon| |evenInfiniteProduct| |character?| - |factorPolynomial| |and?| |lift| |tan| |frst| |rootBound| |coth2trigh| - |expt| |superscript| |stoseInvertibleSetreg| |lookup| |cAtanh| - |exteriorDifferential| |forLoop| |trace2PowMod| |reduce| |normal| - |cot| |completeHensel| |relationsIdeal| |eulerPhi| |ignore?| |over| - |basisOfCentroid| |evaluate| |d01asf| |subResultantGcdEuclidean| |mat| - |sec| |setTopPredicate| |consnewpol| |pushNewContour| |e02ahf| - |adjoint| |sizePascalTriangle| |c05adf| |cyclotomicDecomposition| - |triangulate| |d01alf| |resetBadValues| |csc| |flagFactor| - |setPosition| |palgintegrate| |OMputEndError| |ode| |rootPower| - |basisOfCommutingElements| |intPatternMatch| |prepareDecompose| - |SturmHabicht| |cn| |mainCharacterization| |asin| |reduced?| - |modularGcd| |aCubic| |e04fdf| |OMgetBind| |symbolIfCan| |uniform| - |iiatanh| |ratpart| |baseRDEsys| |acos| |besselJ| |sinIfCan| - |rightFactorIfCan| |point| |denominators| |euler| |splitLinear| - |f07fdf| |colorFunction| |ScanFloatIgnoreSpacesIfCan| |position!| - |atan| |stFunc2| |discreteLog| |conditionP| |complexRoots| - |difference| |reducedSystem| |f01rdf| |irreducibleRepresentation| - |sincos| |normalDenom| |acot| |outputMeasure| |eigenvalues| |overbar| - |linkToFortran| |quotientByP| |rightMinimalPolynomial| |conjugate| - |dualSignature| |groebnerIdeal| |fortranLinkerArgs| |asec| - |readBytes!| |OMgetInteger| |upDateBranches| |series| |reflect| - |commaSeparate| |yCoord| |resetNew| |c06fpf| |f01maf| |acsc| |green| - |adaptive| |startTable!| |leftOne| |hasPredicate?| |port| |tanhIfCan| - |shrinkable| |polCase| |sinh| |totalGroebner| |safeFloor| |measure| - |elseBranch| |allRootsOf| |create| |trigs| |ricDsolve| - |replaceKthElement| |cosh| |subResultantGcd| |goodPoint| - |headRemainder| |coercePreimagesImages| |infRittWu?| |e02baf| - |sts2stst| |edf2df| |number?| |tanh| |genericRightNorm| |plot| - |prepareSubResAlgo| |min| |triangularSystems| |complexForm| - |LagrangeInterpolation| |rationalIfCan| |jacobi| |outputForm| - |moebius| |goto| |leftNorm| |nextColeman| |tab1| - |antisymmetricTensors| |clipSurface| |palgLODE| |isExpt| |conditions| - |copies| |term| |semiDegreeSubResultantEuclidean| |iipow| - |genericLeftNorm| |polyPart| |unit?| |brillhartIrreducible?| - |nthRootIfCan| |match| |OMserve| |cycleElt| |branchPoint?| - |maximumExponent| |normFactors| |bracket| |pop!| |invmod| |acotIfCan| - |oneDimensionalArray| |An| |e04ycf| |exprex| |userOrdered?| |sort!| - |curryLeft| |schwerpunkt| |ramified?| |cAsec| |rootOfIrreduciblePoly| - |stronglyReduce| |sorted?| |zeroSetSplit| |aromberg| |po| |rename!| - |SturmHabichtCoefficients| |removeRoughlyRedundantFactorsInPol| - |explimitedint| |monomials| |rightTraceMatrix| |inverseLaplace| - |pureLex| |cycles| |dmpToP| |leaf?| |f04qaf| |pr2dmp| - |linearDependenceOverZ| |boundOfCauchy| |shiftRight| |ord| - |integerIfCan| |showFortranOutputStack| |mindeg| |log10| |optimize| - |restorePrecision| |movedPoints| |stopTableInvSet!| - |unitsColorDefault| |exprHasWeightCosWXorSinWX| |OMputFloat| - |mapExponents| |seriesToOutputForm| |bitand| |reset| |endSubProgram| - |hexDigit| |commutator| |tableForDiscreteLogarithm| |basis| |toScale| - |check| |dimensionOfIrreducibleRepresentation| |OMunhandledSymbol| - |bitior| |weights| |OMputError| |transcendenceDegree| |pdf2df| - |internalIntegrate0| |addMatch| |points| |roughSubIdeal?| |repeating| - |write| |floor| |laplace| |times!| |abelianGroup| |numberOfVariables| - |retractable?| |removeRedundantFactors| |save| |cAcsc| - |showIntensityFunctions| |reduceLODE| |halfExtendedSubResultantGcd1| - |mindegTerm| |partitions| D |discriminant| |OMputEndAttr| |implies| - |removeRoughlyRedundantFactorsInPols| |operators| |reorder| |double| - |paraboloidal| |prindINFO| |member?| |Aleph| |simplifyPower| |untab| - |blue| |mapExpon| |unrankImproperPartitions1| |idealiser| |prem| - |continuedFraction| |mvar| |generalizedEigenvectors| - |clearFortranOutputStack| |integralMatrixAtInfinity| |kroneckerDelta| - |s18def| |bernoulliB| |setMinPoints| |setnext!| |genericPosition| - |extendedResultant| |lexGroebner| |startPolynomial| - |singularAtInfinity?| |iitan| |sumOfKthPowerDivisors| |xCoord| - |setPoly| |internalSubQuasiComponent?| |divergence| |superHeight| - |unit| |primeFrobenius| |charthRoot| |basisOfRightNucloid| |e01sbf| - |initiallyReduced?| |knownInfBasis| |corrPoly| |atanIfCan| - |perfectNthPower?| |reducedQPowers| |overlabel| |dflist| |integral| - |linears| |roughBasicSet| |alphanumeric| |iterationVar| |composite| - |entry| |primlimitedint| |cCsc| |c02agf| |rombergo| |whitePoint| - |c06ekf| |gramschmidt| |makeEq| |stronglyReduced?| - |rightFactorCandidate| |null?| |declare!| |setProperties!| |ODESolve| - |sec2cos| |radicalSimplify| |principalIdeal| |normalizeIfCan| |f01bsf| - |realZeros| |e02bcf| |OMputBVar| |nextNormalPoly| |lighting| - |factorSquareFree| |taylorRep| |f02bjf| |print| |hdmpToP| - |semiLastSubResultantEuclidean| |stFunc1| |fullDisplay| - |purelyAlgebraic?| |getVariableOrder| |resolve| |pointColorDefault| - |Vectorise| |constant?| |setRow!| |rightScalarTimes!| |Frobenius| - |rootOf| |solve| |genericRightTraceForm| |insertBottom!| |conical| - |autoReduced?| |returns| |acschIfCan| |flatten| |variable?| |bat| - |basicSet| |s19aaf| |qPot| |distribute| |edf2fi| |retractIfCan| - |OMgetEndObject| |inHallBasis?| |degreeSubResultantEuclidean| |solid?| - |shanksDiscLogAlgorithm| |deepestInitial| |att2Result| LODO2FUN - |palgRDE| |isTimes| |complexSolve| |anticoord| |mapGen| |overset?| - |conjug| |numer| |mainSquareFreePart| |uncouplingMatrices| |sdf2lst| - |bag| |roughEqualIdeals?| |viewPosDefault| |setFormula!| |pow| - |e04ucf| |f04mcf| |segment| |top| |denom| |makeYoungTableau| |powern| - |OMgetVariable| |pomopo!| |groebner?| |splitNodeOf!| - |genericLeftTraceForm| |zeroMatrix| |headReduce| |nextPrimitivePoly| - |semicolonSeparate| |euclideanNormalForm| |f07aef| |diff| |contours| - |numericalOptimization| |trueEqual| |flexibleArray| |minimumDegree| - |removeRedundantFactorsInContents| |pi| |lquo| |complexEigenvectors| - |solveLinear| |polyRicDE| |addMatchRestricted| |nextPrime| |name| - |parabolicCylindrical| |exQuo| |dimensionsOf| - |linearlyDependentOverZ?| |infinity| |companionBlocks| - |structuralConstants| |iilog| |rename| |SturmHabichtSequence| - |quasiAlgebraicSet| |body| |newLine| |alphabetic| - |initializeGroupForWordProblem| |lfunc| |coerceListOfPairs| - |divisorCascade| |csubst| |generalizedEigenvector| - |genericRightDiscriminant| |laguerre| |rootNormalize| |logIfCan| - |exquo| |operation| |fortranTypeOf| |createPrimitiveElement| - |leastPower| |bipolar| |leftRegularRepresentation| |perfectSqrt| - |halfExtendedResultant1| |monic?| |cardinality| |LiePolyIfCan| - |iFTable| |t| |div| |tanNa| |tRange| |outerProduct| |kernel| - |pseudoDivide| |besselK| |nthr| |putColorInfo| |logpart| |stirling1| - |prolateSpheroidal| |draw| |map| |rightLcm| |quo| |kovacic| - |getMeasure| |rightRankPolynomial| |axesColorDefault| Y |firstNumer| - |cAtan| |complexIntegrate| |ScanFloatIgnoreSpaces| |iisec| |s17ajf| - |multiplyExponents| |shift| |indicialEquationAtInfinity| |normal?| - |minimumExponent| |viewDeltaYDefault| |startStats!| |sumSquares| - |OMputEndApp| |polynomialZeros| |freeOf?| |rem| |setref| |lifting1| - |regime| |linear| |real?| |subtractIfCan| |rationalPower| |find| - |unprotectedRemoveRedundantFactors| |sumOfDivisors| F |decomposeFunc| - |symmetricTensors| |unrankImproperPartitions0| |pdf2ef| - |zeroSetSplitIntoTriangularSystems| |center| |setImagSteps| - |insertionSort!| |gradient| |complexEigenvalues| |simpson| - |makeObject| |categoryFrame| |parametric?| |makeCrit| - |OMencodingUnknown| |polynomial| |OMParseError?| |orbits| |property| - |orthonormalBasis| |hspace| |closeComponent| |simplify| |convert| - |compactFraction| |nullSpace| |leastMonomial| |explicitEntries?| - |sturmSequence| |clipParametric| |iiatan| |root?| - |monicDecomposeIfCan| |setProperty!| |basisOfLeftNucloid| - |deepestTail| |ScanArabic| |nodeOf?| |leadingExponent| |coef| - |fixPredicate| |fTable| |sizeLess?| |nthFractionalTerm| |s17acf| - |dAndcExp| |basisOfLeftAnnihilator| |stoseInvertible?sqfreg| |redmat| - |startTableInvSet!| |pointLists| |rk4f| |units| |primlimintfrac| - |viewport3D| |leftDivide| |OMsend| |iisech| |primitive?| |c02aff| - |adaptive3D?| |drawToScale| |cotIfCan| |shade| |internalZeroSetSplit| - |transcendentalDecompose| |accuracyIF| |infieldIntegrate| - |extractPoint| |leviCivitaSymbol| |alternatingGroup| - |absolutelyIrreducible?| |reducedDiscriminant| |ParCondList| - |repeating?| |firstSubsetGray| |sum| |sin2csc| |child?| RF2UTS |iicos| - |halfExtendedSubResultantGcd2| |Nul| |central?| - |wordInStrongGenerators| |acosIfCan| |directSum| ** |complex?| - |s17def| |child| |copyInto!| |prinshINFO| |f02ajf| |lp| |qfactor| - |differentiate| |OMputString| |calcRanges| |palgLODE0| |zeroVector| - |multiEuclidean| |failed?| |firstUncouplingMatrix| |pquo| |rightNorm| - |code| |lSpaceBasis| |getOperands| |inGroundField?| |collectUpper| - |shuffle| |decrease| |padicFraction| |cAsin| |lazyPseudoRemainder| EQ - |modularGcdPrimitive| |insertMatch| |rightRank| |deepExpand| - |heapSort| |s19acf| |insert!| |modifyPointData| |primintegrate| - |epilogue| |e02dcf| |balancedBinaryTree| - |selectMultiDimensionalRoutines| |cosSinInfo| |lazyIntegrate| |f02awf| - |ocf2ocdf| |iprint| |dfRange| |binomial| |outputAsFortran| |split| - |partition| |rank| |computeCycleEntry| |optAttributes| - |nextPrimitiveNormalPoly| |viewZoomDefault| |minimize| - |showAllElements| |squareFreePrim| |s17dcf| |transcendent?| - |evaluateInverse| |cRationalPower| |f02agf| |primextendedint| |rroot| - |setProperties| |palgint| |psolve| |quotedOperators| |s17aef| - |mapmult| |read!| |lieAdmissible?| |radicalEigenvector| - |cyclicEntries| |makeSketch| |LyndonWordsList1| |s21bbf| |octon| - |se2rfi| |dom| |quotient| |OMsupportsSymbol?| |lazyIrreducibleFactors| - |removeCosSq| |kind| |setProperty| |stirling2| |univariatePolynomials| - |palgextint0| |intensity| |rightMult| |c06gcf| |getIdentifier| - |s15adf| |category| |curve?| |op| |leadingIdeal| |exists?| - |outputAsScript| |f02wef| |torsionIfCan| |lfextlimint| - |zeroDimensional?| |addBadValue| |trim| |domain| |bsolve| |options| - |declare| |identification| |cSin| |graphStates| |e01saf| |axes| - |hermite| |monicCompleteDecompose| |push| |createMultiplicationMatrix| - |package| |solveRetract| |signature| |multinomial| |c06frf| - |fortranLiteralLine| |karatsubaOnce| |unknown| |asimpson| - |stoseInvertible?| |index?| |lists| |unaryFunction| |bumptab| |infix| - |hasHi| |nonLinearPart| |cycleSplit!| |definingInequation| |nextItem| - |getConstant| |title| |OMopenString| |droot| |lfintegrate| - |rewriteIdealWithRemainder| |string| |airyBi| |Si| |f02adf| - |arrayStack| |cAsech| |createIrreduciblePoly| |leftAlternative?| - |scalarMatrix| |dot| |rightCharacteristicPolynomial| |iisqrt2| - |jordanAlgebra?| |approxSqrt| |hexDigit?| |OMgetSymbol| |maxrank| - |heap| |complexElementary| |swapRows!| |outputList| |duplicates| - |smith| |pushdterm| |phiCoord| |f07fef| |algebraicCoefficients?| - |s14aaf| |e| |ldf2vmf| |front| |createThreeSpace| |setLength!| - |tryFunctionalDecomposition?| |df2st| |mainVariable?| |clipBoolean| - |create3Space| |chebyshevU| |fixedPoint| |numberOfComponents| - |critBonD| |rk4| |outputGeneral| |OMgetEndAtp| |permutations| - |pointData| |parametersOf| |subset?| |scaleRoots| |errorKind| - |setelt!| |factorGroebnerBasis| |inputBinaryFile| |chiSquare1| - |sortConstraints| |setCondition!| |setRealSteps| |nothing| - |rischDEsys| |numberOfNormalPoly| |closedCurve?| |atoms| - |patternMatchTimes| |partialDenominators| |integral?| |f01qef| |pole?| - |currentEnv| |gcdprim| |varselect| |order| |univariatePolynomialsGcds| - |maxint| |numerator| |rightUnit| |mapSolve| |someBasis| - |basisOfRightNucleus| |solveid| |s13acf| |c06fqf| |elementary| - |irreducible?| |d01gbf| |subCase?| |seed| |exprToGenUPS| - |lazyPseudoDivide| |generic?| |distFact| |fortranInteger| - |lfextendedint| |sinhIfCan| |gderiv| |showTheSymbolTable| |mkcomm| - |nthCoef| |OMputAttr| |cond| |henselFact| |width| |rdHack1| - |diagonalProduct| |leftQuotient| |crest| |exp1| |nextsousResultant2| - |closed?| |s19abf| |setsubMatrix!| |secIfCan| - |rewriteSetByReducingWithParticularGenerators| |changeWeightLevel| - |s20acf| |useEisensteinCriterion?| |s17dlf| |minus!| |firstDenom| - |OMlistCDs| |rspace| |createNormalElement| |limitPlus| - |clearTheFTable| |writeByteIfCan!| |fractionPart| - |selectIntegrationRoutines| |viewDeltaXDefault| |cSech| |augment| - |addmod| |lprop| |diophantineSystem| |even?| |legendre| |column| - |iroot| |OMreceive| |qinterval| |clearDenominator| |perfectSquare?| - |lyndon?| |setPrologue!| |setVariableOrder| |OMencodingSGML| |isPower| - |content| |graphs| |nary?| |countRealRootsMultiple| |rk4qc| - |integralDerivationMatrix| |checkPrecision| |bivariate?| |randomR| - |orbit| |powerSum| |positiveSolve| |iiasec| |diag| |reverse| |lo| - |leftGcd| |tower| |infinityNorm| |rubiksGroup| |ridHack1| - |patternMatch| |linearPart| |leftFactor| |optional| |OMsetEncoding| - |symbol?| |generalPosition| |plusInfinity| |condition| |lllip| - |coordinates| |iicoth| |lieAlgebra?| |top!| |infinite?| |c06gbf| - |f02aff| |inv| |polygon| |minusInfinity| |divideExponents| |graeffe| - |randomLC| |f02abf| |functionIsOscillatory| |associative?| - |jordanAdmissible?| |LyndonBasis| |ground?| |complexExpand| - |leftDiscriminant| |mainValue| |changeVar| |thetaCoord| |eq| - |specialTrigs| |tanh2coth| |basisOfLeftNucleus| |iiacos| |ground| - |hue| |typeList| |exponents| |multiEuclideanTree| |extractIndex| - |iter| |/\\| |leadingMonomial| |infLex?| |removeSquaresIfCan| - |stoseInvertible?reg| |complexNumeric| |drawComplexVectorField| - |airyAi| |neglist| |cCsch| |imagj| |prologue| |\\/| |factorials| - |powers| |numberOfPrimitivePoly| |leadingCoefficient| |rules| - |deleteRoutine!| |f02akf| |swap| |LyndonWordsList| |edf2efi| - |getPickedPoints| |outputFloating| |tanIfCan| |extendedIntegrate| - |primitiveMonomials| |kernels| |resetAttributeButtons| |interpolate| - |complexNumericIfCan| |recip| |level| |inverse| |alphabetic?| |cAcos| - |tablePow| |int| |inconsistent?| |reductum| |univariate| |type| - |mesh?| |cyclicEqual?| |partialQuotients| |aspFilename| - |associatedEquations| |purelyAlgebraicLeadingMonomial?| - |makeFloatFunction| |tan2trig| SEGMENT |back| |OMputAtp| |e02ddf| - |HermiteIntegrate| |normalizedDivide| |imagi| |crushedSet| |nullary| - |chebyshevT| |qelt| |getBadValues| |postfix| |clipWithRanges| - |gcdcofactprim| |totalfract| |setStatus!| |colorDef| |qsetelt| |low| - |lfinfieldint| |errorInfo| |quickSort| |factor| |ratDenom| - |isConnected?| |printStatement| |unitNormal| |palgint0| |exp| - |elliptic| |createMultiplicationTable| |xRange| |diagonalMatrix| - |plus!| |sqrt| |makeGraphImage| |twist| |numberOfChildren| |torsion?| - |particularSolution| |swapColumns!| |rischDE| |yRange| |asinIfCan| - |ref| |real| |complementaryBasis| |subHeight| |concat| |determinant| - |pointColor| |fortranLiteral| |exprToUPS| |indices| |zRange| - |OMsupportsCD?| |inverseIntegralMatrix| |imag| |genus| |cCos| - |OMreadStr| |component| |curry| |error| |ldf2lst| |OMopenFile| |map!| - |pushuconst| |directProduct| |critB| |compile| |BasicMethod| |iiabs| - |bytes| |cAcsch| |subresultantVector| |assert| |qsetelt!| - |rightAlternative?| |charpol| |lyndon| |OMencodingBinary| - |completeHermite| |cschIfCan| |generalInfiniteProduct| |appendPoint| - |dimension| |opeval| |exptMod| |linearPolynomials| |geometric| |brace| - |bezoutResultant| |s15aef| |subNodeOf?| |idealSimplify| - |mainExpression| |credPol| |janko2| |abs| |lllp| |destruct| - |eisensteinIrreducible?| |collectUnder| |exponential1| |clip| - |OMgetString| |iifact| |writeBytes!| |monicModulo| |multiple?| - |replace| |rightUnits| |zero?| |primitivePart| |dominantTerm| - |normalize| |mapCoef| |rowEchelon| |externalList| |stoseInvertibleSet| - |writable?| |primPartElseUnitCanonical!| |equality| |finiteBound| - |padecf| |acsch| |stripCommentsAndBlanks| |separate| |listLoops| - |algebraic?| |normalDeriv| |constantKernel| |iiacot| |f01qdf| ~ - |tracePowMod| |shufflein| |linGenPos| |Lazard2| |bandedJacobian| - |monomial| |minrank| |complexLimit| |s18aef| |d01gaf| |complete| - |makeTerm| |satisfy?| |round| |showTheRoutinesTable| |multivariate| - |generalTwoFactor| |semiResultantReduitEuclidean| |denominator| - |linearAssociatedOrder| |minColIndex| |open| |d01amf| |reseed| - |intChoose| |direction| |setAttributeButtonStep| |variables| - |makeUnit| |ef2edf| |square?| |mulmod| |acscIfCan| |algebraicOf| - |clearTheSymbolTable| |cTanh| |lastSubResultantElseSplit| - |outputSpacing| |printingInfo?| |minIndex| |target| |hconcat| - |writeLine!| |functionIsContinuousAtEndPoints| |B1solve| |elRow2!| - |OMgetEndBind| |makeprod| |factorSquareFreeByRecursion| |primes| - |resultantEuclideannaif| |objectOf| |viewDefaults| |elliptic?| - |iiacsch| |complexNormalize| |chiSquare| |primitivePart!| - |useNagFunctions| |rightRemainder| |bright| |powerAssociative?| - |rowEchelonLocal| |leftLcm| |linearAssociatedExp| |leftRemainder| - |strongGenerators| |bezoutDiscriminant| |f04jgf| |zeroDimPrimary?| - |monicDivide| |initial| |returnType!| |d03faf| |c06eaf| |setchildren!| - |submod| |redpps| |lowerCase!| |fintegrate| |zoom| |weakBiRank| - |taylor| |rootsOf| |size?| |radicalEigenvalues| |closedCurve| |inf| - |printStats!| |monomial?| |setErrorBound| |fortranReal| - |rightDiscriminant| |laurent| |select!| |makeRecord| |hermiteH| - |mathieu22| |functionIsFracPolynomial?| |SturmHabichtMultiple| - |setOrder| |cyclic| |cycleTail| |selectOptimizationRoutines| |puiseux| - |createPrimitivePoly| |factorial| |hitherPlane| |setleaves!| - |sylvesterMatrix| |fmecg| |trigs2explogs| |midpoint| UP2UTS |ravel| - |cartesian| |setScreenResolution| |dmpToHdmp| |OMclose| |integer?| - |primeFactor| |OMmakeConn| |truncate| |fortranDoubleComplex| FG2F - |s17aff| |reshape| |inR?| |whatInfinity| |tan2cot| - |isAbsolutelyIrreducible?| |useSingleFactorBound| - |integralLastSubResultant| |e04jaf| |delete| |cyclicSubmodule| |cup| - |hcrf| |UP2ifCan| |idealiserMatrix| |rarrow| |viewSizeDefault| - |multiplyCoefficients| |var1StepsDefault| |setlast!| |OMconnOutDevice| - |numberOfFactors| |setClosed| |zeroDim?| |pmintegrate| |zeroOf| - |leftTrace| |range| |atanhIfCan| |squareFreeLexTriangular| - |wholeRagits| |exactQuotient| |lagrange| |symmetricSquare| - |bandedHessian| |localUnquote| |mightHaveRoots| |trapezoidal| |sup| - |tryFunctionalDecomposition| |eof?| |arg1| |horizConcat| |byte| - |putGraph| |entries| |semiResultantEuclidean2| NOT |complexZeros| - |e02gaf| |setelt| |integralBasisAtInfinity| |listOfLists| - |principalAncestors| |arg2| |acothIfCan| |subTriSet?| |makeResult| - |cot2trig| |update| |constantToUnaryFunction| |printTypes| OR - |arguments| |tubePoints| |dn| |updatF| |rightDivide| - |regularRepresentation| |gethi| |removeCoshSq| |currentScope| - |bottom!| |discriminantEuclidean| AND |innerint| - |createPrimitiveNormalPoly| |copy| |characteristicPolynomial| - |radicalSolve| |constantOpIfCan| |ksec| |realEigenvalues| |qqq| - |fractionFreeGauss!| |multisect| |spherical| |every?| |d01aqf| |trunc| - |drawComplex| |rst| |var1Steps| |degree| |gbasis| |unexpand| - |oblateSpheroidal| |leftRecip| |dark| |cycleRagits| |nextPartition| - |lhs| |HenselLift| |match?| |f04atf| |makeSUP| |c06gqf| |simplifyExp| - |quadraticNorm| |autoCoerce| |withPredicates| |besselI| |printHeader| - |separateDegrees| |rhs| |mergeFactors| |enterPointData| |Gamma| - |position| |screenResolution3D| |cyclotomic| |charClass| |identity| - |quasiComponent| |continue| |chineseRemainder| |d01akf| |totolex| - |divisors| |nthRoot| |probablyZeroDim?| |scanOneDimSubspaces| - |skewSFunction| |d02raf| |e01bgf| |collect| |expr| |monomRDEsys| - |reducedForm| |topPredicate| |leader| |symbolTableOf| |nthExponent| - |indicialEquation| |shellSort| |signAround| |fixedPointExquo| |result| - |rightExactQuotient| |ListOfTerms| |presub| |rotatez| |showRegion| - |rational| |selectODEIVPRoutines| GE |properties| |logical?| - |inverseColeman| |nlde| |power| |splitSquarefree| |tree| |d02gaf| - |monicRightFactorIfCan| |parseString| |taylorQuoByVar| GT - |getProperty| |mkPrim| |linearDependence| |qualifier| |f04arf| - |translate| |createRandomElement| |rootPoly| |critMonD1| - |wronskianMatrix| |middle| * LE |whileLoop| |lazy?| |minset| - |factorSquareFreePolynomial| |variable| |separant| |binomThmExpt| - |max| |scopes| |safeCeiling| |constantOperator| |bivariateSLPEBR| - |build| LT |leadingSupport| |aLinear| |bitLength| |debug| - |removeSinSq| |iterators| |innerSolve1| |resultantnaif| - |combineFeatureCompatibility| |decompose| |rightOne| |normInvertible?| - |goodnessOfFit| |increasePrecision| |ranges| |elements| |fi2df| - |vertConcat| |integralRepresents| |bombieriNorm| |factorOfDegree| - |symmetricDifference| |zeroDimPrime?| |mirror| |setFieldInfo| - |internalDecompose| |rationalFunction| |element?| |d03eef| - |algintegrate| |univcase| |OMputEndBVar| |predicates| |cTan| - |twoFactor| |clipPointsDefault| |fixedPoints| |maxPoints| |generator| - |part?| |getlo| |remainder| |aQuadratic| |rightPower| |OMgetAttr| - |parts| |makeMulti| |iiacosh| |rationalPoint?| |quote| |modulus| - |kmax| |slash| |addPoint| |sub| |coordinate| |harmonic| |vconcat| - |supDimElseRittWu?| |fortranCompilerName| |numberOfComputedEntries| - |fillPascalTriangle| |dimensions| |impliesOperands| |scale| |next| - |newSubProgram| |latex| |generalizedContinuumHypothesisAssumed?| - |rewriteIdealWithHeadRemainder| |csch2sinh| |positive?| |point?| - |exprHasLogarithmicWeights| |bothWays| |quatern| |ode2| |makeop| - |stiffnessAndStabilityOfODEIF| |leftCharacteristicPolynomial| |equiv| - |quartic| |mesh| |curveColorPalette| |oddInfiniteProduct| |e04dgf| - |argscript| |norm| |removeDuplicates!| |generic| |minimalPolynomial| - |interpret| |hasTopPredicate?| |remove!| |failed| |iiperm| - |leadingBasisTerm| |e02dff| |space| |reduction| |leastAffineMultiple| - |andOperands| |fill!| |hypergeometric0F1| |makeSin| |monomialIntPoly| - |KrullNumber| |sn| |f04faf| |trapezoidalo| |s17agf| |iidprod| |call| - |OMconnInDevice| |singular?| |uniform01| |e02agf| |shiftLeft| - |createNormalPrimitivePoly| |setMaxPoints| |normalise| - |expextendedint| |cCot| |directory| |wholePart| |argument| |queue| - |cylindrical| |fortranLogical| |hMonic| |wholeRadix| |factorset| - |listexp| |getButtonValue| |moreAlgebraic?| |rowEchLocal| |symFunc| - |hessian| |sinhcosh| |computeBasis| |areEquivalent?| |contract| - |returnTypeOf| |dmp2rfi| |simpleBounds?| |more?| |yCoordinates| - |cSinh| |d02ejf| |leftExactQuotient| |dim| |resultantEuclidean| - |sqfrFactor| |rotatex| |setOfMinN| |leftMult| |iicosh| |supersub| - |bivariatePolynomials| |e02bbf| |f01ref| |seriesSolve| - |physicalLength!| |function| |normalized?| |d02kef| |prime?| - |OMputBind| |leftMinimalPolynomial| |componentUpperBound| |clearCache| - |mapBivariate| |constant| |solveInField| |incrementKthElement| - |cyclic?| |singleFactorBound| |csc2sin| |reindex| |open?| - |inverseIntegralMatrixAtInfinity| |zCoord| |Hausdorff| |homogeneous?| - |listOfMonoms| |eval| |SFunction| |stFuncN| - |stiffnessAndStabilityFactor| |categories| |leftScalarTimes!| |one?| - |f2df| |algSplitSimple| |algint| |insert| |id| |moebiusMu| - |RemainderList| |coleman| |setfirst!| |nsqfree| |c06ecf| |reify| - |routines| |radicalOfLeftTraceForm| |nor| |mathieu12| |htrigs| - |OMputEndBind| |certainlySubVariety?| |removeConstantTerm| |Ci| - |palginfieldint| |term?| |LiePoly| |e02daf| |ipow| - |fullPartialFraction| |pseudoQuotient| |c05nbf| |table| - |brillhartTrials| |OMgetAtp| |log| |lazyEvaluate| |incr| |aQuartic| - |lazyGintegrate| |in?| |identityMatrix| |sequence| |fractRagits| - |setvalue!| |new| |merge!| |asecIfCan| |comment| |multMonom| |s18dcf| - |Is| |s17adf| |nextLatticePermutation| |argumentList!| |nil| + |Record| |Union| |table| |rk4a| |specialTrigs| |external?| |normalise| + |blankSeparate| |factors| |cosSinInfo| |inR?| |pr2dmp| |new| + |outputFixed| |script| |tanSum| |tanh2coth| |expextendedint| + |normalForm| |lazyIntegrate| |getCurve| |whatInfinity| + |linearDependenceOverZ| |extension| |basisOfLeftNucleus| + |fortranComplex| |cCot| |debug3D| |f02awf| |numericIfCan| + |boundOfCauchy| |tan2cot| |any| |sumOfSquares| |wreath| |iiacos| + |wholePart| |leftRank| |arguments| |ocf2ocdf| |polygamma| + |isAbsolutelyIrreducible?| |shiftRight| |eigenvectors| |wrregime| + |tex| |createNormalPoly| |hue| |argument| |associator| |scalarTypeOf| + |iprint| |ord| |useSingleFactorBound| |s17ahf| |cAsinh| |sparsityIF| + |typeList| |queue| |algebraicDecompose| |dfRange| |f01qcf| + |integerIfCan| |integralLastSubResultant| |imagI| |noLinearFactor?| + |exponents| |cylindrical| |iteratedInitials| + |wordsForStrongGenerators| |binomial| |showFortranOutputStack| + |e04jaf| |createLowComplexityNormalBasis| |multiEuclideanTree| + |factor1| |fortranLogical| |children| |selectfirst| |split| + |cyclicSubmodule| |mindeg| |setprevious!| |nil| + |removeIrreducibleRedundantFactors| |hMonic| |extractIndex| |lcm| + |output| |unmakeSUP| |partition| |perspective| |cup| + |restorePrecision| |internalSubPolSet?| |df2mf| |infLex?| |wholeRadix| + |divideIfCan!| |computeCycleEntry| |arity| |hcrf| |movedPoints| + |bitCoef| |magnitude| |append| |removeSquaresIfCan| |numeric| + |factorset| |lazyPseudoQuotient| |optAttributes| |string?| |UP2ifCan| + |stopTableInvSet!| |radical| |mantissa| |left| |approximate| + |graphState| |stoseInvertible?reg| |cycleLength| |listexp| |gcd| + |nextPrimitiveNormalPoly| GF2FG |idealiserMatrix| |unitsColorDefault| + |right| |complex| |f01rcf| |drawComplexVectorField| + |numberOfImproperPartitions| |getButtonValue| |false| + |topFortranOutputStack| |center| |hasSolution?| |viewZoomDefault| + |exprHasWeightCosWXorSinWX| |rarrow| |setScreenResolution3D| |polar| + |airyAi| |moreAlgebraic?| |expintfldpoly| |minimize| |d01fcf| + |OMputFloat| |viewSizeDefault| |linSolve| |neglist| |isMult| + |rowEchLocal| |OMgetFloat| |close| |showAllElements| |cycleEntry| + |mapExponents| |multiplyCoefficients| |cCsch| |c06ebf| |inc| |symFunc| + |safetyMargin| |squareFreePrim| |upperCase| |seriesToOutputForm| + |var1StepsDefault| |showScalarValues| |imagj| |rational?| |remove| + |hessian| |#| |roughUnitIdeal?| |display| |hex| |s17dcf| BY + |endSubProgram| |setlast!| |prinb| |mr| |prologue| |revert| |sinhcosh| + |cSec| |linearlyDependent?| |transcendent?| |hexDigit| + |OMconnOutDevice| |positiveRemainder| |factorials| |insertTop!| |last| + |computeBasis| |exponent| |showSummary| |numberOfFactors| |commutator| + |algDsolve| |sum| |assoc| |factorsOfCyclicGroupSize| |powers| + |areEquivalent?| |stack| |critMTonD1| |increment| |sturmSequence| + |tableForDiscreteLogarithm| |setClosed| |cyclicParents| |length| + |numberOfPrimitivePoly| |midpoints| |contract| |ratDsolve| + |clipParametric| |exponentialOrder| |zeroDim?| |basis| + |showAttributes| |e01bef| |scripts| |deleteRoutine!| |radicalRoots| + |returnTypeOf| |input| |enqueue!| |iiatan| |zag| |toScale| + |pmintegrate| |systemCommand| |distance| |nonSingularModel| |dmp2rfi| + |library| |possiblyInfinite?| |lp| |root?| |zeroOf| |check| + |changeMeasure| |symbol| |e04mbf| |henselFact| |simpleBounds?| |comp| + |f07adf| |c05pbf| |monicDecomposeIfCan| |leftTrace| + |dimensionOfIrreducibleRepresentation| |testDim| |expression| + |rdHack1| |sh| |more?| |chvar| |setProperty!| |lazyVariations| |range| + |OMunhandledSymbol| |mainMonomials| |normal| |integer| |simpsono| + |diagonalProduct| |yCoordinates| |power!| |basisOfLeftNucloid| + |makeVariable| |cPower| |leftQuotient| |mathieu23| |cSinh| |npcoef| + |set| |LazardQuotient2| |deepestTail| |mulmod| |hasPredicate?| |key?| + |squareFreePart| |crest| |list| |d02ejf| |label| |headReduced?| + |groebnerFactorize| |ScanArabic| |port| |acscIfCan| |exp1| |qroot| + |maxRowIndex| |car| |leftExactQuotient| |reciprocalPolynomial| + |mainContent| |nodeOf?| |tanhIfCan| |algebraicOf| |traverse| + |nextsousResultant2| |subQuasiComponent?| |cdr| |musserTrials| + |leadingExponent| |lazyResidueClass| |shrinkable| + |clearTheSymbolTable| |setDifference| |birth| |rootDirectory| + |closed?| |OMputEndBVar| |monomialIntegrate| |fixPredicate| + |chainSubResultants| |cTanh| |polCase| |GospersMethod| |groebgen| + |setIntersection| |s19abf| |solveLinearPolynomialEquation| + |predicates| |pseudoRemainder| |fTable| |typeLists| |totalGroebner| + |lastSubResultantElseSplit| |setUnion| |setsubMatrix!| |getGoodPrime| + |intersect| |factorFraction| |cTan| |listConjugateBases| |sizeLess?| + |less?| |outputSpacing| |safeFloor| |integralCoordinates| + |antiAssociative?| |apply| |removeRoughlyRedundantFactorsInContents| + |secIfCan| |twoFactor| |pointPlot| |nthFractionalTerm| |realSolve| + |measure| |printingInfo?| |getRef| |coefficients| + |rewriteSetByReducingWithParticularGenerators| |generalSqFr| + |clipPointsDefault| |dec| |defineProperty| |updatD| |s17acf| + |elseBranch| |minIndex| |constructor| |universe| |size| + |mainPrimitivePart| |changeWeightLevel| |fixedPoints| |dAndcExp| + |product| |gcdPolynomial| |hash| |hconcat| |allRootsOf| + |primintfldpoly| |s20acf| |integralBasis| |maxPoints| + |basisOfLeftAnnihilator| |option| |xn| |show| |yellow| |count| + |create| |writeLine!| |leftExtendedGcd| |useEisensteinCriterion?| + |newTypeLists| |part?| = |minPoly| |alternating| + |stoseInvertible?sqfreg| |functionIsContinuousAtEndPoints| |trigs| + |s17dlf| |sqfree| |first| |triangSolve| |leader| |getlo| |trace| + |oddlambert| |integralAtInfinity?| |redmat| |ricDsolve| |B1solve| + |tubeRadius| |tensorProduct| |minus!| |rest| |remainder| < |leftPower| + |copy!| |startTableInvSet!| |elRow2!| |replaceKthElement| |datalist| + |substitute| |s21bcf| |firstDenom| |tab| |aQuadratic| > + |sylvesterSequence| |pointLists| |d02bbf| |OMgetEndBind| + |subResultantGcd| |removeDuplicates| |controlPanel| |OMlistCDs| |ode1| + |rightPower| <= |setleft!| |gcdPrimitive| |rk4f| |fortran| |goodPoint| + |makeprod| |nthFactor| |rightTrim| |e01sef| |rspace| |OMgetAttr| >= + |computeCycleLength| |primlimintfrac| |s18adf| |createGenericMatrix| + |factorSquareFreeByRecursion| |headRemainder| + |removeSuperfluousQuasiComponents| |leftTrim| |createNormalElement| + |makingStats?| |makeMulti| |trailingCoefficient| |mapDown!| + |viewport3D| |coercePreimagesImages| |primes| |internalAugment| + |weighted| |limitPlus| |iiacosh| |mapUp!| |ellipticCylindrical| + |leftDivide| |resultantEuclideannaif| |sort| |infRittWu?| |reset| + |nil?| |unparse| |clearTheFTable| |rationalPoint?| + |mkAnswer| + |normalizedAssociate| |OMsend| |objectOf| |e02baf| + |intermediateResultsIF| |reverse!| |writeByteIfCan!| |quote| - + |critpOrder| |iisech| |highCommonTerms| |viewDefaults| |sts2stst| + |write| |extendedEuclidean| |eigenMatrix| |fractionPart| |modulus| / + |quoted?| |primitive?| |legendreP| |elliptic?| |edf2df| + |normalElement| |save| |padicallyExpand| |selectIntegrationRoutines| + |eyeDistance| |kmax| |zero| |iiacsch| |e02aef| |c02aff| |orOperands| + |number?| |random| |dioSolve| |checkPrecision| |digits| |max| + |simplifyLog| |viewDeltaXDefault| |slash| |pattern| |initials| + |adaptive3D?| |minRowIndex| |genericRightNorm| |complexNormalize| + |palglimint0| |cSech| |rowEch| |addPoint| |And| |viewThetaDefault| + |raisePolynomial| |drawToScale| |plot| |chiSquare| |OMwrite| + |totalLex| |augment| |sub| |Or| |singRicDE| |cotIfCan| + |stoseInternalLastSubResultant| |primitivePart!| |prepareSubResAlgo| + |edf2ef| |addmod| |f04maf| |coordinate| |Not| |subresultantSequence| + |binaryTree| |shade| |useNagFunctions| |triangularSystems| |makeFR| + |invertibleSet| |lprop| |harmonic| |message| |fortranCarriageReturn| + |empty?| |internalZeroSetSplit| |rightRemainder| |retract| + |complexForm| |compiledFunction| |rationalPoints| |diophantineSystem| + |vconcat| |mapMatrixIfCan| |/\\| |messagePrint| + |transcendentalDecompose| |powerAssociative?| |LagrangeInterpolation| + |any?| |badValues| |flatten| |even?| |supDimElseRittWu?| |\\/| + |sech2cosh| |ratPoly| |accuracyIF| |rowEchelonLocal| |rationalIfCan| + |iitanh| |OMconnectTCP| |legendre| |fortranCompilerName| + |degreePartition| |getMatch| |infieldIntegrate| |Lazard| |jacobi| + |leftLcm| |double?| |screenResolution| |column| + |numberOfComputedEntries| |computePowers| |representationType| |critM| + |extractPoint| |linearAssociatedExp| |outputForm| |omError| |iroot| + |removeSinhSq| |fillPascalTriangle| |rationalApproximation| + |leviCivitaSymbol| |expandPower| |moebius| |leftRemainder| |cons| + |subspace| |moduleSum| |OMreceive| |dimensions| |expPot| + |sizeMultiplication| |alternatingGroup| |goto| |strongGenerators| + |f02xef| |qinterval| |invertIfCan| |impliesOperands| |eigenvector| + |absolutelyIrreducible?| |resultantReduitEuclidean| + |bezoutDiscriminant| |leftNorm| |retractIfCan| |infiniteProduct| + |byteBuffer| |clearDenominator| |scale| |branchPointAtInfinity?| + |numFunEvals3D| |reducedDiscriminant| |f04jgf| |nextColeman| + |getMultiplicationMatrix| |perfectSquare?| |extractProperty| + |newSubProgram| |iicot| |ParCondList| |startTableGcd!| + |zeroDimPrimary?| |tab1| |evenlambert| |dictionary| |lyndon?| |latex| + |expenseOfEvaluationIF| |dihedral| |repeating?| |antisymmetricTensors| + |monicDivide| |setPrologue!| |getOperator| |toseLastSubResultant| + |outerProduct| |generalizedContinuumHypothesisAssumed?| |FormatArabic| + |createZechTable| |firstSubsetGray| |returnType!| |clipSurface| + |loopPoints| |biRank| |setVariableOrder| + |rewriteIdealWithHeadRemainder| |notOperand| |fortranDouble| |sin2csc| + |palgLODE| |d03faf| |zeroSquareMatrix| |OMencodingSGML| |radix| + |csch2sinh| |medialSet| |child?| |characteristic| |c06eaf| |isExpt| + |elem?| F2FG |isPower| |positive?| |complement| |changeName| RF2UTS + |copies| |setchildren!| |nullity| |hdmpToDmp| |content| |point?| + |iicos| |usingTable?| |submod| |term| |node| |obj| |negative?| |critT| + |graphs| |exprHasLogarithmicWeights| |OMgetError| + |halfExtendedSubResultantGcd2| |redpps| + |semiDegreeSubResultantEuclidean| |map| |nary?| |style| |infieldint| + 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|schema| |curveColorPalette| |parse| + |binary| |kovacic| |maximumExponent| |printStats!| |iflist2Result| + |null| |critBonD| |constDsolve| |oddInfiniteProduct| |unitCanonical| + |getMeasure| |normFactors| |leaves| |monomial?| |subResultantChain| + |not| |rk4| |assign| |e04dgf| |rightRankPolynomial| |row| + |setErrorBound| |bracket| |outputGeneral| |and| |initTable!| |swap!| + |red| |argscript| |selectAndPolynomials| |axesColorDefault| + |generalizedContinuumHypothesisAssumed| |equation| |choosemon| |or| + |coefChoose| |OMgetEndAtp| |norm| |float| |firstNumer| |setEpilogue!| + |clip| |prepareDecompose| |antisymmetric?| |xor| |maxIndex| + |permutations| |removeDuplicates!| |inspect| |cAtan| |OMgetString| + |SturmHabicht| |buildSyntax| |deriv| |case| |ran| |pointData| + |generic| |complexIntegrate| |subMatrix| |iifact| + |mainCharacterization| |lepol| |Zero| |d01anf| |parametersOf| + |ScanFloatIgnoreSpaces| |concat!| |writeBytes!| |reduced?| |optional?| + |One| |setAdaptive3D| |subset?| |numer| |power| |pointColorDefault| + |iisec| |finite?| |findBinding| |modularGcd| |monicModulo| + |scaleRoots| |laurentIfCan| |Vectorise| |cyclicGroup| + |splitSquarefree| |denom| |df2ef| |s17ajf| |cot2tan| |multiple?| + |aCubic| |virtualDegree| |coerceL| |errorKind| |d02gaf| |constant?| + |minordet| |multiplyExponents| |e04fdf| |replace| |setRow!| + |mappingAst| |setelt!| |refine| |pi| |monicRightFactorIfCan| |index| + |indicialEquationAtInfinity| |hostPlatform| |rightUnits| |OMgetBind| + |factorGroebnerBasis| |solve1| |composites| |declare| |parseString| + |rightScalarTimes!| |infinity| |upperCase?| |normal?| |symbolIfCan| + |zero?| |inputBinaryFile| |stoseIntegralLastSubResultant| |elt| + |taylorQuoByVar| |OMcloseConn| |union| |Frobenius| |minimumExponent| + |setTex!| |uniform| |primitivePart| |readIfCan!| + |semiResultantEuclideannaif| |chiSquare1| |getProperty| |rootOf| + |pair| |setButtonValue| |viewDeltaYDefault| |iiatanh| |dominantTerm| + |sortConstraints| |iisin| |subst| 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|expandLog| + |patternMatchTimes| |wronskianMatrix| |variable?| |coef| + |numberOfCycles| |regime| |equality| |splitLinear| |reopen!| + |partialDenominators| |rectangularMatrix| |middle| |bat| |pdct| + |real?| |finiteBound| |f07fdf| |f02fjf| |has?| |integral?| |whileLoop| + |basicSet| |subtractIfCan| |cCoth| |colorFunction| |padecf| + |unvectorise| |jacobian| |f01qef| |lazy?| |s19aaf| |cscIfCan| + |rationalPower| |ScanFloatIgnoreSpacesIfCan| |stripCommentsAndBlanks| + |s14abf| |rootKerSimp| |pole?| |qPot| |minset| |find| |OMgetType| + |position!| |separate| |FormatRoman| |gcdprim| |lowerCase| + |distribute| |factorSquareFreePolynomial| |loadNativeModule| + |unprotectedRemoveRedundantFactors| |characteristicSerie| |listLoops| + |stFunc2| |resultant| |matrixConcat3D| |nrows| |varselect| + |numFunEvals| |separant| |edf2fi| |saturate| |sumOfDivisors| + |OMreadFile| |discreteLog| |algebraic?| |lastSubResultantEuclidean| + |mapUnivariateIfCan| |ncols| |order| |quoByVar| |binomThmExpt| + 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|sincos| + |basisOfRightNucleus| |repeatUntilLoop| |search| |iter| + |characteristicSet| |series| |rquo| |aLinear| LODO2FUN |gradient| + |normalDenom| |llprop| |Lazard2| |leadingMonomial| |complexNumeric| + |leftFactorIfCan| |expint| |OMputEndAtp| |normalizeAtInfinity| + |solveid| |bitLength| |palgRDE| |outputMeasure| |coerceS| + |complexEigenvalues| |bandedJacobian| |leadingCoefficient| |rules| + |genericRightTrace| |fixedDivisor| |unknown| |dequeue!| |s13acf| + |coefficient| |isTimes| |removeSinSq| |eigenvalues| |simpson| + |reverseLex| |minrank| |primitiveMonomials| |kernels| |f02axf| + |c06fqf| |e02def| |complexSolve| |innerSolve1| |weight| + |categoryFrame| |complexLimit| |lists| |overbar| |reductum| + |univariate| |elementary| |iicsch| |bringDown| |min| |anticoord| + |resultantnaif| |parametric?| |toseInvertible?| |linkToFortran| + |s18aef| |tanQ| |irreducible?| |tube| |combineFeatureCompatibility| + |mapGen| |comment| |makeCrit| |approxNthRoot| |d01gaf| |quotientByP| + |s13aaf| |tubePlot| |d01gbf| |overset?| |decompose| + |OMencodingUnknown| |vspace| |rightMinimalPolynomial| |complete| + |factor| |convergents| |rightOne| |principal?| |true| |subCase?| + |conjug| |exp| |OMParseError?| |exponential| |makeTerm| |conjugate| + |sqrt| |divideIfCan| |transform| |seed| |normInvertible?| + |mainSquareFreePart| ~= |zerosOf| |orbits| |dualSignature| |satisfy?| + |real| |bezoutMatrix| |exprToGenUPS| |getOrder| |uncouplingMatrices| + |goodnessOfFit| |coerce| |orthonormalBasis| |region| |groebnerIdeal| + |round| |imag| |OMputSymbol| |balancedFactorisation| + |lazyPseudoDivide| |sdf2lst| |increasePrecision| |hspace| + |extractIfCan| |fortranLinkerArgs| |showTheRoutinesTable| + |directProduct| |compile| |viewPhiDefault| |e01sff| |generic?| |bag| + |ranges| |showTypeInOutput| |closeComponent| |readBytes!| + |generalTwoFactor| |squareMatrix| |distFact| |upperCase!| + |roughEqualIdeals?| |elements| |simplify| |collectQuasiMonic| + |OMgetInteger| |semiResultantReduitEuclidean| |brace| |fi2df| |empty| + |fortranInteger| |asinhIfCan| |viewPosDefault| |second| + |innerEigenvectors| |compactFraction| |denominator| |upDateBranches| + |destruct| |setFormula!| |lfextendedint| |viewWriteDefault| + |vertConcat| |third| |youngGroup| |nullSpace| |reflect| + |linearAssociatedOrder| |nullary?| |problemPoints| |sinhIfCan| + |integralRepresents| |pow| |intcompBasis| |leastMonomial| + |commaSeparate| |minColIndex| |pair?| |semiDiscriminantEuclidean| + |gderiv| |bombieriNorm| |e04ucf| |compBound| |explicitEntries?| + |d01amf| |yCoord| |const| |setAdaptive| |showTheSymbolTable| + |factorOfDegree| |f04mcf| |rightQuotient| |reseed| |resetNew| + |monomial| |lazyPrem| |mkcomm| |stosePrepareSubResAlgo| + |symmetricDifference| |makeYoungTableau| |totalDegree| |recur| + |semicolonSeparate| |intChoose| |c06fpf| |multivariate| + |identitySquareMatrix| |binaryTournament| |nthCoef| |zeroDimPrime?| + |powern| |readLineIfCan!| |setLabelValue| |euclideanNormalForm| + |f01maf| |direction| 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|OMReadError?| |minimumDegree| + |makeSeries| |numberOfChildren| |puiseux| |e02bef| |unaryFunction| + |subscript| |nextPrimitivePoly| |univcase| |tanAn| + |removeRedundantFactorsInContents| |toseInvertibleSet| |bfEntry| + |torsion?| |compound?| |insertRoot!| |bumptab| |mainVariable| + |extractBottom!| |lquo| |systemSizeIF| |particularSolution| |inv| + |tanintegrate| |iibinom| |infix| |xCoord| |degree| |squareFree| + |complexEigenvectors| |mainVariables| |swapColumns!| |f04asf| + |ground?| |getMultiplicationTable| |float?| |hasHi| |gbasis| |setPoly| + |parameters| |digit?| |addPoint2| |solveLinear| |linear?| |vark| + |rischDE| |ground| |s21baf| |nonLinearPart| |setEmpty!| + |internalSubQuasiComponent?| |unexpand| |sayLength| + |symmetricRemainder| |initiallyReduce| |polyRicDE| + |bipolarCylindrical| |asinIfCan| |clearTheIFTable| |integers| + |cycleSplit!| |oblateSpheroidal| |divergence| |s01eaf| + |rewriteSetWithReduction| |getGraph| |addMatchRestricted| |d02gbf| + |ref| |term?| |arg1| 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|expressIdealMember| |addPointLast| |summation| |companionBlocks| + |exprToUPS| |character?| |c05nbf| |bitand| + |semiIndiceSubResultantEuclidean| |permutationGroup| + |rewriteIdealWithRemainder| |initiallyReduced?| |makeSUP| |drawCurves| + |partialNumerators| |structuralConstants| |indices| |factorPolynomial| + |brillhartTrials| |knownInfBasis| |domainOf| |unravel| |bitior| + |airyBi| |c06gqf| |linear| |iilog| |curve| |formula| |interval| + |OMsupportsCD?| |and?| |OMgetAtp| |debug| |explicitlyFinite?| |Si| + |ddFact| |corrPoly| |simplifyExp| |e01bff| |rename| |setValue!| + |inverseIntegralMatrix| |frst| |lazyEvaluate| |result| |quadraticNorm| + D |just| |partialFraction| |f02adf| |mpsode| |atanIfCan| |polynomial| + |figureUnits| |polarCoordinates| |SturmHabichtSequence| |genus| + |rootBound| |aQuartic| |properties| |transpose| |arrayStack| + |univariateSolve| |perfectNthPower?| |withPredicates| |ScanRoman| + |asech| |paren| |quasiAlgebraicSet| |cCos| |coth2trigh| + |lazyGintegrate| |translate| |cross| |cAsech| |e02ajf| + |reducedQPowers| |besselI| |pointSizeDefault| |newLine| |sechIfCan| + |OMreadStr| |expt| |in?| |commutative?| |createIrreduciblePoly| |pade| + |overlabel| |printHeader| |multiple| |conjugates| |alphabetic| + |drawStyle| |component| |superscript| |identityMatrix| |readable?| + |leftAlternative?| |splitConstant| |separateDegrees| |dflist| + |exprHasAlgebraicWeight| |applyQuote| |deleteProperty!| + |initializeGroupForWordProblem| |curry| |stoseInvertibleSetreg| + |sequence| |subSet| |checkRur| |scalarMatrix| |mergeFactors| + |integral| |internalIntegrate| |iiacsc| |lfunc| |ldf2lst| |lookup| + |fractRagits| |stopTableGcd!| |numberOfHues| |dot| |linears| + |enterPointData| |s17akf| |separateFactors| |coerceListOfPairs| + |cAtanh| |OMopenFile| |setvalue!| |lineColorDefault| + |rightCharacteristicPolynomial| |selectsecond| |roughBasicSet| |Gamma| + |lift| |ruleset| |generators| |divisorCascade| |binaryFunction| + |exteriorDifferential| |pushuconst| |merge!| |head| |iisqrt2| |maxrow| + |alphanumeric| |screenResolution3D| |reduce| |top| |OMencodingXML| + |signatureAst| |csubst| |forLoop| |critB| |asecIfCan| |print| + |reducedContinuedFraction| |jordanAlgebra?| |e04gcf| |iterationVar| + |cyclotomic| |measure2Result| |generalizedEigenvector| + |generalizedInverse| |trace2PowMod| |BasicMethod| |multMonom| + |resolve| |s17dhf| |approxSqrt| |listRepresentation| |charClass| + |composite| |genericRightDiscriminant| |antiCommutator| |suchThat| + |normal01| |infix?| |iiabs| |completeHensel| |s18dcf| |clikeUniv| + |interpret| |symmetricPower| |hexDigit?| |s18acf| |identity| + |primlimitedint| |rootSplit| |solveLinearlyOverQ| |mask| |laguerre| + |relationsIdeal| |bytes| |Is| |denomLODE| |imaginary| |OMputEndObject| + |OMgetSymbol| |cCsc| |quasiComponent| |packageCall| |rootNormalize| + |myDegree| |eulerPhi| |cAcsch| |s17adf| |mergeDifference| |powmod| + |maxrank| |chineseRemainder| |c02agf| |contractSolve| |bernoulli| + |logIfCan| |ignore?| |subresultantVector| |nextLatticePermutation| + |directory| |repSq| |generate| |heap| |possiblyNewVariety?| |d01akf| + |rombergo| |approximants| |outputAsTex| |fortranTypeOf| + |rightAlternative?| |over| |argumentList!| |shallowExpand| |connectTo| + |complexElementary| |totolex| |whitePoint| |basisOfCentroid| + |OMputVariable| |createPrimitiveElement| |karatsuba| |charpol| + |moduloP| |incrementBy| |cExp| |leftUnits| |swapRows!| |divisors| + |c06ekf| |processTemplate| |getSyntaxFormsFromFile| |leastPower| + |lyndon| |asechIfCan| |evaluate| |triangular?| |expand| |limit| + |duplicates| |nthRoot| |gramschmidt| |bipolar| |surface| |d01asf| + |OMputApp| |atom?| |OMencodingBinary| |rootRadius| |distdfact| + |filterWhile| |makeEq| |smith| |probablyZeroDim?| |name| + |associatedSystem| |leftRegularRepresentation| |root| |push!| + |subResultantGcdEuclidean| |completeHermite| |frobenius| |pushdterm| + |filterUntil| |scanOneDimSubspaces| |maxPoints3D| |body| + |stronglyReduced?| |digit| |mat| |perfectSqrt| |list?| + |selectFiniteRoutines| |cschIfCan| Y |LazardQuotient| |select| + |nthFlag| |phiCoord| |skewSFunction| |rightFactorCandidate| |exquo| + |integralMatrix| |minGbasis| |halfExtendedResultant1| |maxdeg| + |setTopPredicate| |generalInfiniteProduct| |categories| |d02raf| + |toseSquareFreePart| |f07fef| |OMgetBVar| |t| |null?| |div| + |appendPoint| |primitiveElement| |meshFun2Var| |monic?| |rightRecip| + |consnewpol| |cyclicCopy| F |mainDefiningPolynomial| + |algebraicCoefficients?| |setProperties!| |e01bgf| |cardinality| |quo| + |host| |shift| |readByteIfCan!| |high| |pushNewContour| |dimension| + |write!| |s14aaf| |laguerreL| |ODESolve| |collect| |lflimitedint| + |constantIfCan| |e02ahf| |LiePolyIfCan| |pToHdmp| |opeval| + |permutationRepresentation| |ldf2vmf| |primPartElseUnitCanonical| + |monomRDEsys| |sec2cos| |rem| |exptMod| |showClipRegion| |iFTable| + |quadraticForm| |karatsubaDivide| |adjoint| |trivialIdeal?| |d01ajf| + |front| |reducedForm| |radicalSimplify| |setColumn!| + |antiCommutative?| |tanNa| |sizePascalTriangle| |linearPolynomials| + |property| |completeEval| |makeRecord| |selectOrPolynomials| + |createThreeSpace| |topPredicate| |principalIdeal| |curryRight| + |constantRight| |tRange| |c05adf| |geometric| |removeZero| + |setLength!| |realRoots| |normalizeIfCan| |symbolTableOf| + |bezoutResultant| |e02akf| |pseudoDivide| |cyclotomicDecomposition| + |cycle| |modTree| |status| |tryFunctionalDecomposition?| |e01bhf| + |nthExponent| |f01bsf| |s15aef| |adaptive?| |besselK| |ParCond| + |triangulate| |units| |df2st| |numberOfMonomials| |depth| + |indicialEquation| |realZeros| |d01alf| |nthr| |maxColIndex| |meatAxe| + |subNodeOf?| |iiexp| |mainVariable?| ** |rotate| |shellSort| |e02bcf| + |capacity| |duplicates?| |putColorInfo| |coHeight| |resetBadValues| + |idealSimplify| |changeThreshhold| |clipBoolean| |getZechTable| + |signAround| |OMputBVar| |toroidal| |exactQuotient!| |logpart| + |mainForm| |flagFactor| |mainExpression| |extensionDegree| |lintgcd| + |create3Space| |nextNormalPoly| |fixedPointExquo| |nextSublist| + |setPosition| |credPol| |stopTable!| EQ |nextSubsetGray| + |primaryDecomp| |chebyshevU| |rightExactQuotient| |lighting| + |scripted?| |tanh2trigh| |palgintegrate| |f04adf| |janko2| |code| + |numericalIntegration| |setright!| |fixedPoint| |ListOfTerms| + |factorSquareFree| |createLowComplexityTable| |validExponential| + |OMputEndError| |abs| |realElementary| |prime| |polyRDE| + |numberOfComponents| |presub| |taylorRep| |normDeriv2| + |patternVariable| |OMgetEndError| |lllp| |ode| |groebSolve| |rotatez| + |f02bjf| |s13adf| |decreasePrecision| |sinh2csch| |rootPower| + |eisensteinIrreducible?| |iCompose| |rightRegularRepresentation| + |evaluateInverse| |recoverAfterFail| |signature| |hdmpToP| + |showRegion| |s17dgf| |basisOfCommutingElements| |OMread| + |collectUnder| |dom| |changeBase| |cRationalPower| |generalLambert| + |semiLastSubResultantEuclidean| |rational| |optpair| |intPatternMatch| + |OMgetApp| |exponential1| |f02bbf| |f02agf| |overlap| |category| + |selectODEIVPRoutines| |stFunc1| |leftUnit| |rightTrace| |headAst| + |primextendedint| |lex| |domain| |logical?| |fullDisplay| + |listBranches| |minPol| |f02akf| |coerceImages| |nodes| |s20adf| + |rroot| |kind| |package| |purelyAlgebraic?| |inverseColeman| |cn| + |checkForZero| |swap| |standardBasisOfCyclicSubmodule| |components| + |singularitiesOf| |setProperties| |invmultisect| |options| |op| |nlde| + |getVariableOrder| |slex| |setClipValue| |LyndonWordsList| + |definingPolynomial| |palgint| |expIfCan| |title| |explogs2trigs| + |symbolTable| |bindings| |var2Steps| |edf2efi| |coord| |ip4Address| + |psolve| |expandTrigProducts| |weights| |atanhIfCan| |terms| + |factorsOfDegree| |getPickedPoints| + |solveLinearPolynomialEquationByFractions| |physicalLength| + |minPoints3D| |pascalTriangle| |quotedOperators| + |squareFreeLexTriangular| |OMputError| |string| |backOldPos| + |outputFloating| |implies?| |tValues| |degreeSubResultant| |e| + |cyclePartition| |s17aef| |factorByRecursion| |wholeRagits| + |transcendenceDegree| |quadratic?| |makeCos| |tanIfCan| |roughBase?| + |relativeApprox| |printCode| |mapmult| |pdf2df| |exactQuotient| |cLog| + |extendedIntegrate| |cos2sec| |resultantEuclidean| |sample| + |extractTop!| |read!| |stopMusserTrials| |internalIntegrate0| + |lagrange| |quadratic| |resetAttributeButtons| |f01mcf| + |doublyTransitive?| |sqfrFactor| |euclideanSize| |curveColor| + |lieAdmissible?| |symmetricSquare| |addMatch| |cond| |endOfFile?| + |odd?| |interpolate| |extract!| |rotatex| |internal?| + |numberOfOperations| |radicalEigenvector| |bandedHessian| |points| + |d02bhf| |complexNumericIfCan| |setrest!| |fibonacci| |setOfMinN| + |palgRDE0| |nothing| |bounds| |cyclicEntries| |localUnquote| + |roughSubIdeal?| |monomRDE| |f04axf| |recip| |recolor| |leftMult| + |makeSketch| |basisOfCenter| |decimal| |say| |pushFortranOutputStack| + |mightHaveRoots| |repeating| |rule| |log2| |mapdiv| |inverse| |cap| + |iicosh| |euclideanGroebner| |entry| |LyndonWordsList1| |lexico| + |trapezoidal| |floor| |lazyPremWithDefault| |alphabetic?| + |setMaxPoints3D| |block| |supersub| |bit?| |comparison| |s21bbf| + |laplace| |sup| |c06fuf| |cAcos| |roman| |bivariatePolynomials| + |noKaratsuba| |mapUnivariate| |octon| |tryFunctionalDecomposition| + |times!| |increase| |width| |sncndn| |tablePow| |e02bbf| |reverse| + |meshPar1Var| |leadingTerm| |se2rfi| |eof?| |abelianGroup| |f02aef| + |getCode| |int| |f01ref| |lo| |popFortranOutputStack| |froot| + |quotient| |lambert| |horizConcat| |numberOfVariables| |dequeue| + |alphanumeric?| |inconsistent?| |seriesSolve| |morphism| |iiacoth| + |OMsupportsSymbol?| |byte| |retractable?| |numberOfComposites| + |semiSubResultantGcdEuclidean2| |mesh?| |physicalLength!| |void| + |pmComplexintegrate| |commutativeEquality| |lazyIrreducibleFactors| + |outputAsFortran| |removeRedundantFactors| |putGraph| |gcdcofact| + |belong?| |cyclicEqual?| |normalized?| |numberOfDivisors| + |doubleFloatFormat| |removeCosSq| |cAcsc| |entries| |permanent| + |partialQuotients| |inRadical?| |d02kef| |setProperty| |ideal| + |useSingleFactorBound?| |showIntensityFunctions| |plusInfinity| + |semiResultantEuclidean2| |localAbs| |aspFilename| |currentSubProgram| + |prime?| |enterInCache| |stirling2| |plenaryPower| |complexZeros| + |d01apf| |reduceLODE| |minusInfinity| |associatedEquations| |optional| + |extendIfCan| |factorAndSplit| |s18aff| |OMputBind| |double| |polyred| + |fortranCharacter| |univariatePolynomials| |e02gaf| + |halfExtendedSubResultantGcd1| |init| |LyndonCoordinates| |is?| + |purelyAlgebraicLeadingMonomial?| |leftMinimalPolynomial| |mathieu11| + |palgextint0| |extendedint| |integralBasisAtInfinity| |mindegTerm| + |noncommutativeJordanAlgebra?| |makeFloatFunction| |selectPolynomials| + |componentUpperBound| |graphCurves| |radPoly| |intensity| |partitions| + |listOfLists| |interpretString| |explicitlyEmpty?| |tan2trig| + |mapBivariate| |pushup| |rightMult| |mix| |principalAncestors| + |discriminant| |coshIfCan| |back| |extendedSubResultantGcd| + |solveInField| |primextintfrac| |c06gcf| |tubePointsDefault| + |OMputEndAttr| |acothIfCan| |compose| |binarySearchTree| |OMputAtp| + |incrementKthElement| |getIdentifier| |numberOfFractionalTerms| |type| + |tubeRadiusDefault| |implies| |subTriSet?| |linearMatrix| |e02ddf| + |var2StepsDefault| |cyclic?| |getDatabase| |bfKeys| |s15adf| + |makeResult| |removeRoughlyRedundantFactorsInPols| |limitedint| + |integerBound| |HermiteIntegrate| |singleFactorBound| |declare!| + |unary?| SEGMENT |pastel| |curve?| |operators| |cot2trig| |scan| + |perfectNthRoot| |normalizedDivide| |csc2sin| |leadingIdeal| |e04naf| + |constant| |integrate| |constantToUnaryFunction| |reorder| + |outlineRender| |redPo| |imagi| |reindex| |move| |exists?| + |genericLeftTrace| |paraboloidal| |printTypes| |subNode?| |crushedSet| + |fractRadix| |open?| |genericRightMinimalPolynomial| |lexTriangular| + |outputAsScript| |tubePoints| |prindINFO| |super| |hyperelliptic| + |nullary| |solveLinearPolynomialEquationByRecursion| + |inverseIntegralMatrixAtInfinity| |subscriptedVariables| |f02wef| + |imagk| |dn| |member?| |color| |chebyshevT| |merge| |zCoord| |s14baf| + |torsionIfCan| |semiSubResultantGcdEuclidean1| |Aleph| |updatF| + |escape| |leadingIndex| |getBadValues| |Hausdorff| |makeViewport3D| + |iicsc| |lfextlimint| |simplifyPower| |rightDivide| |concat| + |monicLeftDivide| |postfix| |badNum| |homogeneous?| |segment| |addiag| + |zeroDimensional?| |rightGcd| |regularRepresentation| |untab| |f02aaf| + |clipWithRanges| |pol| |error| |listOfMonoms| |imports| |addBadValue| + |extend| |gethi| |blue| |OMputInteger| |gcdcofactprim| |imagE| + |SFunction| |assert| |mapExpon| |showAll?| |showArrayValues| |trim| + |removeCoshSq| |varList| |e02adf| |totalfract| |PDESolve| |stFuncN| + |ptFunc| |bsolve| |deepCopy| |currentScope| + |unrankImproperPartitions1| |vector| |isOpen?| |ceiling| |setStatus!| + |stiffnessAndStabilityFactor| |listYoungTableaus| + |setLegalFortranSourceExtensions| |identification| |bottom!| + |idealiser| |differentiate| |iiasin| |realEigenvectors| |colorDef| + |leftScalarTimes!| |ffactor| |cSin| |elColumn2!| + |discriminantEuclidean| |prem| |f2st| |linearAssociatedLog| ~ |low| + |argumentListOf| |one?| |df2fi| |totalDifferential| |graphStates| + |innerint| |continuedFraction| |source| |matrix| |generateIrredPoly| + |interReduce| |lfinfieldint| |c06gsf| |f2df| |notelem| |e01saf| + |countRealRoots| |createPrimitiveNormalPoly| |mvar| |open| + |rewriteIdealWithQuasiMonicGenerators| |errorInfo| |connect| + |algSplitSimple| |PollardSmallFactor| |monicRightDivide| |f01brf| + |axes| |generalizedEigenvectors| |characteristicPolynomial| + |ramifiedAtInfinity?| |ptree| |purelyTranscendental?| |quickSort| + |keys| |algint| |exprToXXP| |hermite| |besselY| + |clearFortranOutputStack| |radicalSolve| |associatorDependence| + |ratDenom| |viewpoint| |moebiusMu| |selectSumOfSquaresRoutines| + |construct| |represents| |newReduc| |monicCompleteDecompose| + |constantOpIfCan| |integralMatrixAtInfinity| + |constantCoefficientRicDE| |expenseOfEvaluation| |isConnected?| + |RemainderList| |internalInfRittWu?| |kroneckerDelta| |push| + |leftTraceMatrix| |largest| |ksec| |bright| |target| |erf| + |basisOfNucleus| |printStatement| |makeViewport2D| |coleman| + |conditionsForIdempotents| |createMultiplicationMatrix| |imagJ| + |s18def| |realEigenvalues| |traceMatrix| |unitNormal| |setfirst!| + |preprocess| |cAcosh| |solveRetract| |bernoulliB| |qqq| |parts| + |rangePascalTriangle| |eq?| |palgint0| |nsqfree| |iisinh| + |multinomial| |pile| |fractionFreeGauss!| |setMinPoints| |dilog| + |OMgetObject| |countable?| |rotatey| |elliptic| |c06ecf| + |pointColorPalette| |derivative| |setnext!| |c06frf| |plus| + |multisect| |sin| |outputBinaryFile| |permutation| + |createMultiplicationTable| |quasiRegular| |reify| |doubleComplex?| + |spherical| |genericPosition| |cos| |bumptab1| |rootSimp| + |diagonalMatrix| |routines| |cCosh| |complex?| |operator| |every?| + |extendedResultant| |ravel| |graphImage| |tan| |plus!| |baseRDE| + |radicalOfLeftTraceForm| |mainCoefficients| |s17def| |nonQsign| + |d01aqf| |lexGroebner| |reshape| |cot| |polygon?| |bits| + |makeGraphImage| |nor| |solid| |localReal?| |child| |startPolynomial| + |trunc| |times| |sec| |delay| |isQuotient| |mathieu12| |e02zaf| + |copyInto!| |split!| |drawComplex| |singularAtInfinity?| |delete| + |csc| |prevPrime| |doubleResultant| |iiasec| NOT |htrigs| |cAcot| + |prinshINFO| |extractClosed| |iitan| |rst| |lhs| |cAcoth| |asin| + |diag| |denomRicDE| OR |rootProduct| |OMputEndBind| |hasoln| |setelt| + |f02ajf| |readLine!| |var1Steps| |sumOfKthPowerDivisors| |rhs| |acos| + |removeSuperfluousCases| |parabolic| |leftGcd| AND |continue| + |certainlySubVariety?| |unitNormalize| |quasiMonic?| |qfactor| + |invertible?| |monom| |rischNormalize| |atan| |update| |infinityNorm| + |supRittWu?| |removeConstantTerm| |romberg| |copy| |OMputString| + |invertibleElseSplit?| |fortranReal| |pop!| |fglmIfCan| |acot| |pack!| + |rubiksGroup| |Ci| |height| |sin?| |calcRanges| |randnum| + |rightDiscriminant| |invmod| |asec| |selectNonFiniteRoutines| + |ridHack1| |nextsubResultant2| |palginfieldint| |binding| |palgLODE0| + |isOp| |select!| |acotIfCan| |common| |acsc| |lazyPquo| + |exportedOperators| |patternMatch| |oneDimensionalArray| + |leftRankPolynomial| |autoCoerce| |zeroVector| |acoshIfCan| |hermiteH| + |tree| |linearPart| |s19adf| |sinh| |squareTop| |qelt| + |minimalPolynomial| |relerror| |numerators| |multiEuclidean| |An| + |mathieu22| |qsetelt| |socf2socdf| |match?| |cosh| |position| + |modularFactor| |leftFactor| |hasTopPredicate?| |divisor| + |associates?| |taylorIfCan| |failed?| |expr| + |functionIsFracPolynomial?| |e04ycf| |tanh| |OMsetEncoding| + |stoseInvertibleSetsqfreg| |resetVariableOrder| |xRange| |remove!| + |prinpolINFO| |printInfo!| |firstUncouplingMatrix| |prod| |exprex| + |SturmHabichtMultiple| |anfactor| |tail| |expintegrate| |coth| + |symbol?| |yRange| |iiperm| |mainKernel| |pquo| |cosh2sech| |setOrder| + |userOrdered?| |generalPosition| |compdegd| |sech| |selectPDERoutines| + |zRange| |leadingBasisTerm| * |extractSplittingLeaf| |rightNorm| + |bitTruth| |cyclic| |sort!| |outputList| |coerceP| |rightZero| |map!| + |csch| |e02dff| |lllip| |printInfo| GE |lSpaceBasis| |curryLeft| |or?| + |equiv?| |substring?| |variable| |generator| |cycleTail| |qsetelt!| + |asinh| |setMinPoints3D| |coordinates| |digamma| |space| GT |elRow1!| + |ReduceOrder| |delta| |getOperands| |iterators| |schwerpunkt| + |selectOptimizationRoutines| |jacobiIdentity?| |acosh| |iicoth| + |branchIfCan| |reduction| LE |applyRules| |factorSFBRlcUnit| + |inGroundField?| |suffix?| |ramified?| |createPrimitivePoly| |atanh| + |modifyPoint| |lieAlgebra?| |Beta| |leastAffineMultiple| LT + |univariate?| |collectUpper| |lastSubResultant| |factorial| |cAsec| + |iisqrt3| |acoth| |top!| |innerSolve| |andOperands| |doubleRank| + |lifting| |shuffle| |prefix?| |rootOfIrreduciblePoly| |hitherPlane| + |basisOfRightAnnihilator| |delete!| |infinite?| |fill!| + |splitDenominator| |decrease| |leadingCoefficientRicDE| |setleaves!| + |stronglyReduce| |numberOfIrreduciblePoly| |c06gbf| + |commonDenominator| |acsch| |hypergeometric0F1| |laurentRep| + |padicFraction| |RittWuCompare| |sylvesterMatrix| |sorted?| |call| + |definingEquations| |f02aff| |univariatePolynomial| |next| |makeSin| + |iiasinh| |cAsin| |precision| |currentCategoryFrame| |zeroSetSplit| + |fmecg| |rur| |iExquo| |polygon| |monomialIntPoly| |lambda| |isPlus| + |f04mbf| |lazyPseudoRemainder| |trigs2explogs| |aromberg| |objects| + |failed| |genericLeftMinimalPolynomial| |groebner| |divideExponents| + |KrullNumber| |setStatus| |modularGcdPrimitive| |viewport2D| |po| + |midpoint| |base| |doubleDisc| |graeffe| |lowerPolynomial| |sn| + |minPoints| |insertMatch| |cosIfCan| |rename!| UP2UTS + |useEisensteinCriterion| |randomLC| |eulerE| |f04faf| |logGamma| + |rightRank| |tableau| |cartesian| |SturmHabichtCoefficients| |parents| + |rotate!| |arbitrary| |f02abf| |trapezoidalo| |bumprow| |deepExpand| + |unitVector| |setScreenResolution| + |removeRoughlyRedundantFactorsInPol| |completeSmith| + |functionIsOscillatory| |sPol| |s17agf| |close!| |heapSort| + |getStream| |explimitedint| |dmpToHdmp| |palgextint| |associative?| + UTS2UP |iidprod| |removeZeroes| |symmetricProduct| |s19acf| |OMclose| + |monomials| |limitedIntegrate| |jordanAdmissible?| + |stoseSquareFreePart| |OMconnInDevice| |bubbleSort!| |leftZero| + |insert!| |rightTraceMatrix| |integer?| |matrixDimensions| + |LyndonBasis| |rightExtendedGcd| |singular?| |OMputObject| + |modifyPointData| |weierstrass| |primeFactor| |inverseLaplace| |test| + |parent| |complexExpand| |vectorise| |uniform01| |incr| + |wordInGenerators| |contains?| |primintegrate| |OMmakeConn| |pureLex| + |clearCache| |indiceSubResultantEuclidean| |leftDiscriminant| + |irreducibleFactor| |function| |e02agf| |getProperties| + |squareFreePolynomial| |epilogue| |cycles| |truncate| |resize| + |variationOfParameters| |mainValue| |shiftLeft| |hi| + |genericLeftDiscriminant| |prefix| |e02dcf| |deref| + |fortranDoubleComplex| |dmpToP| |id| |iomode| |changeVar| + |resultantReduit| |log| |createNormalPrimitivePoly| |eval| |d02cjf| + |balancedBinaryTree| |option?| FG2F |leaf?| |dim| |previous| |insert| + |shiftRoots| |thetaCoord| |radicalEigenvectors| |setMaxPoints| |node?| + |mathieu24| |selectMultiDimensionalRoutines| |f04qaf| |s17aff| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 9ad39bce..8a7ab5a2 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4602 +1,4603 @@ -(3184524 . 3439752277) -((-2827 (((-112) (-1 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-406 (-558))) -3996 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-38 |#1|) . T) ((-38 $) -3996 (|has| |#1| (-550)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-35) |has| |#1| (-1185)) ((-95) |has| |#1| (-1185)) ((-102) . T) ((-111 #0# #0#) -3996 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-130) . T) ((-144) -3996 (|has| |#1| (-348)) (|has| |#1| (-144))) ((-146) |has| |#1| (-146)) ((-608 #0#) -3996 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-348)) (|has| |#1| (-362))) ((-608 (-558)) . T) ((-608 |#1|) . T) ((-608 $) -3996 (|has| |#1| (-550)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-605 (-853)) . T) ((-171) . T) ((-606 (-168 (-224))) |has| |#1| (-1012)) ((-606 (-168 (-378))) |has| |#1| (-1012)) ((-606 (-534)) |has| |#1| (-606 (-534))) ((-606 (-882 (-378))) |has| |#1| (-606 (-882 (-378)))) ((-606 (-882 (-558))) |has| |#1| (-606 (-882 (-558)))) ((-606 #1=(-1159 |#1|)) . 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T) ((-899) -12 (|has| |#1| (-306)) (|has| |#1| (-899))) ((-910) -3996 (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-992) -12 (|has| |#1| (-992)) (|has| |#1| (-1185))) ((-1028 (-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((-1028 (-558)) |has| |#1| (-1028 (-558))) ((-1028 |#1|) . T) ((-1045 #0#) -3996 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-1045 |#1|) . T) ((-1045 $) . T) ((-1039) . T) ((-1046) . T) ((-1099) . T) ((-1087) . T) ((-1138) |has| |#1| (-348)) ((-1185) |has| |#1| (-1185)) ((-1188) |has| |#1| (-1185)) ((-1200) . 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(-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -3986 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3986 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-608 #0=(-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-608 (-558)) -3986 (|has| |#2| (-1039)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-608 |#2|) -3986 (|has| |#2| (-1087)) (|has| |#2| (-171))) ((-605 (-853)) -3986 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-605 (-853))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-605 (-1246 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1039)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1039))) ((-285 #1=(-558) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1039)) ((-410 |#2|) |has| |#2| (-1087)) ((-487 |#2|) . T) ((-596 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-638 |#2|) -3986 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-638 $) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-631 (-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039))) ((-631 |#2|) |has| |#2| (-1039)) ((-708 |#2|) -3986 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-717) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-782) |has| |#2| (-839)) ((-783) -3986 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-784) |has| |#2| (-784)) ((-785) -3986 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-786) -3986 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-839) |has| |#2| (-839)) ((-841) -3986 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-890 (-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039))) ((-1028 #0#) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-1028 (-558)) -12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) ((-1028 |#2|) |has| |#2| (-1087)) ((-1045 |#2|) -3986 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1045 $) |has| |#2| (-171)) ((-1039) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1046) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1099) -3986 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-1087) -3986 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1200) . T) ((-1253 |#2|) |has| |#2| (-362))) -((-1978 (((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 21)) (-2651 ((|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 23)) (-3124 (((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)) 18))) -(((-238 |#1| |#2| |#3|) (-10 -7 (-15 -1978 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -2651 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3124 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) (-762) (-1200) (-1200)) (T -238)) -((-3124 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *7 (-1200)) (-5 *2 (-239 *5 *7)) (-5 *1 (-238 *5 *6 *7)))) (-2651 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *2 (-1200)) (-5 *1 (-238 *5 *6 *2)))) (-1978 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-239 *6 *7)) (-14 *6 (-762)) (-4 *7 (-1200)) (-4 *5 (-1200)) (-5 *2 (-239 *6 *5)) (-5 *1 (-238 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -3996 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3996 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-608 #0=(-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-608 (-558)) -3996 (|has| |#2| (-1039)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-608 |#2|) -3996 (|has| |#2| (-1087)) (|has| |#2| (-171))) ((-605 (-853)) -3996 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-605 (-853))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-605 (-1246 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1039)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1039))) ((-285 #1=(-558) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1039)) ((-410 |#2|) |has| |#2| (-1087)) ((-487 |#2|) . T) ((-596 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-638 |#2|) -3996 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-638 $) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-631 (-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039))) ((-631 |#2|) |has| |#2| (-1039)) ((-708 |#2|) -3996 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-717) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-782) |has| |#2| (-839)) ((-783) -3996 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-784) |has| |#2| (-784)) ((-785) -3996 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-786) -3996 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-839) |has| |#2| (-839)) ((-841) -3996 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-890 (-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039))) ((-1028 #0#) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-1028 (-558)) -12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) ((-1028 |#2|) |has| |#2| (-1087)) ((-1045 |#2|) -3996 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1045 $) |has| |#2| (-171)) ((-1039) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1046) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1099) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-1087) -3996 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1200) . T) ((-1253 |#2|) |has| |#2| (-362))) +((-3703 (((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 21)) (-3024 ((|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 23)) (-2009 (((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)) 18))) +(((-238 |#1| |#2| |#3|) (-10 -7 (-15 -3703 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3024 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -2009 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) (-762) (-1200) (-1200)) (T -238)) +((-2009 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *7 (-1200)) (-5 *2 (-239 *5 *7)) (-5 *1 (-238 *5 *6 *7)))) (-3024 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *2 (-1200)) (-5 *1 (-238 *5 *6 *2)))) (-3703 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-239 *6 *7)) (-14 *6 (-762)) (-4 *7 (-1200)) (-4 *5 (-1200)) (-5 *2 (-239 *6 *5)) (-5 *1 (-238 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-1204) |has| |#1| (-899))) -((-2526 (((-112) $ $) 19 (|has| |#1| (-1087)))) (-3578 ((|#1| $) 54)) (-3043 ((|#1| $) 44)) (-3883 (((-112) $ (-762)) 8)) (-1334 (($) 7 T CONST)) (-1909 (($ $) 60)) (-2463 (($ $) 48)) (-1301 ((|#1| |#1| $) 46)) (-2812 ((|#1| $) 45)) (-4164 (((-635 |#1|) $) 30 (|has| $ (-6 -4382)))) (-4264 (((-112) $ (-762)) 9)) (-2105 (((-635 |#1|) $) 29 (|has| $ (-6 -4382)))) (-2907 (((-112) |#1| $) 27 (-12 (|has| |#1| (-1087)) (|has| $ (-6 -4382))))) (-3729 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4383)))) (-3124 (($ (-1 |#1| |#1|) $) 35)) (-2147 (((-112) $ (-762)) 10)) (-1742 (((-762) $) 61)) (-4186 (((-1145) $) 22 (|has| |#1| (-1087)))) (-2076 ((|#1| $) 39)) (-2554 ((|#1| |#1| $) 52)) (-3002 ((|#1| |#1| $) 51)) (-3285 (($ |#1| $) 40)) (-2091 (((-762) $) 55)) (-1671 (((-1107) $) 21 (|has| |#1| (-1087)))) (-3428 ((|#1| $) 62)) (-1611 ((|#1| $) 50)) (-2014 ((|#1| $) 49)) (-1338 ((|#1| $) 41)) (-4011 (((-112) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4382)))) (-4304 (($ $ (-635 (-293 |#1|))) 26 (-12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (($ $ (-293 |#1|)) 25 (-12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (($ $ (-635 |#1|) (-635 |#1|)) 23 (-12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))))) (-2615 (((-112) $ $) 14)) (-1472 ((|#1| |#1| $) 58)) (-1508 (((-112) $) 11)) (-1811 (($) 12)) (-1798 ((|#1| $) 59)) (-1964 (($) 57) (($ (-635 |#1|)) 56)) (-1414 (((-762) $) 43)) (-1680 (((-762) (-1 (-112) |#1|) $) 31 (|has| $ (-6 -4382))) (((-762) |#1| $) 28 (-12 (|has| |#1| (-1087)) (|has| $ (-6 -4382))))) (-4001 (($ $) 13)) (-2540 (((-853) $) 18 (|has| |#1| (-605 (-853))))) (-3996 ((|#1| $) 53)) (-3035 (($ (-635 |#1|)) 42)) (-3663 ((|#1| $) 63)) (-2473 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4382)))) (-1692 (((-112) $ $) 20 (|has| |#1| (-1087)))) (-1427 (((-762) $) 6 (|has| $ (-6 -4382))))) +((-1550 (*1 *2 *3) (-12 (-4 *4 (-1039)) (-4 *3 (-841)) (-4 *5 (-265 *3)) (-4 *6 (-784)) (-5 *2 (-1 *1 (-762))) (-4 *1 (-252 *4 *3 *5 *6)))) (-2059 (*1 *2 *1) (-12 (-4 *1 (-252 *3 *4 *5 *6)) (-4 *3 (-1039)) (-4 *4 (-841)) (-4 *5 (-265 *4)) (-4 *6 (-784)) (-5 *2 (-635 *4)))) (-2379 (*1 *2 *1 *3) (-12 (-4 *1 (-252 *4 *3 *5 *6)) (-4 *4 (-1039)) (-4 *3 (-841)) (-4 *5 (-265 *3)) (-4 *6 (-784)) (-5 *2 (-762)))) (-2379 (*1 *2 *1) (-12 (-4 *1 (-252 *3 *4 *5 *6)) (-4 *3 (-1039)) (-4 *4 (-841)) (-4 *5 (-265 *4)) (-4 *6 (-784)) (-5 *2 (-762)))) (-2763 (*1 *2 *1 *3) (-12 (-4 *1 (-252 *4 *3 *5 *6)) (-4 *4 (-1039)) (-4 *3 (-841)) (-4 *5 (-265 *3)) (-4 *6 (-784)) (-5 *2 (-762)))) (-3434 (*1 *2 *1) (-12 (-4 *1 (-252 *3 *4 *5 *6)) (-4 *3 (-1039)) (-4 *4 (-841)) (-4 *5 (-265 *4)) (-4 *6 (-784)) (-5 *2 (-635 (-762))))) (-2495 (*1 *2 *1) (-12 (-4 *1 (-252 *3 *4 *5 *6)) (-4 *3 (-1039)) (-4 *4 (-841)) (-4 *5 (-265 *4)) (-4 *6 (-784)) (-5 *2 (-762)))) (-3434 (*1 *2 *1 *3) (-12 (-4 *1 (-252 *4 *3 *5 *6)) (-4 *4 (-1039)) (-4 *3 (-841)) (-4 *5 (-265 *3)) (-4 *6 (-784)) (-5 *2 (-635 (-762))))) (-2495 (*1 *2 *1 *3) (-12 (-4 *1 (-252 *4 *3 *5 *6)) (-4 *4 (-1039)) (-4 *3 (-841)) (-4 *5 (-265 *3)) (-4 *6 (-784)) (-5 *2 (-762)))) (-2262 (*1 *2 *1) (-12 (-4 *1 (-252 *3 *4 *5 *6)) (-4 *3 (-1039)) (-4 *4 (-841)) (-4 *5 (-265 *4)) (-4 *6 (-784)) (-5 *2 (-112)))) (-1683 (*1 *2 *1) (-12 (-4 *1 (-252 *3 *4 *2 *5)) (-4 *3 (-1039)) (-4 *4 (-841)) (-4 *5 (-784)) (-4 *2 (-265 *4)))) (-2704 (*1 *1 *1) (-12 (-4 *1 (-252 *2 *3 *4 *5)) (-4 *2 (-1039)) (-4 *3 (-841)) (-4 *4 (-265 *3)) (-4 *5 (-784)))) (-2369 (*1 *1 *1) (-12 (-4 *1 (-252 *2 *3 *4 *5)) (-4 *2 (-1039)) (-4 *3 (-841)) (-4 *4 (-265 *3)) (-4 *5 (-784)))) (-1550 (*1 *2 *1) (-12 (-4 *3 (-232)) (-4 *3 (-1039)) (-4 *4 (-841)) (-4 *5 (-265 *4)) (-4 *6 (-784)) (-5 *2 (-1 *1 (-762))) (-4 *1 (-252 *3 *4 *5 *6))))) +(-13 (-939 |t#1| |t#4| |t#3|) (-230 |t#1|) (-1028 |t#2|) (-10 -8 (-15 -1550 ((-1 $ (-762)) |t#2|)) (-15 -2059 ((-635 |t#2|) $)) (-15 -2379 ((-762) $ |t#2|)) (-15 -2379 ((-762) $)) (-15 -2763 ((-762) $ |t#2|)) (-15 -3434 ((-635 (-762)) $)) (-15 -2495 ((-762) $)) (-15 -3434 ((-635 (-762)) $ |t#2|)) (-15 -2495 ((-762) $ |t#2|)) (-15 -2262 ((-112) $)) (-15 -1683 (|t#3| $)) (-15 -2704 ($ $)) (-15 -2369 ($ $)) (IF (|has| |t#1| (-232)) (PROGN (-6 (-512 |t#2| |t#1|)) (-6 (-512 |t#2| $)) (-6 (-308 $)) (-15 -1550 ((-1 $ (-762)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #0#) -3996 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 |#1|) . T) ((-608 |#2|) . T) ((-608 |#3|) . T) ((-608 $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450))) ((-605 (-853)) . 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T) ((-638 |#2|) |has| |#1| (-362)) ((-638 $) . T) ((-631 (-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-631 (-558)))) ((-631 |#2|) |has| |#1| (-362)) ((-708 #1#) -3996 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-708 |#1|) |has| |#1| (-171)) ((-708 |#2|) |has| |#1| (-362)) ((-708 $) -3996 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-717) . 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T) ((-23) . T) ((-47 |#1| #0=(-762)) . T) ((-25) . T) ((-38 #1=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3986 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 #2=(-1069)) . T) ((-608 |#1|) . T) ((-608 $) -3986 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-605 (-853)) . 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T) ((-23) . T) ((-47 |#1| #0=(-762)) . T) ((-25) . T) ((-38 #1=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3996 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 #2=(-1069)) . T) ((-608 |#1|) . T) ((-608 $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-605 (-853)) . T) ((-171) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-606 (-534)) -12 (|has| (-1069) (-606 (-534))) (|has| |#1| (-606 (-534)))) ((-606 (-882 (-378))) -12 (|has| (-1069) (-606 (-882 (-378)))) (|has| |#1| (-606 (-882 (-378))))) ((-606 (-882 (-558))) -12 (|has| (-1069) (-606 (-882 (-558)))) (|has| |#1| (-606 (-882 (-558))))) ((-230 |#1|) . T) ((-232) . T) ((-285 (-406 $) (-406 $)) |has| |#1| (-550)) ((-285 |#1| |#1|) . T) ((-285 $ $) . T) ((-289) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-306) |has| |#1| (-362)) ((-308 $) . T) ((-325 |#1| #0#) . T) ((-376 |#1|) . T) ((-410 |#1|) . T) ((-450) -3996 (|has| |#1| (-899)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-512 #2# |#1|) . T) ((-512 #2# $) . T) ((-512 $ $) . T) ((-550) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-638 #1#) |has| |#1| (-38 (-406 (-558)))) ((-638 |#1|) . T) ((-638 $) . T) ((-631 (-558)) |has| |#1| (-631 (-558))) ((-631 |#1|) . T) ((-708 #1#) |has| |#1| (-38 (-406 (-558)))) ((-708 |#1|) |has| |#1| (-171)) ((-708 $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-717) . T) ((-841) |has| |#1| (-841)) ((-890 #2#) . T) ((-890 (-1163)) |has| |#1| (-890 (-1163))) ((-876 (-378)) -12 (|has| (-1069) (-876 (-378))) (|has| |#1| (-876 (-378)))) ((-876 (-558)) -12 (|has| (-1069) (-876 (-558))) (|has| |#1| (-876 (-558)))) ((-939 |#1| #0# #2#) . T) ((-899) |has| |#1| (-899)) ((-910) |has| |#1| (-362)) ((-1028 (-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((-1028 (-558)) |has| |#1| (-1028 (-558))) ((-1028 #2#) . T) ((-1028 |#1|) . T) ((-1045 #1#) |has| |#1| (-38 (-406 (-558)))) ((-1045 |#1|) . T) ((-1045 $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-1039) . T) ((-1046) . T) ((-1099) . T) ((-1087) . T) ((-1138) |has| |#1| (-1138)) ((-1204) |has| |#1| (-899))) +((-2664 (((-635 (-1069)) $) 28)) (-2500 (($ $) 25)) (-2642 (($ |#2| |#3|) NIL) (($ $ (-1069) |#3|) 22) (($ $ (-635 (-1069)) (-635 |#3|)) 21)) (-2461 (($ $) 14)) (-2474 ((|#2| $) 12)) (-2763 ((|#3| $) 10))) +(((-1223 |#1| |#2| |#3|) (-10 -8 (-15 -2664 ((-635 (-1069)) |#1|)) (-15 -2642 (|#1| |#1| (-635 (-1069)) (-635 |#3|))) (-15 -2642 (|#1| |#1| (-1069) |#3|)) (-15 -2500 (|#1| |#1|)) (-15 -2642 (|#1| |#2| |#3|)) (-15 -2763 (|#3| |#1|)) (-15 -2461 (|#1| |#1|)) (-15 -2474 (|#2| |#1|))) (-1224 |#2| |#3|) (-1039) (-783)) (T -1223)) +NIL +(-10 -8 (-15 -2664 ((-635 (-1069)) |#1|)) (-15 -2642 (|#1| |#1| (-635 (-1069)) (-635 |#3|))) (-15 -2642 (|#1| |#1| (-1069) |#3|)) (-15 -2500 (|#1| |#1|)) (-15 -2642 (|#1| |#2| |#3|)) (-15 -2763 (|#3| |#1|)) (-15 -2461 (|#1| |#1|)) (-15 -2474 (|#2| |#1|))) +((-2549 (((-112) $ $) 7)) (-2212 (((-112) $) 16)) (-2664 (((-635 (-1069)) $) 77)) (-4139 (((-1163) $) 106)) (-3899 (((-2 (|:| -2822 $) (|:| 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) |has| |#1| (-550)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3986 (|has| |#1| (-550)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #0#) |has| |#1| (-38 (-406 (-558)))) ((-608 (-558)) . T) ((-608 |#1|) |has| |#1| (-171)) ((-608 $) |has| |#1| (-550)) ((-605 (-853)) . T) ((-171) -3986 (|has| |#1| (-550)) (|has| |#1| (-171))) ((-232) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-285 $ $) |has| |#2| (-1099)) ((-289) |has| |#1| (-550)) ((-550) |has| |#1| (-550)) ((-638 #0#) |has| |#1| (-38 (-406 (-558)))) ((-638 |#1|) . T) ((-638 $) . T) ((-708 #0#) |has| |#1| (-38 (-406 (-558)))) ((-708 |#1|) |has| |#1| (-171)) ((-708 $) |has| |#1| (-550)) ((-717) . 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T) ((-23) . T) ((-47 |#1| #0=(-406 (-558))) . T) ((-25) . T) ((-38 #1=(-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3996 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-35) |has| |#1| (-38 (-406 (-558)))) ((-95) |has| |#1| (-38 (-406 (-558)))) ((-102) . T) ((-111 #1# #1#) -3996 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3996 (|has| |#1| (-550)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3996 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 |#1|) |has| |#1| (-171)) ((-608 $) -3996 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-605 (-853)) . 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"TRANFUN-" 2871460 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1183 2870788 2870820 2870881 "TOPSP" 2870945 T TOPSP (NIL) -7 NIL NIL NIL) (-1182 2870136 2870251 2870405 "TOOLSIGN" 2870669 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1181 2868797 2869313 2869552 "TEXTFILE" 2869919 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1180 2866736 2867250 2867679 "TEX" 2868390 T TEX (NIL) -8 NIL NIL NIL) (-1179 2866517 2866548 2866620 "TEX1" 2866699 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1178 2866165 2866228 2866318 "TEMUTL" 2866449 T TEMUTL (NIL) -7 NIL NIL NIL) (-1177 2864319 2864599 2864924 "TBCMPPK" 2865888 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1176 2856207 2862479 2862535 "TBAGG" 2862935 NIL TBAGG (NIL T T) -9 NIL 2863146 NIL) (-1175 2851277 2852765 2854519 "TBAGG-" 2854524 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1174 2850661 2850768 2850913 "TANEXP" 2851166 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1173 2844162 2850518 2850611 "TABLE" 2850616 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1172 2843574 2843673 2843811 "TABLEAU" 2844059 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1171 2838182 2839402 2840650 "TABLBUMP" 2842360 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1170 2837610 2837710 2837838 "SYSTEM" 2838076 T SYSTEM (NIL) -7 NIL NIL NIL) (-1169 2834073 2834768 2835551 "SYSSOLP" 2836861 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1168 2830407 2831334 2832050 "SYNTAX" 2833379 T SYNTAX (NIL) -8 NIL NIL NIL) (-1167 2827565 2828167 2828799 "SYMTAB" 2829797 T SYMTAB (NIL) -8 NIL NIL NIL) (-1166 2822814 2823716 2824699 "SYMS" 2826604 T SYMS (NIL) -8 NIL NIL NIL) (-1165 2820086 2822272 2822502 "SYMPOLY" 2822619 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1164 2819603 2819678 2819801 "SYMFUNC" 2819998 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1163 2815655 2816915 2817728 "SYMBOL" 2818812 T SYMBOL (NIL) -8 NIL NIL NIL) (-1162 2809194 2810883 2812603 "SWITCH" 2813957 T SWITCH (NIL) -8 NIL NIL NIL) (-1161 2802464 2808015 2808318 "SUTS" 2808949 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2794565 2801711 2801984 "SUPXS" 2802249 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2786095 2794183 2794309 "SUP" 2794474 NIL SUP (NIL T) -8 NIL NIL NIL) (-1158 2785254 2785381 2785598 "SUPFRACF" 2785963 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1157 2784875 2784934 2785047 "SUP2" 2785189 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1156 2783288 2783562 2783925 "SUMRF" 2784574 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1155 2782602 2782668 2782867 "SUMFS" 2783209 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1154 2766609 2781779 2782030 "SULS" 2782409 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1153 2766238 2766431 2766501 "SUCHTAST" 2766561 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1152 2765560 2765763 2765903 "SUCH" 2766146 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1151 2759454 2760466 2761425 "SUBSPACE" 2764648 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1150 2758884 2758974 2759138 "SUBRESP" 2759342 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1149 2752253 2753549 2754860 "STTF" 2757620 NIL STTF (NIL T) -7 NIL NIL NIL) (-1148 2746426 2747546 2748693 "STTFNC" 2751153 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1147 2737741 2739608 2741402 "STTAYLOR" 2744667 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1146 2730985 2737605 2737688 "STRTBL" 2737693 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1145 2726376 2730940 2730971 "STRING" 2730976 T STRING (NIL) -8 NIL NIL NIL) (-1144 2721264 2725749 2725779 "STRICAT" 2725838 T STRICAT (NIL) -9 NIL 2725900 NIL) (-1143 2714074 2718883 2719494 "STREAM" 2720688 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1142 2713584 2713661 2713805 "STREAM3" 2713991 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1141 2712566 2712749 2712984 "STREAM2" 2713397 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1140 2712254 2712306 2712399 "STREAM1" 2712508 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1139 2711270 2711451 2711682 "STINPROD" 2712070 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1138 2710848 2711032 2711062 "STEP" 2711142 T STEP (NIL) -9 NIL 2711220 NIL) (-1137 2704391 2710747 2710824 "STBL" 2710829 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1136 2699565 2703612 2703655 "STAGG" 2703808 NIL STAGG (NIL T) -9 NIL 2703897 NIL) (-1135 2697267 2697869 2698741 "STAGG-" 2698746 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1134 2695462 2697037 2697129 "STACK" 2697210 NIL STACK (NIL T) -8 NIL NIL NIL) (-1133 2688187 2693603 2694059 "SREGSET" 2695092 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1132 2680613 2681981 2683494 "SRDCMPK" 2686793 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2673580 2678053 2678083 "SRAGG" 2679386 T SRAGG (NIL) -9 NIL 2679994 NIL) (-1130 2672597 2672852 2673231 "SRAGG-" 2673236 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1129 2667092 2671544 2671965 "SQMATRIX" 2672223 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1128 2660841 2663810 2664537 "SPLTREE" 2666437 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1127 2656831 2657497 2658143 "SPLNODE" 2660267 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1126 2655878 2656111 2656141 "SPFCAT" 2656585 T SPFCAT (NIL) -9 NIL NIL NIL) (-1125 2654615 2654825 2655089 "SPECOUT" 2655636 T SPECOUT (NIL) -7 NIL NIL NIL) (-1124 2646267 2648011 2648041 "SPADXPT" 2652433 T SPADXPT (NIL) -9 NIL 2654467 NIL) (-1123 2646028 2646068 2646137 "SPADPRSR" 2646220 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1122 2644211 2645983 2646014 "SPADAST" 2646019 T SPADAST (NIL) -8 NIL NIL NIL) (-1121 2636182 2637929 2637972 "SPACEC" 2642345 NIL SPACEC (NIL T) -9 NIL 2644161 NIL) (-1120 2634353 2636114 2636163 "SPACE3" 2636168 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1119 2633105 2633276 2633567 "SORTPAK" 2634158 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1118 2631155 2631458 2631877 "SOLVETRA" 2632769 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1117 2630166 2630388 2630662 "SOLVESER" 2630928 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1116 2625386 2626267 2627269 "SOLVERAD" 2629218 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1115 2621201 2621810 2622539 "SOLVEFOR" 2624753 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1114 2615498 2620550 2620647 "SNTSCAT" 2620652 NIL SNTSCAT (NIL T T T T) -9 NIL 2620722 NIL) (-1113 2609641 2613821 2614212 "SMTS" 2615188 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1112 2604092 2609529 2609606 "SMP" 2609611 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1111 2602251 2602552 2602950 "SMITH" 2603789 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1110 2595146 2599302 2599405 "SMATCAT" 2600756 NIL SMATCAT (NIL NIL T T T) -9 NIL 2601306 NIL) (-1109 2592086 2592909 2594087 "SMATCAT-" 2594092 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1108 2589799 2591322 2591365 "SKAGG" 2591626 NIL SKAGG (NIL T) -9 NIL 2591761 NIL) (-1107 2586141 2589215 2589410 "SINT" 2589597 T SINT (NIL) -8 NIL NIL 2589770) (-1106 2585913 2585951 2586017 "SIMPAN" 2586097 T SIMPAN (NIL) -7 NIL NIL NIL) (-1105 2585220 2585448 2585588 "SIG" 2585795 T SIG (NIL) -8 NIL NIL NIL) (-1104 2584058 2584279 2584554 "SIGNRF" 2584979 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1103 2582863 2583014 2583305 "SIGNEF" 2583887 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1102 2582196 2582446 2582570 "SIGAST" 2582761 T SIGAST (NIL) -8 NIL NIL NIL) (-1101 2579886 2580340 2580846 "SHP" 2581737 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1100 2573792 2579787 2579863 "SHDP" 2579868 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1099 2573391 2573557 2573587 "SGROUP" 2573680 T SGROUP (NIL) -9 NIL 2573742 NIL) (-1098 2573249 2573275 2573348 "SGROUP-" 2573353 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1097 2570085 2570782 2571505 "SGCF" 2572548 T SGCF (NIL) -7 NIL NIL NIL) (-1096 2564480 2569532 2569629 "SFRTCAT" 2569634 NIL SFRTCAT (NIL T T T T) -9 NIL 2569673 NIL) (-1095 2557904 2558919 2560055 "SFRGCD" 2563463 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1094 2551032 2552103 2553289 "SFQCMPK" 2556837 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2550654 2550743 2550853 "SFORT" 2550973 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1092 2549799 2550494 2550615 "SEXOF" 2550620 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1091 2548933 2549680 2549748 "SEX" 2549753 T SEX (NIL) -8 NIL NIL NIL) (-1090 2544472 2545161 2545256 "SEXCAT" 2548193 NIL SEXCAT (NIL T T T T T) -9 NIL 2548771 NIL) (-1089 2541652 2544406 2544454 "SET" 2544459 NIL SET (NIL T) -8 NIL NIL NIL) (-1088 2539903 2540365 2540670 "SETMN" 2541393 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1087 2539509 2539635 2539665 "SETCAT" 2539782 T SETCAT (NIL) -9 NIL 2539867 NIL) (-1086 2539289 2539341 2539440 "SETCAT-" 2539445 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1085 2535676 2537750 2537793 "SETAGG" 2538663 NIL SETAGG (NIL T) -9 NIL 2539003 NIL) (-1084 2535134 2535250 2535487 "SETAGG-" 2535492 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1083 2534604 2534830 2534931 "SEQAST" 2535055 T SEQAST (NIL) -8 NIL NIL NIL) (-1082 2533803 2534097 2534158 "SEGXCAT" 2534444 NIL SEGXCAT (NIL T T) -9 NIL 2534564 NIL) (-1081 2532859 2533469 2533651 "SEG" 2533656 NIL SEG (NIL T) -8 NIL NIL NIL) (-1080 2531838 2532052 2532095 "SEGCAT" 2532617 NIL SEGCAT (NIL T) -9 NIL 2532838 NIL) (-1079 2530887 2531217 2531417 "SEGBIND" 2531673 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1078 2530508 2530567 2530680 "SEGBIND2" 2530822 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1077 2530109 2530309 2530386 "SEGAST" 2530453 T SEGAST (NIL) -8 NIL NIL NIL) (-1076 2529328 2529454 2529658 "SEG2" 2529953 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1075 2528765 2529263 2529310 "SDVAR" 2529315 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1074 2521055 2528535 2528665 "SDPOL" 2528670 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1073 2519648 2519914 2520233 "SCPKG" 2520770 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1072 2518784 2518964 2519164 "SCOPE" 2519470 T SCOPE (NIL) -8 NIL NIL NIL) (-1071 2518005 2518138 2518317 "SCACHE" 2518639 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1070 2517677 2517837 2517867 "SASTCAT" 2517872 T SASTCAT (NIL) -9 NIL 2517885 NIL) (-1069 2517191 2517512 2517588 "SAOS" 2517623 T SAOS (NIL) -8 NIL NIL NIL) (-1068 2516756 2516791 2516964 "SAERFFC" 2517150 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1067 2510730 2516653 2516733 "SAE" 2516738 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1066 2510323 2510358 2510517 "SAEFACT" 2510689 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1065 2508644 2508958 2509359 "RURPK" 2509989 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1064 2507280 2507559 2507871 "RULESET" 2508478 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1063 2504467 2504970 2505435 "RULE" 2506961 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1062 2504106 2504261 2504344 "RULECOLD" 2504419 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1061 2503604 2503823 2503917 "RSTRCAST" 2504034 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1060 2498453 2499247 2500167 "RSETGCD" 2502803 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1059 2487710 2492762 2492859 "RSETCAT" 2496978 NIL RSETCAT (NIL T T T T) -9 NIL 2498075 NIL) (-1058 2485637 2486176 2487000 "RSETCAT-" 2487005 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1057 2478024 2479399 2480919 "RSDCMPK" 2484236 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2476029 2476470 2476544 "RRCC" 2477630 NIL RRCC (NIL T T) -9 NIL 2477974 NIL) (-1055 2475380 2475554 2475833 "RRCC-" 2475838 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1054 2474850 2475076 2475177 "RPTAST" 2475301 T RPTAST (NIL) -8 NIL NIL NIL) (-1053 2448856 2458443 2458510 "RPOLCAT" 2469174 NIL RPOLCAT (NIL T T T) -9 NIL 2472333 NIL) (-1052 2440356 2442694 2445816 "RPOLCAT-" 2445821 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1051 2431403 2438567 2439049 "ROUTINE" 2439896 T ROUTINE (NIL) -8 NIL NIL NIL) (-1050 2428236 2431029 2431169 "ROMAN" 2431285 T ROMAN (NIL) -8 NIL NIL NIL) (-1049 2426511 2427096 2427356 "ROIRC" 2428041 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1048 2422904 2425147 2425177 "RNS" 2425481 T RNS (NIL) -9 NIL 2425754 NIL) (-1047 2421413 2421796 2422330 "RNS-" 2422405 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1046 2420862 2421244 2421274 "RNG" 2421279 T RNG (NIL) -9 NIL 2421300 NIL) (-1045 2420254 2420616 2420659 "RMODULE" 2420721 NIL RMODULE (NIL T) -9 NIL 2420763 NIL) (-1044 2419090 2419184 2419520 "RMCAT2" 2420155 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1043 2415967 2418436 2418733 "RMATRIX" 2418852 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1042 2408909 2411143 2411258 "RMATCAT" 2414617 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2415599 NIL) (-1041 2408284 2408431 2408738 "RMATCAT-" 2408743 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1040 2407851 2407926 2408054 "RINTERP" 2408203 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1039 2406984 2407504 2407534 "RING" 2407590 T RING (NIL) -9 NIL 2407676 NIL) (-1038 2406776 2406820 2406917 "RING-" 2406922 NIL RING- (NIL T) -8 NIL NIL NIL) (-1037 2405617 2405854 2406112 "RIDIST" 2406540 T RIDIST (NIL) -7 NIL NIL NIL) (-1036 2396933 2405085 2405291 "RGCHAIN" 2405465 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1035 2396309 2396689 2396730 "RGBCSPC" 2396788 NIL RGBCSPC (NIL T) -9 NIL 2396840 NIL) (-1034 2395493 2395848 2395889 "RGBCMDL" 2396121 NIL RGBCMDL (NIL T) -9 NIL 2396235 NIL) (-1033 2392487 2393101 2393771 "RF" 2394857 NIL RF (NIL T) -7 NIL NIL NIL) (-1032 2392133 2392196 2392299 "RFFACTOR" 2392418 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1031 2391858 2391893 2391990 "RFFACT" 2392092 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1030 2389975 2390339 2390721 "RFDIST" 2391498 T RFDIST (NIL) -7 NIL NIL NIL) (-1029 2389428 2389520 2389683 "RETSOL" 2389877 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1028 2389064 2389144 2389187 "RETRACT" 2389320 NIL RETRACT (NIL T) -9 NIL 2389407 NIL) (-1027 2388913 2388938 2389025 "RETRACT-" 2389030 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1026 2388542 2388735 2388805 "RETAST" 2388865 T RETAST (NIL) -8 NIL NIL NIL) (-1025 2381396 2388195 2388322 "RESULT" 2388437 T RESULT (NIL) -8 NIL NIL NIL) (-1024 2380022 2380665 2380864 "RESRING" 2381299 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1023 2379658 2379707 2379805 "RESLATC" 2379959 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1022 2379364 2379398 2379505 "REPSQ" 2379617 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1021 2376786 2377366 2377968 "REP" 2378784 T REP (NIL) -7 NIL NIL NIL) (-1020 2376484 2376518 2376629 "REPDB" 2376745 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1019 2370394 2371773 2372996 "REP2" 2375296 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1018 2366771 2367452 2368260 "REP1" 2369621 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1017 2359497 2364912 2365368 "REGSET" 2366401 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2358310 2358645 2358895 "REF" 2359282 NIL REF (NIL T) -8 NIL NIL NIL) (-1015 2357687 2357790 2357957 "REDORDER" 2358194 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1014 2353692 2356900 2357127 "RECLOS" 2357515 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1013 2352744 2352925 2353140 "REALSOLV" 2353499 T REALSOLV (NIL) -7 NIL NIL NIL) (-1012 2352590 2352631 2352661 "REAL" 2352666 T REAL (NIL) -9 NIL 2352701 NIL) (-1011 2349073 2349875 2350759 "REAL0Q" 2351755 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1010 2344674 2345662 2346723 "REAL0" 2348054 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1009 2344172 2344391 2344485 "RDUCEAST" 2344602 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1008 2343577 2343649 2343856 "RDIV" 2344094 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1007 2342645 2342819 2343032 "RDIST" 2343399 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1006 2341242 2341529 2341901 "RDETRS" 2342353 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1005 2339054 2339508 2340046 "RDETR" 2340784 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1004 2337665 2337943 2338347 "RDEEFS" 2338770 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1003 2336160 2336466 2336898 "RDEEF" 2337353 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1002 2330421 2333296 2333326 "RCFIELD" 2334621 T RCFIELD (NIL) -9 NIL 2335351 NIL) (-1001 2328485 2328989 2329685 "RCFIELD-" 2329760 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1000 2324801 2326586 2326629 "RCAGG" 2327713 NIL RCAGG (NIL T) -9 NIL 2328178 NIL) (-999 2324431 2324525 2324686 "RCAGG-" 2324691 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-998 2323771 2323883 2324046 "RATRET" 2324315 NIL RATRET (NIL T) -7 NIL NIL NIL) (-997 2323328 2323395 2323514 "RATFACT" 2323699 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-996 2322643 2322763 2322913 "RANDSRC" 2323198 T RANDSRC (NIL) -7 NIL NIL NIL) (-995 2322380 2322424 2322495 "RADUTIL" 2322592 T RADUTIL (NIL) -7 NIL NIL NIL) (-994 2315542 2321222 2321530 "RADIX" 2322104 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-993 2307199 2315386 2315514 "RADFF" 2315519 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-992 2306851 2306926 2306954 "RADCAT" 2307111 T RADCAT (NIL) -9 NIL NIL NIL) (-991 2306636 2306684 2306781 "RADCAT-" 2306786 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-990 2304787 2306411 2306500 "QUEUE" 2306580 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-989 2301363 2304724 2304769 "QUAT" 2304774 NIL QUAT (NIL T) -8 NIL NIL NIL) (-988 2301001 2301044 2301171 "QUATCT2" 2301314 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2294748 2298050 2298090 "QUATCAT" 2298870 NIL QUATCAT (NIL T) -9 NIL 2299636 NIL) (-986 2290892 2291929 2293316 "QUATCAT-" 2293410 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-985 2288412 2289976 2290017 "QUAGG" 2290392 NIL QUAGG (NIL T) -9 NIL 2290567 NIL) (-984 2288044 2288237 2288305 "QQUTAST" 2288364 T QQUTAST (NIL) -8 NIL NIL NIL) (-983 2286969 2287442 2287614 "QFORM" 2287916 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-982 2278181 2283386 2283426 "QFCAT" 2284084 NIL QFCAT (NIL T) -9 NIL 2285085 NIL) (-981 2273753 2274954 2276545 "QFCAT-" 2276639 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-980 2273391 2273434 2273561 "QFCAT2" 2273704 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-979 2272851 2272961 2273091 "QEQUAT" 2273281 T QEQUAT (NIL) -8 NIL NIL NIL) (-978 2265999 2267070 2268254 "QCMPACK" 2271784 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-977 2263575 2263996 2264424 "QALGSET" 2265654 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-976 2262820 2262994 2263226 "QALGSET2" 2263395 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-975 2261511 2261734 2262051 "PWFFINTB" 2262593 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-974 2259693 2259861 2260215 "PUSHVAR" 2261325 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-973 2255611 2256665 2256706 "PTRANFN" 2258590 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-972 2254013 2254304 2254626 "PTPACK" 2255322 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-971 2253645 2253702 2253811 "PTFUNC2" 2253950 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-970 2248172 2252517 2252558 "PTCAT" 2252854 NIL PTCAT (NIL T) -9 NIL 2253007 NIL) (-969 2247830 2247865 2247989 "PSQFR" 2248131 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-968 2246425 2246723 2247057 "PSEUDLIN" 2247528 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-967 2233195 2235559 2237883 "PSETPK" 2244185 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-966 2226239 2228953 2229049 "PSETCAT" 2232070 NIL PSETCAT (NIL T T T T) -9 NIL 2232884 NIL) (-965 2224075 2224709 2225530 "PSETCAT-" 2225535 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-964 2223424 2223589 2223617 "PSCURVE" 2223885 T PSCURVE (NIL) -9 NIL 2224052 NIL) (-963 2219780 2221262 2221327 "PSCAT" 2222171 NIL PSCAT (NIL T T T) -9 NIL 2222411 NIL) (-962 2218843 2219059 2219459 "PSCAT-" 2219464 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-961 2217575 2218208 2218413 "PRTITION" 2218658 T PRTITION (NIL) -8 NIL NIL NIL) (-960 2217077 2217296 2217388 "PRTDAST" 2217503 T PRTDAST (NIL) -8 NIL NIL NIL) (-959 2206175 2208381 2210569 "PRS" 2214939 NIL PRS (NIL T T) -7 NIL NIL NIL) (-958 2204033 2205525 2205565 "PRQAGG" 2205748 NIL PRQAGG (NIL T) -9 NIL 2205850 NIL) (-957 2203419 2203648 2203676 "PROPLOG" 2203861 T PROPLOG (NIL) -9 NIL 2203983 NIL) (-956 2200589 2201233 2201697 "PROPFRML" 2202987 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-955 2200049 2200159 2200289 "PROPERTY" 2200479 T PROPERTY (NIL) -8 NIL NIL NIL) (-954 2194134 2198215 2199035 "PRODUCT" 2199275 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-953 2191447 2193592 2193826 "PR" 2193945 NIL PR (NIL T T) -8 NIL NIL NIL) (-952 2191243 2191275 2191334 "PRINT" 2191408 T PRINT (NIL) -7 NIL NIL NIL) (-951 2190583 2190700 2190852 "PRIMES" 2191123 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-950 2188648 2189049 2189515 "PRIMELT" 2190162 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-949 2188377 2188426 2188454 "PRIMCAT" 2188578 T PRIMCAT (NIL) -9 NIL NIL NIL) (-948 2184538 2188315 2188360 "PRIMARR" 2188365 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-947 2183545 2183723 2183951 "PRIMARR2" 2184356 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-946 2183188 2183244 2183355 "PREASSOC" 2183483 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-945 2182663 2182796 2182824 "PPCURVE" 2183029 T PPCURVE (NIL) -9 NIL 2183165 NIL) (-944 2182285 2182458 2182541 "PORTNUM" 2182600 T PORTNUM (NIL) -8 NIL NIL NIL) (-943 2179644 2180043 2180635 "POLYROOT" 2181866 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-942 2173589 2179248 2179408 "POLY" 2179517 NIL POLY (NIL T) -8 NIL NIL NIL) (-941 2172972 2173030 2173264 "POLYLIFT" 2173525 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-940 2169247 2169696 2170325 "POLYCATQ" 2172517 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-939 2156064 2161422 2161487 "POLYCAT" 2165001 NIL POLYCAT (NIL T T T) -9 NIL 2166929 NIL) (-938 2149514 2151375 2153759 "POLYCAT-" 2153764 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-937 2149101 2149169 2149289 "POLY2UP" 2149440 NIL POLY2UP (NIL NIL T) 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2134309 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-924 2133401 2133477 2133658 "PMKERNEL" 2133844 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-923 2133018 2133093 2133206 "PMINS" 2133320 NIL PMINS (NIL T) -7 NIL NIL NIL) (-922 2132446 2132515 2132731 "PMFS" 2132943 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-921 2131674 2131792 2131997 "PMDOWN" 2132323 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-920 2130837 2130996 2131178 "PMASS" 2131512 T PMASS (NIL) -7 NIL NIL NIL) (-919 2130111 2130222 2130385 "PMASSFS" 2130723 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-918 2129766 2129834 2129928 "PLOTTOOL" 2130037 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-917 2124388 2125577 2126725 "PLOT" 2128638 T PLOT (NIL) -8 NIL NIL NIL) (-916 2120202 2121236 2122157 "PLOT3D" 2123487 T PLOT3D (NIL) -8 NIL NIL NIL) (-915 2119114 2119291 2119526 "PLOT1" 2120006 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-914 2094508 2099180 2104031 "PLEQN" 2114380 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-913 2093826 2093948 2094128 "PINTERP" 2094373 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-912 2093519 2093566 2093669 "PINTERPA" 2093773 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-911 2092767 2093288 2093375 "PI" 2093415 T PI (NIL) -8 NIL NIL 2093482) (-910 2091164 2092105 2092133 "PID" 2092315 T PID (NIL) -9 NIL 2092449 NIL) (-909 2090889 2090926 2091014 "PICOERCE" 2091121 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-908 2090209 2090348 2090524 "PGROEB" 2090745 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-907 2085796 2086610 2087515 "PGE" 2089324 T PGE (NIL) -7 NIL NIL NIL) (-906 2083920 2084166 2084532 "PGCD" 2085513 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-905 2083258 2083361 2083522 "PFRPAC" 2083804 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-904 2079938 2081806 2082159 "PFR" 2082937 NIL PFR (NIL T) -8 NIL NIL NIL) (-903 2078327 2078571 2078896 "PFOTOOLS" 2079685 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-902 2076860 2077099 2077450 "PFOQ" 2078084 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-901 2075333 2075545 2075908 "PFO" 2076644 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-900 2071921 2075222 2075291 "PF" 2075296 NIL PF (NIL NIL) -8 NIL NIL NIL) (-899 2069355 2070592 2070620 "PFECAT" 2071205 T PFECAT (NIL) -9 NIL 2071589 NIL) (-898 2068800 2068954 2069168 "PFECAT-" 2069173 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-897 2067404 2067655 2067956 "PFBRU" 2068549 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-896 2065271 2065622 2066054 "PFBR" 2067055 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-895 2061187 2062647 2063323 "PERM" 2064628 NIL PERM (NIL T) -8 NIL NIL NIL) (-894 2056453 2057394 2058264 "PERMGRP" 2060350 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-893 2054585 2055516 2055557 "PERMCAT" 2056003 NIL PERMCAT (NIL T) -9 NIL 2056308 NIL) (-892 2054238 2054279 2054403 "PERMAN" 2054538 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-891 2051774 2053903 2054025 "PENDTREE" 2054149 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-890 2049867 2050601 2050642 "PDRING" 2051299 NIL PDRING (NIL T) -9 NIL 2051585 NIL) (-889 2048970 2049188 2049550 "PDRING-" 2049555 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-888 2046212 2046963 2047631 "PDEPROB" 2048322 T PDEPROB (NIL) -8 NIL NIL NIL) (-887 2043759 2044261 2044816 "PDEPACK" 2045677 T PDEPACK (NIL) -7 NIL NIL NIL) (-886 2042671 2042861 2043112 "PDECOMP" 2043558 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-885 2040276 2041093 2041121 "PDECAT" 2041908 T PDECAT (NIL) -9 NIL 2042621 NIL) (-884 2040027 2040060 2040150 "PCOMP" 2040237 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-883 2038232 2038828 2039125 "PBWLB" 2039756 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-882 2030737 2032305 2033643 "PATTERN" 2036915 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-881 2030369 2030426 2030535 "PATTERN2" 2030674 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-880 2028126 2028514 2028971 "PATTERN1" 2029958 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-879 2025521 2026075 2026556 "PATRES" 2027691 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-878 2025085 2025152 2025284 "PATRES2" 2025448 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-877 2022968 2023373 2023780 "PATMATCH" 2024752 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-876 2022504 2022687 2022728 "PATMAB" 2022835 NIL PATMAB (NIL T) -9 NIL 2022918 NIL) (-875 2021049 2021358 2021616 "PATLRES" 2022309 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-874 2020595 2020718 2020759 "PATAB" 2020764 NIL PATAB (NIL T) -9 NIL 2020936 NIL) (-873 2018076 2018608 2019181 "PARTPERM" 2020042 T PARTPERM (NIL) -7 NIL NIL NIL) (-872 2017697 2017760 2017862 "PARSURF" 2018007 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-871 2017329 2017386 2017495 "PARSU2" 2017634 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-870 2017093 2017133 2017200 "PARSER" 2017282 T PARSER (NIL) -7 NIL NIL NIL) (-869 2016714 2016777 2016879 "PARSCURV" 2017024 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-868 2016346 2016403 2016512 "PARSC2" 2016651 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-867 2015985 2016043 2016140 "PARPCURV" 2016282 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-866 2015617 2015674 2015783 "PARPC2" 2015922 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-865 2015137 2015223 2015342 "PAN2EXPR" 2015518 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-864 2013943 2014258 2014486 "PALETTE" 2014929 T PALETTE (NIL) -8 NIL NIL NIL) (-863 2012411 2012948 2013308 "PAIR" 2013629 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-862 2006317 2011670 2011864 "PADICRC" 2012266 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-861 1999581 2005663 2005847 "PADICRAT" 2006165 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-860 1997931 1999518 1999563 "PADIC" 1999568 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-859 1995141 1996671 1996711 "PADICCT" 1997292 NIL PADICCT (NIL NIL) -9 NIL 1997574 NIL) (-858 1994098 1994298 1994566 "PADEPAC" 1994928 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-857 1993310 1993443 1993649 "PADE" 1993960 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-856 1991732 1992518 1992798 "OWP" 1993114 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-855 1990805 1991337 1991509 "OVAR" 1991600 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-854 1990069 1990190 1990351 "OUT" 1990664 T OUT (NIL) -7 NIL NIL NIL) (-853 1978976 1981178 1983378 "OUTFORM" 1987889 T OUTFORM (NIL) -8 NIL NIL NIL) (-852 1978397 1978573 1978700 "OUTBFILE" 1978869 T OUTBFILE (NIL) -8 NIL NIL NIL) (-851 1978034 1978117 1978145 "OUTBCON" 1978296 T OUTBCON (NIL) -9 NIL 1978381 NIL) (-850 1977874 1977909 1977985 "OUTBCON-" 1977990 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-849 1977282 1977603 1977692 "OSI" 1977805 T OSI (NIL) -8 NIL NIL NIL) (-848 1976838 1977150 1977178 "OSGROUP" 1977183 T OSGROUP (NIL) -9 NIL 1977205 NIL) (-847 1975583 1975810 1976095 "ORTHPOL" 1976585 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-846 1973169 1975418 1975539 "OREUP" 1975544 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-845 1970607 1972860 1972987 "ORESUP" 1973111 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-844 1968135 1968635 1969196 "OREPCTO" 1970096 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-843 1961959 1964126 1964167 "OREPCAT" 1966515 NIL OREPCAT (NIL T) -9 NIL 1967619 NIL) (-842 1959106 1959888 1960946 "OREPCAT-" 1960951 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-841 1958283 1958555 1958583 "ORDSET" 1958892 T ORDSET (NIL) -9 NIL 1959056 NIL) (-840 1957802 1957924 1958117 "ORDSET-" 1958122 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-839 1956436 1957193 1957221 "ORDRING" 1957423 T ORDRING (NIL) -9 NIL 1957548 NIL) (-838 1956081 1956175 1956319 "ORDRING-" 1956324 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-837 1955487 1955924 1955952 "ORDMON" 1955957 T ORDMON (NIL) -9 NIL 1955978 NIL) (-836 1954649 1954796 1954991 "ORDFUNS" 1955336 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-835 1954013 1954406 1954434 "ORDFIN" 1954499 T ORDFIN (NIL) -9 NIL 1954573 NIL) (-834 1950605 1952599 1953008 "ORDCOMP" 1953637 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-833 1949871 1949998 1950184 "ORDCOMP2" 1950465 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1946479 1947362 1948176 "OPTPROB" 1949077 T OPTPROB (NIL) -8 NIL NIL NIL) (-831 1943281 1943920 1944624 "OPTPACK" 1945795 T OPTPACK (NIL) -7 NIL NIL NIL) (-830 1940994 1941734 1941762 "OPTCAT" 1942581 T OPTCAT (NIL) -9 NIL 1943231 NIL) (-829 1940437 1940671 1940776 "OPSIG" 1940909 T OPSIG (NIL) -8 NIL NIL NIL) (-828 1940205 1940244 1940310 "OPQUERY" 1940391 T OPQUERY (NIL) -7 NIL NIL NIL) (-827 1937371 1938516 1939020 "OP" 1939734 NIL OP (NIL T) -8 NIL NIL NIL) (-826 1936906 1937077 1937118 "OPERCAT" 1937253 NIL OPERCAT (NIL T) -9 NIL 1937321 NIL) (-825 1936752 1936779 1936865 "OPERCAT-" 1936870 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-824 1933597 1935549 1935918 "ONECOMP" 1936416 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-823 1932902 1933017 1933191 "ONECOMP2" 1933469 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-822 1932321 1932427 1932557 "OMSERVER" 1932792 T OMSERVER (NIL) -7 NIL NIL NIL) (-821 1929209 1931761 1931801 "OMSAGG" 1931862 NIL OMSAGG (NIL T) -9 NIL 1931926 NIL) (-820 1927832 1928095 1928377 "OMPKG" 1928947 T OMPKG (NIL) -7 NIL NIL NIL) (-819 1927262 1927365 1927393 "OM" 1927692 T OM (NIL) -9 NIL NIL NIL) (-818 1925844 1926811 1926980 "OMLO" 1927143 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-817 1924769 1924916 1925143 "OMEXPR" 1925670 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-816 1924087 1924315 1924451 "OMERR" 1924653 T OMERR (NIL) -8 NIL NIL NIL) (-815 1923265 1923508 1923668 "OMERRK" 1923947 T OMERRK (NIL) -8 NIL NIL NIL) (-814 1922743 1922942 1923050 "OMENC" 1923177 T OMENC (NIL) -8 NIL NIL NIL) (-813 1916638 1917823 1918994 "OMDEV" 1921592 T OMDEV (NIL) -8 NIL NIL NIL) (-812 1915707 1915878 1916072 "OMCONN" 1916464 T OMCONN (NIL) -8 NIL NIL NIL) (-811 1914328 1915270 1915298 "OINTDOM" 1915303 T OINTDOM (NIL) -9 NIL 1915324 NIL) (-810 1910134 1911318 1912034 "OFMONOID" 1913644 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-809 1909572 1910071 1910116 "ODVAR" 1910121 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-808 1907030 1909317 1909472 "ODR" 1909477 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-807 1899374 1906806 1906932 "ODPOL" 1906937 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-806 1893250 1899246 1899351 "ODP" 1899356 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-805 1892016 1892231 1892506 "ODETOOLS" 1893024 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-804 1888985 1889641 1890357 "ODESYS" 1891349 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-803 1883867 1884775 1885800 "ODERTRIC" 1888060 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-802 1883293 1883375 1883569 "ODERED" 1883779 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-801 1880181 1880729 1881406 "ODERAT" 1882716 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-800 1877141 1877605 1878202 "ODEPRRIC" 1879710 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-799 1875111 1875680 1876166 "ODEPROB" 1876675 T ODEPROB (NIL) -8 NIL NIL NIL) (-798 1871633 1872116 1872763 "ODEPRIM" 1874590 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-797 1870882 1870984 1871244 "ODEPAL" 1871525 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-796 1867044 1867835 1868699 "ODEPACK" 1870038 T ODEPACK (NIL) -7 NIL NIL NIL) (-795 1866077 1866184 1866413 "ODEINT" 1866933 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-794 1860178 1861603 1863050 "ODEIFTBL" 1864650 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-793 1855513 1856299 1857258 "ODEEF" 1859337 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-792 1854848 1854937 1855167 "ODECONST" 1855418 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-791 1852999 1853634 1853662 "ODECAT" 1854267 T ODECAT (NIL) -9 NIL 1854798 NIL) (-790 1849906 1852711 1852830 "OCT" 1852912 NIL OCT (NIL T) -8 NIL NIL NIL) (-789 1849544 1849587 1849714 "OCTCT2" 1849857 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-788 1844318 1846718 1846758 "OC" 1847855 NIL OC (NIL T) -9 NIL 1848713 NIL) (-787 1841545 1842293 1843283 "OC-" 1843377 NIL OC- (NIL T T) -8 NIL NIL NIL) (-786 1840923 1841365 1841393 "OCAMON" 1841398 T OCAMON (NIL) -9 NIL 1841419 NIL) (-785 1840480 1840795 1840823 "OASGP" 1840828 T OASGP (NIL) -9 NIL 1840848 NIL) (-784 1839767 1840230 1840258 "OAMONS" 1840298 T OAMONS (NIL) -9 NIL 1840341 NIL) (-783 1839207 1839614 1839642 "OAMON" 1839647 T OAMON (NIL) -9 NIL 1839667 NIL) (-782 1838511 1839003 1839031 "OAGROUP" 1839036 T OAGROUP (NIL) -9 NIL 1839056 NIL) (-781 1838201 1838251 1838339 "NUMTUBE" 1838455 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-780 1831774 1833292 1834828 "NUMQUAD" 1836685 T NUMQUAD (NIL) -7 NIL NIL NIL) (-779 1827530 1828518 1829543 "NUMODE" 1830769 T NUMODE (NIL) -7 NIL NIL NIL) (-778 1824911 1825765 1825793 "NUMINT" 1826716 T NUMINT (NIL) -9 NIL 1827480 NIL) (-777 1823859 1824056 1824274 "NUMFMT" 1824713 T NUMFMT (NIL) -7 NIL NIL NIL) (-776 1810218 1813163 1815695 "NUMERIC" 1821366 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-775 1804615 1809667 1809762 "NTSCAT" 1809767 NIL NTSCAT (NIL T T T T) -9 NIL 1809806 NIL) (-774 1803809 1803974 1804167 "NTPOLFN" 1804454 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-773 1791649 1800634 1801446 "NSUP" 1803030 NIL NSUP (NIL T) -8 NIL NIL NIL) (-772 1791281 1791338 1791447 "NSUP2" 1791586 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-771 1781278 1791055 1791188 "NSMP" 1791193 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-770 1779710 1780011 1780368 "NREP" 1780966 NIL NREP (NIL T) -7 NIL NIL NIL) (-769 1778301 1778553 1778911 "NPCOEF" 1779453 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-768 1777367 1777482 1777698 "NORMRETR" 1778182 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-767 1775408 1775698 1776107 "NORMPK" 1777075 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-766 1775093 1775121 1775245 "NORMMA" 1775374 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-765 1774920 1775050 1775079 "NONE" 1775084 T NONE (NIL) -8 NIL NIL NIL) (-764 1774709 1774738 1774807 "NONE1" 1774884 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-763 1774192 1774254 1774440 "NODE1" 1774641 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-762 1772463 1773286 1773541 "NNI" 1773888 T NNI (NIL) -8 NIL NIL 1774123) (-761 1770883 1771196 1771560 "NLINSOL" 1772131 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-760 1767151 1768119 1769018 "NIPROB" 1770004 T NIPROB (NIL) -8 NIL NIL NIL) (-759 1765908 1766142 1766444 "NFINTBAS" 1766913 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-758 1765352 1765559 1765600 "NETCLT" 1765764 NIL NETCLT (NIL T) -9 NIL 1765853 NIL) (-757 1764060 1764291 1764572 "NCODIV" 1765120 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-756 1763822 1763859 1763934 "NCNTFRAC" 1764017 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-755 1762002 1762366 1762786 "NCEP" 1763447 NIL NCEP (NIL T) -7 NIL NIL NIL) (-754 1760913 1761652 1761680 "NASRING" 1761790 T NASRING (NIL) -9 NIL 1761864 NIL) (-753 1760708 1760752 1760846 "NASRING-" 1760851 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-752 1759861 1760360 1760388 "NARNG" 1760505 T NARNG (NIL) -9 NIL 1760596 NIL) (-751 1759553 1759620 1759754 "NARNG-" 1759759 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-750 1758432 1758639 1758874 "NAGSP" 1759338 T NAGSP (NIL) -7 NIL NIL NIL) (-749 1749704 1751388 1753061 "NAGS" 1756779 T NAGS (NIL) -7 NIL NIL NIL) (-748 1748252 1748560 1748891 "NAGF07" 1749393 T NAGF07 (NIL) -7 NIL NIL NIL) (-747 1742790 1744081 1745388 "NAGF04" 1746965 T NAGF04 (NIL) -7 NIL NIL NIL) (-746 1735758 1737372 1739005 "NAGF02" 1741177 T NAGF02 (NIL) -7 NIL NIL NIL) (-745 1730982 1732082 1733199 "NAGF01" 1734661 T NAGF01 (NIL) -7 NIL NIL NIL) (-744 1724610 1726176 1727761 "NAGE04" 1729417 T NAGE04 (NIL) -7 NIL NIL NIL) (-743 1715779 1717900 1720030 "NAGE02" 1722500 T NAGE02 (NIL) -7 NIL NIL NIL) (-742 1711732 1712679 1713643 "NAGE01" 1714835 T NAGE01 (NIL) -7 NIL NIL NIL) (-741 1709527 1710061 1710619 "NAGD03" 1711194 T NAGD03 (NIL) -7 NIL NIL NIL) (-740 1701277 1703205 1705159 "NAGD02" 1707593 T NAGD02 (NIL) -7 NIL NIL NIL) (-739 1695088 1696513 1697953 "NAGD01" 1699857 T NAGD01 (NIL) -7 NIL NIL NIL) (-738 1691297 1692119 1692956 "NAGC06" 1694271 T NAGC06 (NIL) -7 NIL NIL NIL) (-737 1689762 1690094 1690450 "NAGC05" 1690961 T NAGC05 (NIL) -7 NIL NIL NIL) (-736 1689138 1689257 1689401 "NAGC02" 1689638 T NAGC02 (NIL) -7 NIL NIL NIL) (-735 1688198 1688755 1688795 "NAALG" 1688874 NIL NAALG (NIL T) -9 NIL 1688935 NIL) (-734 1688033 1688062 1688152 "NAALG-" 1688157 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-733 1681983 1683091 1684278 "MULTSQFR" 1686929 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-732 1681302 1681377 1681561 "MULTFACT" 1681895 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-731 1674395 1678265 1678318 "MTSCAT" 1679388 NIL MTSCAT (NIL T T) -9 NIL 1679902 NIL) (-730 1674107 1674161 1674253 "MTHING" 1674335 NIL MTHING (NIL T) -7 NIL NIL NIL) (-729 1673899 1673932 1673992 "MSYSCMD" 1674067 T MSYSCMD (NIL) -7 NIL NIL NIL) (-728 1670011 1672654 1672974 "MSET" 1673612 NIL MSET (NIL T) -8 NIL NIL NIL) (-727 1667106 1669572 1669613 "MSETAGG" 1669618 NIL MSETAGG (NIL T) -9 NIL 1669652 NIL) (-726 1662989 1664485 1665230 "MRING" 1666406 NIL MRING (NIL T T) -8 NIL NIL NIL) (-725 1662555 1662622 1662753 "MRF2" 1662916 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-724 1662173 1662208 1662352 "MRATFAC" 1662514 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-723 1659785 1660080 1660511 "MPRFF" 1661878 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-722 1653845 1659639 1659736 "MPOLY" 1659741 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-721 1653335 1653370 1653578 "MPCPF" 1653804 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-720 1652849 1652892 1653076 "MPC3" 1653286 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-719 1652044 1652125 1652346 "MPC2" 1652764 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-718 1650345 1650682 1651072 "MONOTOOL" 1651704 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-717 1649596 1649887 1649915 "MONOID" 1650134 T MONOID (NIL) -9 NIL 1650281 NIL) (-716 1649142 1649261 1649442 "MONOID-" 1649447 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-715 1640001 1645909 1645968 "MONOGEN" 1646642 NIL MONOGEN (NIL T T) -9 NIL 1647098 NIL) (-714 1637219 1637954 1638954 "MONOGEN-" 1639073 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-713 1636078 1636498 1636526 "MONADWU" 1636918 T MONADWU (NIL) -9 NIL 1637156 NIL) (-712 1635450 1635609 1635857 "MONADWU-" 1635862 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-711 1634835 1635053 1635081 "MONAD" 1635288 T MONAD (NIL) -9 NIL 1635400 NIL) (-710 1634520 1634598 1634730 "MONAD-" 1634735 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-709 1632836 1633433 1633712 "MOEBIUS" 1634273 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-708 1632228 1632606 1632646 "MODULE" 1632651 NIL MODULE (NIL T) -9 NIL 1632677 NIL) (-707 1631796 1631892 1632082 "MODULE-" 1632087 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-706 1629511 1630160 1630487 "MODRING" 1631620 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1626497 1627616 1628137 "MODOP" 1629040 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-704 1625112 1625564 1625841 "MODMONOM" 1626360 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-703 1614919 1623403 1623817 "MODMON" 1624749 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-702 1612110 1613763 1614039 "MODFIELD" 1614794 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-701 1611114 1611391 1611581 "MMLFORM" 1611940 T MMLFORM (NIL) -8 NIL NIL NIL) (-700 1610640 1610683 1610862 "MMAP" 1611065 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-699 1608857 1609590 1609631 "MLO" 1610054 NIL MLO (NIL T) -9 NIL 1610296 NIL) (-698 1606224 1606739 1607341 "MLIFT" 1608338 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-697 1605615 1605699 1605853 "MKUCFUNC" 1606135 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-696 1605214 1605284 1605407 "MKRECORD" 1605538 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-695 1604262 1604423 1604651 "MKFUNC" 1605025 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-694 1603650 1603754 1603910 "MKFLCFN" 1604145 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-693 1603193 1603560 1603619 "MKCHSET" 1603624 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-692 1602470 1602572 1602757 "MKBCFUNC" 1603086 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-691 1599212 1602024 1602160 "MINT" 1602354 T MINT (NIL) -8 NIL NIL NIL) (-690 1598024 1598267 1598544 "MHROWRED" 1598967 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-689 1593450 1596559 1596964 "MFLOAT" 1597639 T MFLOAT (NIL) -8 NIL NIL NIL) (-688 1592807 1592883 1593054 "MFINFACT" 1593362 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-687 1589122 1589970 1590854 "MESH" 1591943 T MESH (NIL) -7 NIL NIL NIL) (-686 1587512 1587824 1588177 "MDDFACT" 1588809 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-685 1584354 1586671 1586712 "MDAGG" 1586967 NIL MDAGG (NIL T) -9 NIL 1587110 NIL) (-684 1574132 1583647 1583854 "MCMPLX" 1584167 T MCMPLX (NIL) -8 NIL NIL NIL) (-683 1573273 1573419 1573619 "MCDEN" 1573981 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-682 1571163 1571433 1571813 "MCALCFN" 1573003 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-681 1570074 1570247 1570488 "MAYBE" 1570961 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-680 1567686 1568209 1568771 "MATSTOR" 1569545 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-679 1563692 1567058 1567306 "MATRIX" 1567471 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-678 1559461 1560165 1560901 "MATLIN" 1563049 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-677 1549615 1552753 1552830 "MATCAT" 1557710 NIL MATCAT (NIL T T T) -9 NIL 1559127 NIL) (-676 1545979 1546992 1548348 "MATCAT-" 1548353 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-675 1544573 1544726 1545059 "MATCAT2" 1545814 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-674 1542685 1543009 1543393 "MAPPKG3" 1544248 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-673 1541666 1541839 1542061 "MAPPKG2" 1542509 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-672 1540165 1540449 1540776 "MAPPKG1" 1541372 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-671 1539271 1539571 1539748 "MAPPAST" 1540008 T MAPPAST (NIL) -8 NIL NIL NIL) (-670 1538882 1538940 1539063 "MAPHACK3" 1539207 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-669 1538474 1538535 1538649 "MAPHACK2" 1538814 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-668 1537912 1538015 1538157 "MAPHACK1" 1538365 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-667 1536018 1536612 1536916 "MAGMA" 1537640 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-666 1535524 1535742 1535833 "MACROAST" 1535947 T MACROAST (NIL) -8 NIL NIL NIL) (-665 1531991 1533763 1534224 "M3D" 1535096 NIL M3D (NIL T) -8 NIL NIL NIL) (-664 1526145 1530360 1530401 "LZSTAGG" 1531183 NIL LZSTAGG (NIL T) -9 NIL 1531478 NIL) (-663 1522119 1523276 1524733 "LZSTAGG-" 1524738 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-662 1519233 1520010 1520497 "LWORD" 1521664 NIL LWORD (NIL T) -8 NIL NIL NIL) (-661 1518836 1519037 1519112 "LSTAST" 1519178 T LSTAST (NIL) -8 NIL NIL NIL) (-660 1512037 1518607 1518741 "LSQM" 1518746 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-659 1511261 1511400 1511628 "LSPP" 1511892 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-658 1509073 1509374 1509830 "LSMP" 1510950 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-657 1505852 1506526 1507256 "LSMP1" 1508375 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-656 1499777 1505019 1505060 "LSAGG" 1505122 NIL LSAGG (NIL T) -9 NIL 1505200 NIL) (-655 1496472 1497396 1498609 "LSAGG-" 1498614 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-654 1494098 1495616 1495865 "LPOLY" 1496267 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-653 1493680 1493765 1493888 "LPEFRAC" 1494007 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-652 1492027 1492774 1493027 "LO" 1493512 NIL LO (NIL T T T) -8 NIL NIL NIL) (-651 1491679 1491791 1491819 "LOGIC" 1491930 T LOGIC (NIL) -9 NIL 1492011 NIL) (-650 1491541 1491564 1491635 "LOGIC-" 1491640 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-649 1490734 1490874 1491067 "LODOOPS" 1491397 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-648 1488192 1490650 1490716 "LODO" 1490721 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-647 1486730 1486965 1487318 "LODOF" 1487939 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-646 1483086 1485483 1485524 "LODOCAT" 1485962 NIL LODOCAT (NIL T) -9 NIL 1486173 NIL) (-645 1482819 1482877 1483004 "LODOCAT-" 1483009 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-644 1480174 1482660 1482778 "LODO2" 1482783 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-643 1477644 1480111 1480156 "LODO1" 1480161 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-642 1476504 1476669 1476981 "LODEEF" 1477467 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-641 1471790 1474634 1474675 "LNAGG" 1475622 NIL LNAGG (NIL T) -9 NIL 1476066 NIL) (-640 1470937 1471151 1471493 "LNAGG-" 1471498 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-639 1467100 1467862 1468501 "LMOPS" 1470352 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-638 1466495 1466857 1466898 "LMODULE" 1466959 NIL LMODULE (NIL T) -9 NIL 1467001 NIL) (-637 1463741 1466140 1466263 "LMDICT" 1466405 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-636 1463467 1463649 1463709 "LITERAL" 1463714 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-635 1456694 1462413 1462711 "LIST" 1463202 NIL LIST (NIL T) -8 NIL NIL NIL) (-634 1456219 1456293 1456432 "LIST3" 1456614 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-633 1455226 1455404 1455632 "LIST2" 1456037 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-632 1453360 1453672 1454071 "LIST2MAP" 1454873 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-631 1452090 1452726 1452767 "LINEXP" 1453022 NIL LINEXP (NIL T) -9 NIL 1453171 NIL) (-630 1450737 1450997 1451294 "LINDEP" 1451842 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-629 1447504 1448223 1449000 "LIMITRF" 1449992 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-628 1445780 1446075 1446491 "LIMITPS" 1447199 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-627 1440235 1445291 1445519 "LIE" 1445601 NIL LIE (NIL T T) -8 NIL NIL NIL) (-626 1439284 1439727 1439767 "LIECAT" 1439907 NIL LIECAT (NIL T) -9 NIL 1440058 NIL) (-625 1439125 1439152 1439240 "LIECAT-" 1439245 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-624 1431737 1438574 1438739 "LIB" 1438980 T LIB (NIL) -8 NIL NIL NIL) (-623 1427374 1428255 1429190 "LGROBP" 1430854 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-622 1425240 1425514 1425876 "LF" 1427095 NIL LF (NIL T T) -7 NIL NIL NIL) (-621 1424080 1424772 1424800 "LFCAT" 1425007 T LFCAT (NIL) -9 NIL 1425146 NIL) (-620 1420984 1421612 1422300 "LEXTRIPK" 1423444 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-619 1417755 1418554 1419057 "LEXP" 1420564 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-618 1417258 1417476 1417568 "LETAST" 1417683 T LETAST (NIL) -8 NIL NIL NIL) (-617 1415656 1415969 1416370 "LEADCDET" 1416940 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-616 1414846 1414920 1415149 "LAZM3PK" 1415577 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-615 1409801 1412923 1413461 "LAUPOL" 1414358 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-614 1409366 1409410 1409578 "LAPLACE" 1409751 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-613 1407340 1408467 1408718 "LA" 1409199 NIL LA (NIL T T T) -8 NIL NIL NIL) (-612 1406421 1406971 1407012 "LALG" 1407074 NIL LALG (NIL T) -9 NIL 1407133 NIL) (-611 1406135 1406194 1406330 "LALG-" 1406335 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-610 1405970 1405994 1406035 "KVTFROM" 1406097 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-609 1404770 1405187 1405416 "KTVLOGIC" 1405761 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-608 1404605 1404629 1404670 "KRCFROM" 1404732 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-607 1403509 1403696 1403995 "KOVACIC" 1404405 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-606 1403344 1403368 1403409 "KONVERT" 1403471 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-605 1403179 1403203 1403244 "KOERCE" 1403306 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-604 1400913 1401673 1402066 "KERNEL" 1402818 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-603 1400415 1400496 1400626 "KERNEL2" 1400827 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-602 1394266 1398954 1399008 "KDAGG" 1399385 NIL KDAGG (NIL T T) -9 NIL 1399591 NIL) (-601 1393795 1393919 1394124 "KDAGG-" 1394129 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386970 1393456 1393611 "KAFILE" 1393673 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-599 1381425 1386481 1386709 "JORDAN" 1386791 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-598 1380831 1381074 1381195 "JOINAST" 1381324 T JOINAST (NIL) -8 NIL NIL NIL) (-597 1380677 1380736 1380791 "JAVACODE" 1380796 T JAVACODE (NIL) -8 NIL NIL NIL) (-596 1376976 1378882 1378936 "IXAGG" 1379865 NIL IXAGG (NIL T T) -9 NIL 1380324 NIL) (-595 1375895 1376201 1376620 "IXAGG-" 1376625 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-594 1371475 1375817 1375876 "IVECTOR" 1375881 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-593 1370241 1370478 1370744 "ITUPLE" 1371242 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-592 1368677 1368854 1369160 "ITRIGMNP" 1370063 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-591 1367422 1367626 1367909 "ITFUN3" 1368453 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-590 1367054 1367111 1367220 "ITFUN2" 1367359 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-589 1364891 1365916 1366215 "ITAYLOR" 1366788 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-588 1353874 1359028 1360191 "ISUPS" 1363761 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-587 1352978 1353118 1353354 "ISUMP" 1353721 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-586 1348242 1352779 1352858 "ISTRING" 1352931 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-585 1347745 1347963 1348055 "ISAST" 1348170 T ISAST (NIL) -8 NIL NIL NIL) (-584 1346955 1347036 1347252 "IRURPK" 1347659 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-583 1345891 1346092 1346332 "IRSN" 1346735 T IRSN (NIL) -7 NIL NIL NIL) (-582 1343920 1344275 1344711 "IRRF2F" 1345529 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-581 1343667 1343705 1343781 "IRREDFFX" 1343876 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-580 1342282 1342541 1342840 "IROOT" 1343400 NIL IROOT (NIL T) -7 NIL NIL NIL) (-579 1338914 1339966 1340658 "IR" 1341622 NIL IR (NIL T) -8 NIL NIL NIL) (-578 1336527 1337022 1337588 "IR2" 1338392 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-577 1335599 1335712 1335933 "IR2F" 1336410 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-576 1335390 1335424 1335484 "IPRNTPK" 1335559 T IPRNTPK (NIL) -7 NIL NIL NIL) (-575 1332009 1335279 1335348 "IPF" 1335353 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-574 1330372 1331934 1331991 "IPADIC" 1331996 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-573 1329703 1329930 1330067 "IP4ADDR" 1330255 T IP4ADDR (NIL) -8 NIL NIL NIL) (-572 1329203 1329407 1329517 "IOMODE" 1329613 T IOMODE (NIL) -8 NIL NIL NIL) (-571 1328561 1328800 1328927 "IOBFILE" 1329096 T IOBFILE (NIL) -8 NIL NIL NIL) (-570 1328325 1328465 1328493 "IOBCON" 1328498 T IOBCON (NIL) -9 NIL 1328519 NIL) (-569 1327822 1327880 1328070 "INVLAPLA" 1328261 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-568 1317471 1319824 1322210 "INTTR" 1325486 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-567 1313815 1314557 1315421 "INTTOOLS" 1316656 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-566 1313401 1313492 1313609 "INTSLPE" 1313718 T INTSLPE (NIL) -7 NIL NIL NIL) (-565 1311396 1313324 1313383 "INTRVL" 1313388 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-564 1308998 1309510 1310085 "INTRF" 1310881 NIL INTRF (NIL T) -7 NIL NIL NIL) (-563 1308409 1308506 1308648 "INTRET" 1308896 NIL INTRET (NIL T) -7 NIL NIL NIL) (-562 1306406 1306795 1307265 "INTRAT" 1308017 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-561 1303634 1304217 1304843 "INTPM" 1305891 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-560 1300337 1300936 1301681 "INTPAF" 1303020 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-559 1295516 1296478 1297529 "INTPACK" 1299306 T INTPACK (NIL) -7 NIL NIL NIL) (-558 1292428 1295245 1295372 "INT" 1295409 T INT (NIL) -8 NIL NIL NIL) (-557 1291680 1291832 1292040 "INTHERTR" 1292270 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-556 1291119 1291199 1291387 "INTHERAL" 1291594 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-555 1288965 1289408 1289865 "INTHEORY" 1290682 T INTHEORY (NIL) -7 NIL NIL NIL) (-554 1280273 1281894 1283673 "INTG0" 1287317 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-553 1260846 1265636 1270446 "INTFTBL" 1275483 T INTFTBL (NIL) -8 NIL NIL NIL) (-552 1260095 1260233 1260406 "INTFACT" 1260705 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-551 1257480 1257926 1258490 "INTEF" 1259649 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-550 1255947 1256652 1256680 "INTDOM" 1256981 T INTDOM (NIL) -9 NIL 1257188 NIL) (-549 1255316 1255490 1255732 "INTDOM-" 1255737 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-548 1251811 1253700 1253754 "INTCAT" 1254553 NIL INTCAT (NIL T) -9 NIL 1254873 NIL) (-547 1251284 1251386 1251514 "INTBIT" 1251703 T INTBIT (NIL) -7 NIL NIL NIL) (-546 1249955 1250109 1250423 "INTALG" 1251129 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-545 1249412 1249502 1249672 "INTAF" 1249859 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-544 1242866 1249222 1249362 "INTABL" 1249367 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-543 1237881 1240555 1240583 "INS" 1241517 T INS (NIL) -9 NIL 1242182 NIL) (-542 1235121 1235892 1236866 "INS-" 1236939 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1233896 1234123 1234421 "INPSIGN" 1234874 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1233014 1233131 1233328 "INPRODPF" 1233776 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1231908 1232025 1232262 "INPRODFF" 1232894 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1230908 1231060 1231320 "INNMFACT" 1231744 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1230105 1230202 1230390 "INMODGCD" 1230807 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1228614 1228858 1229182 "INFSP" 1229850 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1227798 1227915 1228098 "INFPROD0" 1228494 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1224680 1225863 1226378 "INFORM" 1227291 T INFORM (NIL) -8 NIL NIL NIL) (-533 1224290 1224350 1224448 "INFORM1" 1224615 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1223813 1223902 1224016 "INFINITY" 1224196 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1223258 1223531 1223639 "INETCLTS" 1223725 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1221875 1222124 1222445 "INEP" 1223006 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1221151 1221772 1221837 "INDE" 1221842 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1220715 1220783 1220900 "INCRMAPS" 1221078 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1219733 1219984 1220190 "INBFILE" 1220529 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1215044 1215969 1216913 "INBFF" 1218821 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1214713 1214789 1214817 "INBCON" 1214950 T INBCON (NIL) -9 NIL 1215028 NIL) (-524 1214553 1214588 1214664 "INBCON-" 1214669 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1214055 1214274 1214366 "INAST" 1214481 T INAST (NIL) -8 NIL NIL NIL) (-522 1213509 1213734 1213840 "IMPTAST" 1213969 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1210003 1213353 1213457 "IMATRIX" 1213462 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208715 1208838 1209153 "IMATQF" 1209859 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206935 1207162 1207499 "IMATLIN" 1208471 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201561 1206859 1206917 "ILIST" 1206922 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199514 1201421 1201534 "IIARRAY2" 1201539 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194947 1199425 1199489 "IFF" 1199494 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194321 1194564 1194680 "IFAST" 1194851 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189364 1193613 1193801 "IFARRAY" 1194178 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188571 1189268 1189341 "IFAMON" 1189346 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188155 1188220 1188274 "IEVALAB" 1188481 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187830 1187898 1188058 "IEVALAB-" 1188063 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187488 1187744 1187807 "IDPO" 1187812 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186765 1187377 1187452 "IDPOAMS" 1187457 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1186099 1186654 1186729 "IDPOAM" 1186734 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185184 1185434 1185487 "IDPC" 1185900 NIL IDPC (NIL T T) -9 NIL 1186049 NIL) (-506 1184680 1185076 1185149 "IDPAM" 1185154 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1184083 1184572 1184645 "IDPAG" 1184650 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183851 1183998 1184048 "IDENT" 1184053 T IDENT (NIL) -8 NIL NIL NIL) (-503 1180106 1180954 1181849 "IDECOMP" 1183008 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172980 1174029 1175076 "IDEAL" 1179142 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172144 1172256 1172455 "ICDEN" 1172864 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171243 1171624 1171771 "ICARD" 1172017 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169303 1169616 1170021 "IBPTOOLS" 1170920 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164937 1168923 1169036 "IBITS" 1169222 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161660 1162236 1162931 "IBATOOL" 1164354 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159440 1159901 1160434 "IBACHIN" 1161195 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157317 1159286 1159389 "IARRAY2" 1159394 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153470 1157243 1157300 "IARRAY1" 1157305 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147464 1151882 1152363 "IAN" 1153009 T IAN (NIL) -8 NIL NIL NIL) (-492 1146975 1147032 1147205 "IALGFACT" 1147401 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146503 1146616 1146644 "HYPCAT" 1146851 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1146041 1146158 1146344 "HYPCAT-" 1146349 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145663 1145836 1145919 "HOSTNAME" 1145978 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145508 1145545 1145586 "HOMOTOP" 1145591 NIL HOMOTOP (NIL T) -9 NIL 1145624 NIL) (-487 1142187 1143518 1143559 "HOAGG" 1144540 NIL HOAGG (NIL T) -9 NIL 1145219 NIL) (-486 1140781 1141180 1141706 "HOAGG-" 1141711 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134823 1140378 1140526 "HEXADEC" 1140653 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133571 1133793 1134056 "HEUGCD" 1134600 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132674 1133408 1133538 "HELLFDIV" 1133543 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130902 1132451 1132539 "HEAP" 1132618 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130193 1130454 1130588 "HEADAST" 1130788 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1124113 1130108 1130170 "HDP" 1130175 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117864 1123748 1123900 "HDMP" 1124014 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117189 1117328 1117492 "HB" 1117720 T HB (NIL) -7 NIL NIL NIL) (-477 1110686 1117035 1117139 "HASHTBL" 1117144 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110189 1110407 1110499 "HASAST" 1110614 T HASAST (NIL) -8 NIL NIL NIL) (-475 1108001 1109811 1109993 "HACKPI" 1110027 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103696 1107854 1107967 "GTSET" 1107972 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097222 1103574 1103672 "GSTBL" 1103677 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089535 1096253 1096518 "GSERIES" 1097013 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088702 1089093 1089121 "GROUP" 1089324 T GROUP (NIL) -9 NIL 1089458 NIL) (-470 1088068 1088227 1088478 "GROUP-" 1088483 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086437 1086756 1087143 "GROEBSOL" 1087745 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085377 1085639 1085690 "GRMOD" 1086219 NIL GRMOD (NIL T T) -9 NIL 1086387 NIL) (-467 1085145 1085181 1085309 "GRMOD-" 1085314 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080471 1081499 1082499 "GRIMAGE" 1084165 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078938 1079198 1079522 "GRDEF" 1080167 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078382 1078498 1078639 "GRAY" 1078817 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077595 1077975 1078026 "GRALG" 1078179 NIL GRALG (NIL T T) -9 NIL 1078272 NIL) (-462 1077256 1077329 1077492 "GRALG-" 1077497 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1074060 1076841 1077019 "GPOLSET" 1077163 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073414 1073471 1073729 "GOSPER" 1073997 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069173 1069852 1070378 "GMODPOL" 1073113 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068178 1068362 1068600 "GHENSEL" 1068985 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062229 1063072 1064099 "GENUPS" 1067262 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061926 1061977 1062066 "GENUFACT" 1062172 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061338 1061415 1061580 "GENPGCD" 1061844 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060812 1060847 1061060 "GENMFACT" 1061297 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059380 1059635 1059942 "GENEEZ" 1060555 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053293 1058991 1059153 "GDMP" 1059303 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042670 1047064 1048170 "GCNAALG" 1052276 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1041097 1041925 1041953 "GCDDOM" 1042208 T GCDDOM (NIL) -9 NIL 1042365 NIL) (-449 1040567 1040694 1040909 "GCDDOM-" 1040914 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039239 1039424 1039728 "GB" 1040346 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027859 1030185 1032577 "GBINTERN" 1036930 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025696 1025988 1026409 "GBF" 1027534 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024477 1024642 1024909 "GBEUCLID" 1025512 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023826 1023951 1024100 "GAUSSFAC" 1024348 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022193 1022495 1022809 "GALUTIL" 1023545 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020501 1020775 1021099 "GALPOLYU" 1021920 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017866 1018156 1018563 "GALFACTU" 1020198 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009672 1011171 1012779 "GALFACT" 1016298 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1007060 1007718 1007746 "FVFUN" 1008902 T FVFUN (NIL) -9 NIL 1009622 NIL) (-438 1006326 1006508 1006536 "FVC" 1006827 T FVC (NIL) -9 NIL 1007010 NIL) (-437 1005968 1006123 1006204 "FUNCTION" 1006278 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003739 1004290 1004756 "FT" 1005522 T FT (NIL) -8 NIL NIL NIL) (-435 1002557 1003040 1003243 "FTEM" 1003556 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000813 1001102 1001506 "FSUPFACT" 1002248 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999210 999499 999831 "FST" 1000501 T FST (NIL) -8 NIL NIL NIL) (-432 998381 998487 998682 "FSRED" 999092 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 997060 997315 997669 "FSPRMELT" 998096 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994145 994583 995082 "FSPECF" 996623 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976205 984648 984688 "FS" 988536 NIL FS (NIL T) -9 NIL 990825 NIL) (-428 964855 967845 971901 "FS-" 972198 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964369 964423 964600 "FSINT" 964796 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962696 963362 963665 "FSERIES" 964148 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961710 961826 962057 "FSCINT" 962576 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957944 960654 960695 "FSAGG" 961065 NIL FSAGG (NIL T) -9 NIL 961324 NIL) (-423 955706 956307 957103 "FSAGG-" 957198 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954748 954891 955118 "FSAGG2" 955559 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952403 952682 953236 "FS2UPS" 954466 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951985 952028 952183 "FS2" 952354 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950842 951013 951322 "FS2EXPXP" 951810 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950268 950383 950535 "FRUTIL" 950722 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941723 945763 947121 "FR" 948942 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936798 939441 939481 "FRNAALG" 940877 NIL FRNAALG (NIL T) -9 NIL 941484 NIL) (-415 932476 933547 934822 "FRNAALG-" 935572 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 932114 932157 932284 "FRNAAF2" 932427 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930521 930968 931263 "FRMOD" 931926 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928300 928904 929221 "FRIDEAL" 930312 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927495 927582 927871 "FRIDEAL2" 928207 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926628 927042 927083 "FRETRCT" 927088 NIL FRETRCT (NIL T) -9 NIL 927264 NIL) (-409 925740 925971 926322 "FRETRCT-" 926327 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922952 924128 924187 "FRAMALG" 925069 NIL FRAMALG (NIL T T) -9 NIL 925361 NIL) (-407 921086 921541 922171 "FRAMALG-" 922394 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 915044 920561 920837 "FRAC" 920842 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914680 914737 914844 "FRAC2" 914981 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914316 914373 914480 "FR2" 914617 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908989 911841 911869 "FPS" 912988 T FPS (NIL) -9 NIL 913545 NIL) (-402 908438 908547 908711 "FPS-" 908857 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905892 907527 907555 "FPC" 907780 T FPC (NIL) -9 NIL 907922 NIL) (-400 905685 905725 905822 "FPC-" 905827 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904563 905173 905214 "FPATMAB" 905219 NIL FPATMAB (NIL T) -9 NIL 905371 NIL) (-398 902263 902739 903165 "FPARFRAC" 904200 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897657 898155 898837 "FORTRAN" 901695 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895373 895873 896412 "FORT" 897138 T FORT (NIL) -7 NIL NIL NIL) (-395 893049 893611 893639 "FORTFN" 894699 T FORTFN (NIL) -9 NIL 895323 NIL) (-394 892813 892863 892891 "FORTCAT" 892950 T FORTCAT (NIL) -9 NIL 893012 NIL) (-393 890946 891429 891819 "FORMULA" 892443 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890734 890764 890833 "FORMULA1" 890910 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890257 890309 890482 "FORDER" 890676 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889353 889517 889710 "FOP" 890084 T FOP (NIL) -7 NIL NIL NIL) (-389 887961 888633 888807 "FNLA" 889235 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886716 887105 887133 "FNCAT" 887593 T FNCAT (NIL) -9 NIL 887853 NIL) (-387 886282 886675 886703 "FNAME" 886708 T FNAME (NIL) -8 NIL NIL NIL) (-386 884945 885874 885902 "FMTC" 885907 T FMTC (NIL) -9 NIL 885943 NIL) (-385 881307 882468 883097 "FMONOID" 884349 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880526 881049 881198 "FM" 881203 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877950 878596 878624 "FMFUN" 879768 T FMFUN (NIL) -9 NIL 880476 NIL) (-382 877219 877400 877428 "FMC" 877718 T FMC (NIL) -9 NIL 877900 NIL) (-381 874413 875247 875301 "FMCAT" 876496 NIL FMCAT (NIL T T) -9 NIL 876991 NIL) (-380 873306 874179 874279 "FM1" 874358 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 871080 871496 871990 "FLOATRP" 872857 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864704 868809 869430 "FLOAT" 870479 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862142 862642 863220 "FLOATCP" 864171 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860951 861755 861796 "FLINEXP" 861801 NIL FLINEXP (NIL T) -9 NIL 861894 NIL) (-375 860105 860340 860668 "FLINEXP-" 860673 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859181 859325 859549 "FLASORT" 859957 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856398 857240 857292 "FLALG" 858519 NIL FLALG (NIL T T) -9 NIL 858986 NIL) (-372 850182 853884 853925 "FLAGG" 855187 NIL FLAGG (NIL T) -9 NIL 855839 NIL) (-371 848908 849247 849737 "FLAGG-" 849742 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847950 848093 848320 "FLAGG2" 848761 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844925 845899 845958 "FINRALG" 847086 NIL FINRALG (NIL T T) -9 NIL 847594 NIL) (-368 844085 844314 844653 "FINRALG-" 844658 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843491 843704 843732 "FINITE" 843928 T FINITE (NIL) -9 NIL 844035 NIL) (-366 835949 838110 838150 "FINAALG" 841817 NIL FINAALG (NIL T) -9 NIL 843270 NIL) (-365 831290 832331 833475 "FINAALG-" 834854 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830685 831045 831148 "FILE" 831220 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829369 829681 829735 "FILECAT" 830419 NIL FILECAT (NIL T T) -9 NIL 830635 NIL) (-362 827237 828731 828759 "FIELD" 828799 T FIELD (NIL) -9 NIL 828879 NIL) (-361 825857 826242 826753 "FIELD-" 826758 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823735 824492 824839 "FGROUP" 825543 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822825 822989 823209 "FGLMICPK" 823567 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818692 822750 822807 "FFX" 822812 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818293 818354 818489 "FFSLPE" 818625 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814286 815065 815861 "FFPOLY" 817529 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813790 813826 814035 "FFPOLY2" 814244 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809676 813709 813772 "FFP" 813777 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 805109 809587 809651 "FF" 809656 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800270 804452 804642 "FFNBX" 804963 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795244 799405 799663 "FFNBP" 800124 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789912 794528 794739 "FFNB" 795077 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788744 788942 789257 "FFINTBAS" 789709 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784972 787151 787179 "FFIELDC" 787799 T FFIELDC (NIL) -9 NIL 788175 NIL) (-347 783635 784005 784502 "FFIELDC-" 784507 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783205 783250 783374 "FFHOM" 783577 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780903 781387 781904 "FFF" 782720 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776556 780645 780746 "FFCGX" 780846 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772223 776288 776395 "FFCGP" 776499 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767441 771950 772058 "FFCG" 772159 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749274 758312 758398 "FFCAT" 763563 NIL FFCAT (NIL T T T) -9 NIL 765014 NIL) (-340 744472 745519 746833 "FFCAT-" 748063 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743883 743926 744161 "FFCAT2" 744423 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 733095 736855 738075 "FEXPR" 742735 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 732095 732530 732571 "FEVALAB" 732655 NIL FEVALAB (NIL T) -9 NIL 732916 NIL) (-336 731254 731464 731802 "FEVALAB-" 731807 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729847 730637 730840 "FDIV" 731153 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726913 727628 727743 "FDIVCAT" 729311 NIL FDIVCAT (NIL T T T T) -9 NIL 729748 NIL) (-333 726675 726702 726872 "FDIVCAT-" 726877 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725895 725982 726259 "FDIV2" 726582 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724581 724840 725129 "FCPAK1" 725626 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723709 724081 724222 "FCOMP" 724472 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707446 710859 714397 "FC" 720191 T FC (NIL) -8 NIL NIL NIL) (-328 700025 704010 704050 "FAXF" 705852 NIL FAXF (NIL T) -9 NIL 706544 NIL) (-327 697304 697959 698784 "FAXF-" 699249 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692404 696680 696856 "FARRAY" 697161 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687657 689689 689742 "FAMR" 690765 NIL FAMR (NIL T T) -9 NIL 691225 NIL) (-324 686547 686849 687284 "FAMR-" 687289 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685743 686469 686522 "FAMONOID" 686527 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683555 684239 684292 "FAMONC" 685233 NIL FAMONC (NIL T T) -9 NIL 685619 NIL) (-321 682247 683309 683446 "FAGROUP" 683451 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 680042 680361 680764 "FACUTIL" 681928 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679141 679326 679548 "FACTFUNC" 679852 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671546 678392 678604 "EXPUPXS" 678997 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 669029 669569 670155 "EXPRTUBE" 670980 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665223 665815 666552 "EXPRODE" 668368 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650597 663878 664306 "EXPR" 664827 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 645004 645591 646404 "EXPR2UPS" 649895 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644640 644697 644804 "EXPR2" 644941 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 636045 643772 644069 "EXPEXPAN" 644477 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635872 636002 636031 "EXIT" 636036 T EXIT (NIL) -8 NIL NIL NIL) (-310 635379 635596 635687 "EXITAST" 635801 T EXITAST (NIL) -8 NIL NIL NIL) (-309 635006 635068 635181 "EVALCYC" 635311 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634547 634665 634706 "EVALAB" 634876 NIL EVALAB (NIL T) -9 NIL 634980 NIL) (-307 634028 634150 634371 "EVALAB-" 634376 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631496 632764 632792 "EUCDOM" 633347 T EUCDOM (NIL) -9 NIL 633697 NIL) (-305 629901 630343 630933 "EUCDOM-" 630938 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617441 620199 622949 "ESTOOLS" 627171 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 617073 617130 617239 "ESTOOLS2" 617378 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616824 616866 616946 "ESTOOLS1" 617025 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610729 612457 612485 "ES" 615253 T ES (NIL) -9 NIL 616662 NIL) (-300 605677 606963 608780 "ES-" 608944 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 602052 602812 603592 "ESCONT" 604917 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601797 601829 601911 "ESCONT1" 602014 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601472 601522 601622 "ES2" 601741 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 601102 601160 601269 "ES1" 601408 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600318 600447 600623 "ERROR" 600946 T ERROR (NIL) -7 NIL NIL NIL) (-294 593821 600177 600268 "EQTBL" 600273 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586378 589135 590584 "EQ" 592405 NIL -3278 (NIL T) -8 NIL NIL NIL) (-292 586010 586067 586176 "EQ2" 586315 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581302 582348 583441 "EP" 584949 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579884 580185 580502 "ENV" 581005 T ENV (NIL) -8 NIL NIL NIL) (-289 579063 579583 579611 "ENTIRER" 579616 T ENTIRER (NIL) -9 NIL 579662 NIL) (-288 575565 577018 577388 "EMR" 578862 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574709 574894 574948 "ELTAGG" 575328 NIL ELTAGG (NIL T T) -9 NIL 575539 NIL) (-286 574428 574490 574631 "ELTAGG-" 574636 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574217 574246 574300 "ELTAB" 574384 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573343 573489 573688 "ELFUTS" 574068 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 573085 573141 573169 "ELEMFUN" 573274 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572955 572976 573044 "ELEMFUN-" 573049 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567846 571055 571096 "ELAGG" 572036 NIL ELAGG (NIL T) -9 NIL 572499 NIL) (-280 566131 566565 567228 "ELAGG-" 567233 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564788 565068 565363 "ELABEXPR" 565856 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557654 559455 560282 "EFUPXS" 564064 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 551104 552905 553715 "EFULS" 556930 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548526 548884 549363 "EFSTRUC" 550736 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537598 539163 540723 "EF" 547041 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536699 537083 537232 "EAB" 537469 T EAB (NIL) -8 NIL NIL NIL) (-273 535908 536658 536686 "E04UCFA" 536691 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 535117 535867 535895 "E04NAFA" 535900 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534326 535076 535104 "E04MBFA" 535109 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533535 534285 534313 "E04JAFA" 534318 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532746 533494 533522 "E04GCFA" 533527 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531957 532705 532733 "E04FDFA" 532738 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531166 531916 531944 "E04DGFA" 531949 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525344 526691 528055 "E04AGNT" 529822 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 524050 524530 524570 "DVARCAT" 525045 NIL DVARCAT (NIL T) -9 NIL 525244 NIL) (-264 523254 523466 523780 "DVARCAT-" 523785 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516154 523053 523182 "DSMP" 523187 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510964 512099 513167 "DROPT" 515106 T DROPT (NIL) -8 NIL NIL NIL) (-261 510629 510688 510786 "DROPT1" 510899 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505744 506870 508007 "DROPT0" 509512 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 504089 504414 504800 "DRAWPT" 505378 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498676 499599 500678 "DRAW" 503063 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498309 498362 498480 "DRAWHACK" 498617 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 497040 497309 497600 "DRAWCX" 498038 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496556 496624 496775 "DRAWCURV" 496966 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 487027 488986 491101 "DRAWCFUN" 494461 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483840 485722 485763 "DQAGG" 486392 NIL DQAGG (NIL T) -9 NIL 486665 NIL) (-252 472119 478818 478901 "DPOLCAT" 480753 NIL DPOLCAT (NIL T T T T) -9 NIL 481298 NIL) (-251 466958 468304 470262 "DPOLCAT-" 470267 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 460113 466819 466917 "DPMO" 466922 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453171 459893 460060 "DPMM" 460065 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452835 453090 453138 "DOMCTOR" 453143 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452130 452357 452494 "DOMAIN" 452718 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445881 451765 451917 "DMP" 452031 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445481 445537 445681 "DLP" 445819 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439351 444808 444998 "DLIST" 445323 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436195 438204 438245 "DLAGG" 438795 NIL DLAGG (NIL T) -9 NIL 439025 NIL) (-242 435008 435638 435666 "DIVRING" 435758 T DIVRING (NIL) -9 NIL 435841 NIL) (-241 434245 434435 434735 "DIVRING-" 434740 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432347 432704 433110 "DISPLAY" 433859 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426289 432261 432324 "DIRPROD" 432329 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425137 425340 425605 "DIRPROD2" 426082 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414400 420352 420405 "DIRPCAT" 420815 NIL DIRPCAT (NIL NIL T) -9 NIL 421655 NIL) (-236 411726 412368 413249 "DIRPCAT-" 413586 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 411013 411173 411359 "DIOSP" 411560 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407715 409925 409966 "DIOPS" 410400 NIL DIOPS (NIL T) -9 NIL 410629 NIL) (-233 407264 407378 407569 "DIOPS-" 407574 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406156 406750 406778 "DIFRING" 406965 T DIFRING (NIL) -9 NIL 407075 NIL) (-231 405802 405879 406031 "DIFRING-" 406036 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403607 404845 404886 "DIFEXT" 405249 NIL DIFEXT (NIL T) -9 NIL 405543 NIL) (-229 401892 402320 402986 "DIFEXT-" 402991 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399214 401424 401465 "DIAGG" 401470 NIL DIAGG (NIL T) -9 NIL 401490 NIL) (-227 398598 398755 399007 "DIAGG-" 399012 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 394063 397557 397834 "DHMATRIX" 398367 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389675 390584 391594 "DFSFUN" 393073 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384791 388606 388918 "DFLOAT" 389383 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 383019 383300 383696 "DFINTTLS" 384499 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 380084 381040 381440 "DERHAM" 382685 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377933 379859 379948 "DEQUEUE" 380028 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377148 377281 377477 "DEGRED" 377795 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373543 374288 375141 "DEFINTRF" 376376 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 371070 371539 372138 "DEFINTEF" 373062 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370447 370690 370805 "DEFAST" 370975 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364489 370044 370192 "DECIMAL" 370319 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 362001 362459 362965 "DDFACT" 364033 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361597 361640 361791 "DBLRESP" 361952 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359496 359830 360190 "DBASE" 361364 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358765 358976 359122 "DATAARY" 359395 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357898 358724 358752 "D03FAFA" 358757 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 357032 357857 357885 "D03EEFA" 357890 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354982 355448 355937 "D03AGNT" 356563 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354298 354941 354969 "D02EJFA" 354974 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353614 354257 354285 "D02CJFA" 354290 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352930 353573 353601 "D02BHFA" 353606 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352246 352889 352917 "D02BBFA" 352922 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345444 347032 348638 "D02AGNT" 350660 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343213 343735 344281 "D01WGTS" 344918 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342308 343172 343200 "D01TRNS" 343205 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341403 342267 342295 "D01GBFA" 342300 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340498 341362 341390 "D01FCFA" 341395 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339593 340457 340485 "D01ASFA" 340490 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338688 339552 339580 "D01AQFA" 339585 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337783 338647 338675 "D01APFA" 338680 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336878 337742 337770 "D01ANFA" 337775 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335973 336837 336865 "D01AMFA" 336870 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 335068 335932 335960 "D01ALFA" 335965 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334163 335027 335055 "D01AKFA" 335060 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333258 334122 334150 "D01AJFA" 334155 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326555 328106 329667 "D01AGNT" 331717 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 325892 326020 326172 "CYCLOTOM" 326423 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322627 323340 324067 "CYCLES" 325185 T CYCLES (NIL) -7 NIL NIL NIL) (-188 321939 322073 322244 "CVMP" 322488 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319710 319968 320344 "CTRIGMNP" 321667 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319433 319669 319697 "CTOR" 319702 T CTOR (NIL) -8 NIL NIL NIL) (-185 318969 319164 319265 "CTORKIND" 319352 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318440 318668 318696 "CTORCAT" 318816 T CTORCAT (NIL) -9 NIL 318899 NIL) (-183 318135 318215 318341 "CTORCAT-" 318346 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317651 317838 317936 "CTORCALL" 318057 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 317025 317124 317277 "CSTTOOLS" 317548 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312824 313481 314239 "CRFP" 316337 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312326 312545 312637 "CRCEAST" 312752 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311373 311558 311786 "CRAPACK" 312130 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310757 310858 311062 "CPMATCH" 311249 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310482 310510 310616 "CPIMA" 310723 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306846 307518 308236 "COORDSYS" 309817 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306230 306359 306509 "CONTOUR" 306716 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302156 304233 304725 "CONTFRAC" 305770 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 302036 302057 302085 "CONDUIT" 302122 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301209 301729 301757 "COMRING" 301762 T COMRING (NIL) -9 NIL 301814 NIL) (-170 300290 300567 300751 "COMPPROP" 301045 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299951 299986 300114 "COMPLPAT" 300249 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 290008 299760 299869 "COMPLEX" 299874 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289644 289701 289808 "COMPLEX2" 289945 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289362 289397 289495 "COMPFACT" 289603 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273535 283755 283795 "COMPCAT" 284799 NIL COMPCAT (NIL T) -9 NIL 286184 NIL) (-164 263051 265974 269601 "COMPCAT-" 269957 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262780 262808 262911 "COMMUPC" 263017 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262575 262608 262667 "COMMONOP" 262741 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262158 262326 262413 "COMM" 262508 T COMM (NIL) -8 NIL NIL NIL) (-160 261762 261962 262037 "COMMAAST" 262103 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 261011 261205 261233 "COMBOPC" 261571 T COMBOPC (NIL) -9 NIL 261746 NIL) (-158 259907 260117 260359 "COMBINAT" 260801 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 256105 256678 257318 "COMBF" 259329 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254891 255221 255456 "COLOR" 255890 T COLOR (NIL) -8 NIL NIL NIL) (-155 254394 254612 254704 "COLONAST" 254819 T COLONAST (NIL) -8 NIL NIL NIL) (-154 254034 254081 254206 "CMPLXRT" 254341 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253509 253734 253833 "CLLCTAST" 253955 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 249011 250039 251119 "CLIP" 252449 T CLIP (NIL) -7 NIL NIL NIL) (-151 247393 248117 248356 "CLIF" 248838 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243615 245539 245580 "CLAGG" 246509 NIL CLAGG (NIL T) -9 NIL 247045 NIL) (-149 242037 242494 243077 "CLAGG-" 243082 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241581 241666 241806 "CINTSLPE" 241946 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 239082 239553 240101 "CHVAR" 241109 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238325 238845 238873 "CHARZ" 238878 T CHARZ (NIL) -9 NIL 238893 NIL) (-145 238079 238119 238197 "CHARPOL" 238279 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237206 237759 237787 "CHARNZ" 237834 T CHARNZ (NIL) -9 NIL 237890 NIL) (-143 235195 235896 236231 "CHAR" 236891 T CHAR (NIL) -8 NIL NIL NIL) (-142 234921 234982 235010 "CFCAT" 235121 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234166 234277 234459 "CDEN" 234805 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230158 233319 233599 "CCLASS" 233906 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229465 229608 229771 "CATEGORY" 230015 T -10 (NIL) -8 NIL NIL NIL) (-138 229129 229384 229432 "CATCTOR" 229437 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228603 228829 228928 "CATAST" 229050 T CATAST (NIL) -8 NIL NIL NIL) (-136 228106 228324 228416 "CASEAST" 228531 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223158 224135 224888 "CARTEN" 227409 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222266 222414 222635 "CARTEN2" 223005 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220608 221416 221673 "CARD" 222029 T CARD (NIL) -8 NIL NIL NIL) (-132 220211 220412 220487 "CAPSLAST" 220553 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219583 219911 219939 "CACHSET" 220071 T CACHSET (NIL) -9 NIL 220148 NIL) (-130 219079 219375 219403 "CABMON" 219453 T CABMON (NIL) -9 NIL 219509 NIL) (-129 218107 218535 218708 "BYTE" 218926 T BYTE (NIL) -8 NIL NIL NIL) (-128 213516 217575 217738 "BYTEBUF" 217964 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211073 213208 213315 "BTREE" 213442 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208571 210721 210843 "BTOURN" 210983 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205988 208041 208082 "BTCAT" 208150 NIL BTCAT (NIL T) -9 NIL 208227 NIL) (-124 205655 205735 205884 "BTCAT-" 205889 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200947 204798 204826 "BTAGG" 205048 T BTAGG (NIL) -9 NIL 205209 NIL) (-122 200437 200562 200768 "BTAGG-" 200773 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197481 199715 199930 "BSTREE" 200254 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196619 196745 196929 "BRILL" 197337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193318 195345 195386 "BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293 NIL) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861 NIL) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127098 127712 127823 "ASP24" 127934 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126175 126900 127012 "ASP20" 127017 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125263 125876 125986 "ASP1" 126096 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124207 124937 125056 "ASP19" 125175 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 123944 124011 124087 "ASP12" 124162 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122796 123543 123687 "ASP10" 123831 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120695 122640 122731 "ARRAY2" 122736 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116511 120343 120457 "ARRAY1" 120612 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115543 115716 115937 "ARRAY12" 116334 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109902 111773 111848 "ARR2CAT" 114478 NIL ARR2CAT (NIL T T T) -9 NIL 115236 NIL) (-56 107336 108080 109034 "ARR2CAT-" 109039 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106930 107163 107242 "ARITY" 107275 T ARITY (NIL) -8 NIL NIL NIL) (-54 105678 105830 106136 "APPRULE" 106766 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105329 105377 105496 "APPLYORE" 105624 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104303 104594 104789 "ANY" 105152 T ANY (NIL) -8 NIL NIL NIL) (-51 103581 103704 103861 "ANY1" 104177 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101146 102018 102345 "ANTISYM" 103305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100661 100850 100947 "ANON" 101067 T ANON (NIL) -8 NIL NIL NIL) (-48 94793 99200 99654 "AN" 100225 T AN (NIL) -8 NIL NIL NIL) (-47 91049 92403 92454 "AMR" 93202 NIL AMR (NIL T T) -9 NIL 93802 NIL) (-46 90161 90382 90745 "AMR-" 90750 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74711 90078 90139 "ALIST" 90144 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71548 74305 74474 "ALGSC" 74629 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68104 68658 69265 "ALGPKG" 70988 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67381 67482 67666 "ALGMFACT" 67990 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63120 63805 64460 "ALGMANIP" 66904 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437 NIL) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856 NIL) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283 NIL) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332 NIL) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3184375 3184380 3184385 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3184360 3184365 3184370 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3184345 3184350 3184355 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3184330 3184335 3184340 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1274 3183506 3184205 3184282 "ZMOD" 3184287 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1273 3182616 3182780 3182989 "ZLINDEP" 3183338 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1272 3171920 3173684 3175656 "ZDSOLVE" 3180746 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1271 3171166 3171307 3171496 "YSTREAM" 3171766 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1270 3168977 3170467 3170671 "XRPOLY" 3171009 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1269 3165565 3166848 3167423 "XPR" 3168449 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1268 3163321 3164896 3165100 "XPOLY" 3165396 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1267 3161112 3162446 3162501 "XPOLYC" 3162789 NIL XPOLYC (NIL T T) -9 NIL 3162902 NIL) (-1266 3157530 3159629 3160017 "XPBWPOLY" 3160770 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1265 3153441 3155693 3155735 "XF" 3156356 NIL XF (NIL T) -9 NIL 3156756 NIL) (-1264 3153062 3153150 3153319 "XF-" 3153324 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1263 3148396 3149651 3149706 "XFALG" 3151878 NIL XFALG (NIL T T) -9 NIL 3152667 NIL) (-1262 3147529 3147633 3147838 "XEXPPKG" 3148288 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1261 3145673 3147379 3147475 "XDPOLY" 3147480 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1260 3144618 3145184 3145227 "XALG" 3145232 NIL XALG (NIL T) -9 NIL 3145343 NIL) (-1259 3138087 3142595 3143089 "WUTSET" 3144210 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1258 3136378 3137139 3137462 "WP" 3137898 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1257 3136007 3136200 3136270 "WHILEAST" 3136330 T WHILEAST (NIL) -8 NIL NIL NIL) (-1256 3135506 3135724 3135818 "WHEREAST" 3135935 T WHEREAST (NIL) -8 NIL NIL NIL) (-1255 3134392 3134590 3134885 "WFFINTBS" 3135303 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1254 3132296 3132723 3133185 "WEIER" 3133964 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1253 3131443 3131867 3131909 "VSPACE" 3132045 NIL VSPACE (NIL T) -9 NIL 3132119 NIL) (-1252 3131281 3131308 3131399 "VSPACE-" 3131404 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1251 3131089 3131132 3131200 "VOID" 3131235 T VOID (NIL) -8 NIL NIL NIL) (-1250 3129225 3129584 3129990 "VIEW" 3130705 T VIEW (NIL) -7 NIL NIL NIL) (-1249 3125650 3126288 3127025 "VIEWDEF" 3128510 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1248 3114986 3117198 3119371 "VIEW3D" 3123499 T VIEW3D (NIL) -8 NIL NIL NIL) (-1247 3107268 3108897 3110476 "VIEW2D" 3113429 T VIEW2D (NIL) -8 NIL NIL NIL) (-1246 3102672 3107038 3107130 "VECTOR" 3107211 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1245 3101249 3101508 3101826 "VECTOR2" 3102402 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1244 3094776 3099033 3099076 "VECTCAT" 3100069 NIL VECTCAT (NIL T) -9 NIL 3100655 NIL) (-1243 3093790 3094044 3094434 "VECTCAT-" 3094439 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1242 3093271 3093441 3093561 "VARIABLE" 3093705 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1241 3093204 3093209 3093239 "UTYPE" 3093244 T UTYPE (NIL) -9 NIL NIL NIL) (-1240 3092034 3092188 3092450 "UTSODETL" 3093030 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1239 3089474 3089934 3090458 "UTSODE" 3091575 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1238 3081350 3087100 3087589 "UTS" 3089043 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1237 3072593 3077917 3077960 "UTSCAT" 3079072 NIL UTSCAT (NIL T) -9 NIL 3079829 NIL) (-1236 3069948 3070663 3071652 "UTSCAT-" 3071657 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1235 3069575 3069618 3069751 "UTS2" 3069899 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1234 3063848 3066413 3066456 "URAGG" 3068526 NIL URAGG (NIL T) -9 NIL 3069249 NIL) (-1233 3060787 3061650 3062773 "URAGG-" 3062778 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1232 3056511 3059401 3059873 "UPXSSING" 3060451 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1231 3048613 3055758 3056031 "UPXS" 3056296 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1230 3041726 3048517 3048589 "UPXSCONS" 3048594 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1229 3031971 3038721 3038783 "UPXSCCA" 3039357 NIL UPXSCCA (NIL T T) -9 NIL 3039590 NIL) (-1228 3031609 3031694 3031868 "UPXSCCA-" 3031873 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1227 3021707 3028230 3028273 "UPXSCAT" 3028921 NIL UPXSCAT (NIL T) -9 NIL 3029529 NIL) (-1226 3021137 3021216 3021395 "UPXS2" 3021622 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1225 3019791 3020044 3020395 "UPSQFREE" 3020880 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1224 3013579 3016593 3016648 "UPSCAT" 3017809 NIL UPSCAT (NIL T T) -9 NIL 3018583 NIL) (-1223 3012783 3012990 3013317 "UPSCAT-" 3013322 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1222 2998633 3006631 3006674 "UPOLYC" 3008775 NIL UPOLYC (NIL T) -9 NIL 3009996 NIL) (-1221 2989962 2992387 2995534 "UPOLYC-" 2995539 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1220 2989589 2989632 2989765 "UPOLYC2" 2989913 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1219 2981163 2989272 2989401 "UP" 2989508 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1218 2980502 2980609 2980773 "UPMP" 2981052 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1217 2980055 2980136 2980275 "UPDIVP" 2980415 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1216 2978623 2978872 2979188 "UPDECOMP" 2979804 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1215 2977858 2977970 2978155 "UPCDEN" 2978507 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1214 2977377 2977446 2977595 "UP2" 2977783 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1213 2975894 2976581 2976858 "UNISEG" 2977135 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1212 2975109 2975236 2975441 "UNISEG2" 2975737 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1211 2974169 2974349 2974575 "UNIFACT" 2974925 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1210 2958136 2973346 2973597 "ULS" 2973976 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1209 2946176 2958040 2958112 "ULSCONS" 2958117 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1208 2928792 2940734 2940796 "ULSCCAT" 2941434 NIL ULSCCAT (NIL T T) -9 NIL 2941722 NIL) (-1207 2927842 2928087 2928475 "ULSCCAT-" 2928480 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1206 2917717 2924154 2924197 "ULSCAT" 2925060 NIL ULSCAT (NIL T) -9 NIL 2925790 NIL) (-1205 2917147 2917226 2917405 "ULS2" 2917632 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1204 2915550 2916473 2916503 "UFD" 2916715 T UFD (NIL) -9 NIL 2916829 NIL) (-1203 2915344 2915390 2915485 "UFD-" 2915490 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1202 2914426 2914609 2914825 "UDVO" 2915150 T UDVO (NIL) -7 NIL NIL NIL) (-1201 2912242 2912651 2913122 "UDPO" 2913990 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1200 2912175 2912180 2912210 "TYPE" 2912215 T TYPE (NIL) -9 NIL NIL NIL) (-1199 2911962 2912130 2912161 "TYPEAST" 2912166 T TYPEAST (NIL) -8 NIL NIL NIL) (-1198 2910933 2911135 2911375 "TWOFACT" 2911756 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1197 2910005 2910342 2910577 "TUPLE" 2910733 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1196 2907696 2908215 2908754 "TUBETOOL" 2909488 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1195 2906545 2906750 2906991 "TUBE" 2907489 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1194 2901309 2905517 2905800 "TS" 2906297 NIL TS (NIL T) -8 NIL NIL NIL) (-1193 2889976 2894068 2894165 "TSETCAT" 2899434 NIL TSETCAT (NIL T T T T) -9 NIL 2900965 NIL) (-1192 2884711 2886308 2888199 "TSETCAT-" 2888204 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1191 2878974 2879820 2880762 "TRMANIP" 2883847 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1190 2878415 2878478 2878641 "TRIMAT" 2878906 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1189 2876211 2876448 2876812 "TRIGMNIP" 2878164 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1188 2875731 2875844 2875874 "TRIGCAT" 2876087 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1187 2875400 2875479 2875620 "TRIGCAT-" 2875625 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1186 2872297 2874258 2874539 "TREE" 2875154 NIL TREE (NIL T) -8 NIL NIL NIL) (-1185 2871571 2872099 2872129 "TRANFUN" 2872164 T TRANFUN (NIL) -9 NIL 2872230 NIL) (-1184 2870850 2871041 2871321 "TRANFUN-" 2871326 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1183 2870654 2870686 2870747 "TOPSP" 2870811 T TOPSP (NIL) -7 NIL NIL NIL) (-1182 2870002 2870117 2870271 "TOOLSIGN" 2870535 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1181 2868663 2869179 2869418 "TEXTFILE" 2869785 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1180 2866602 2867116 2867545 "TEX" 2868256 T TEX (NIL) -8 NIL NIL NIL) (-1179 2866383 2866414 2866486 "TEX1" 2866565 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1178 2866031 2866094 2866184 "TEMUTL" 2866315 T TEMUTL (NIL) -7 NIL NIL NIL) (-1177 2864185 2864465 2864790 "TBCMPPK" 2865754 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1176 2856073 2862345 2862401 "TBAGG" 2862801 NIL TBAGG (NIL T T) -9 NIL 2863012 NIL) (-1175 2851143 2852631 2854385 "TBAGG-" 2854390 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1174 2850527 2850634 2850779 "TANEXP" 2851032 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1173 2844028 2850384 2850477 "TABLE" 2850482 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1172 2843440 2843539 2843677 "TABLEAU" 2843925 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1171 2838048 2839268 2840516 "TABLBUMP" 2842226 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1170 2837476 2837576 2837704 "SYSTEM" 2837942 T SYSTEM (NIL) -7 NIL NIL NIL) (-1169 2833939 2834634 2835417 "SYSSOLP" 2836727 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1168 2830273 2831200 2831916 "SYNTAX" 2833245 T SYNTAX (NIL) -8 NIL NIL NIL) (-1167 2827431 2828033 2828665 "SYMTAB" 2829663 T SYMTAB (NIL) -8 NIL NIL NIL) (-1166 2822680 2823582 2824565 "SYMS" 2826470 T SYMS (NIL) -8 NIL NIL NIL) (-1165 2819952 2822138 2822368 "SYMPOLY" 2822485 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1164 2819469 2819544 2819667 "SYMFUNC" 2819864 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1163 2815521 2816781 2817594 "SYMBOL" 2818678 T SYMBOL (NIL) -8 NIL NIL NIL) (-1162 2809060 2810749 2812469 "SWITCH" 2813823 T SWITCH (NIL) -8 NIL NIL NIL) (-1161 2802330 2807881 2808184 "SUTS" 2808815 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2794431 2801577 2801850 "SUPXS" 2802115 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2785961 2794049 2794175 "SUP" 2794340 NIL SUP (NIL T) -8 NIL NIL NIL) (-1158 2785120 2785247 2785464 "SUPFRACF" 2785829 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1157 2784741 2784800 2784913 "SUP2" 2785055 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1156 2783154 2783428 2783791 "SUMRF" 2784440 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1155 2782468 2782534 2782733 "SUMFS" 2783075 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1154 2766475 2781645 2781896 "SULS" 2782275 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1153 2766104 2766297 2766367 "SUCHTAST" 2766427 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1152 2765426 2765629 2765769 "SUCH" 2766012 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1151 2759320 2760332 2761291 "SUBSPACE" 2764514 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1150 2758750 2758840 2759004 "SUBRESP" 2759208 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1149 2752119 2753415 2754726 "STTF" 2757486 NIL STTF (NIL T) -7 NIL NIL NIL) (-1148 2746292 2747412 2748559 "STTFNC" 2751019 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1147 2737607 2739474 2741268 "STTAYLOR" 2744533 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1146 2730851 2737471 2737554 "STRTBL" 2737559 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1145 2726242 2730806 2730837 "STRING" 2730842 T STRING (NIL) -8 NIL NIL NIL) (-1144 2721130 2725615 2725645 "STRICAT" 2725704 T STRICAT (NIL) -9 NIL 2725766 NIL) (-1143 2713940 2718749 2719360 "STREAM" 2720554 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1142 2713450 2713527 2713671 "STREAM3" 2713857 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1141 2712432 2712615 2712850 "STREAM2" 2713263 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1140 2712120 2712172 2712265 "STREAM1" 2712374 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1139 2711136 2711317 2711548 "STINPROD" 2711936 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1138 2710714 2710898 2710928 "STEP" 2711008 T STEP (NIL) -9 NIL 2711086 NIL) (-1137 2704257 2710613 2710690 "STBL" 2710695 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1136 2699431 2703478 2703521 "STAGG" 2703674 NIL STAGG (NIL T) -9 NIL 2703763 NIL) (-1135 2697133 2697735 2698607 "STAGG-" 2698612 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1134 2695328 2696903 2696995 "STACK" 2697076 NIL STACK (NIL T) -8 NIL NIL NIL) (-1133 2688053 2693469 2693925 "SREGSET" 2694958 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1132 2680479 2681847 2683360 "SRDCMPK" 2686659 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2673446 2677919 2677949 "SRAGG" 2679252 T SRAGG (NIL) -9 NIL 2679860 NIL) (-1130 2672463 2672718 2673097 "SRAGG-" 2673102 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1129 2666958 2671410 2671831 "SQMATRIX" 2672089 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1128 2660707 2663676 2664403 "SPLTREE" 2666303 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1127 2656697 2657363 2658009 "SPLNODE" 2660133 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1126 2655744 2655977 2656007 "SPFCAT" 2656451 T SPFCAT (NIL) -9 NIL NIL NIL) (-1125 2654481 2654691 2654955 "SPECOUT" 2655502 T SPECOUT (NIL) -7 NIL NIL NIL) (-1124 2646133 2647877 2647907 "SPADXPT" 2652299 T SPADXPT (NIL) -9 NIL 2654333 NIL) (-1123 2645894 2645934 2646003 "SPADPRSR" 2646086 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1122 2644077 2645849 2645880 "SPADAST" 2645885 T SPADAST (NIL) -8 NIL NIL NIL) (-1121 2636048 2637795 2637838 "SPACEC" 2642211 NIL SPACEC (NIL T) -9 NIL 2644027 NIL) (-1120 2634219 2635980 2636029 "SPACE3" 2636034 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1119 2632971 2633142 2633433 "SORTPAK" 2634024 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1118 2631021 2631324 2631743 "SOLVETRA" 2632635 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1117 2630032 2630254 2630528 "SOLVESER" 2630794 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1116 2625252 2626133 2627135 "SOLVERAD" 2629084 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1115 2621067 2621676 2622405 "SOLVEFOR" 2624619 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1114 2615364 2620416 2620513 "SNTSCAT" 2620518 NIL SNTSCAT (NIL T T T T) -9 NIL 2620588 NIL) (-1113 2609507 2613687 2614078 "SMTS" 2615054 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1112 2603958 2609395 2609472 "SMP" 2609477 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1111 2602117 2602418 2602816 "SMITH" 2603655 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1110 2595012 2599168 2599271 "SMATCAT" 2600622 NIL SMATCAT (NIL NIL T T T) -9 NIL 2601172 NIL) (-1109 2591952 2592775 2593953 "SMATCAT-" 2593958 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1108 2589665 2591188 2591231 "SKAGG" 2591492 NIL SKAGG (NIL T) -9 NIL 2591627 NIL) (-1107 2586007 2589081 2589276 "SINT" 2589463 T SINT (NIL) -8 NIL NIL 2589636) (-1106 2585779 2585817 2585883 "SIMPAN" 2585963 T SIMPAN (NIL) -7 NIL NIL NIL) (-1105 2585086 2585314 2585454 "SIG" 2585661 T SIG (NIL) -8 NIL NIL NIL) (-1104 2583924 2584145 2584420 "SIGNRF" 2584845 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1103 2582729 2582880 2583171 "SIGNEF" 2583753 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1102 2582062 2582312 2582436 "SIGAST" 2582627 T SIGAST (NIL) -8 NIL NIL NIL) (-1101 2579752 2580206 2580712 "SHP" 2581603 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1100 2573658 2579653 2579729 "SHDP" 2579734 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1099 2573257 2573423 2573453 "SGROUP" 2573546 T SGROUP (NIL) -9 NIL 2573608 NIL) (-1098 2573115 2573141 2573214 "SGROUP-" 2573219 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1097 2569951 2570648 2571371 "SGCF" 2572414 T SGCF (NIL) -7 NIL NIL NIL) (-1096 2564346 2569398 2569495 "SFRTCAT" 2569500 NIL SFRTCAT (NIL T T T T) -9 NIL 2569539 NIL) (-1095 2557770 2558785 2559921 "SFRGCD" 2563329 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1094 2550898 2551969 2553155 "SFQCMPK" 2556703 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2550520 2550609 2550719 "SFORT" 2550839 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1092 2549665 2550360 2550481 "SEXOF" 2550486 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1091 2548799 2549546 2549614 "SEX" 2549619 T SEX (NIL) -8 NIL NIL NIL) (-1090 2544338 2545027 2545122 "SEXCAT" 2548059 NIL SEXCAT (NIL T T T T T) -9 NIL 2548637 NIL) (-1089 2541518 2544272 2544320 "SET" 2544325 NIL SET (NIL T) -8 NIL NIL NIL) (-1088 2539769 2540231 2540536 "SETMN" 2541259 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1087 2539375 2539501 2539531 "SETCAT" 2539648 T SETCAT (NIL) -9 NIL 2539733 NIL) (-1086 2539155 2539207 2539306 "SETCAT-" 2539311 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1085 2535542 2537616 2537659 "SETAGG" 2538529 NIL SETAGG (NIL T) -9 NIL 2538869 NIL) (-1084 2535000 2535116 2535353 "SETAGG-" 2535358 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1083 2534470 2534696 2534797 "SEQAST" 2534921 T SEQAST (NIL) -8 NIL NIL NIL) (-1082 2533669 2533963 2534024 "SEGXCAT" 2534310 NIL SEGXCAT (NIL T T) -9 NIL 2534430 NIL) (-1081 2532725 2533335 2533517 "SEG" 2533522 NIL SEG (NIL T) -8 NIL NIL NIL) (-1080 2531704 2531918 2531961 "SEGCAT" 2532483 NIL SEGCAT (NIL T) -9 NIL 2532704 NIL) (-1079 2530753 2531083 2531283 "SEGBIND" 2531539 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1078 2530374 2530433 2530546 "SEGBIND2" 2530688 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1077 2529975 2530175 2530252 "SEGAST" 2530319 T SEGAST (NIL) -8 NIL NIL NIL) (-1076 2529194 2529320 2529524 "SEG2" 2529819 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1075 2528631 2529129 2529176 "SDVAR" 2529181 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1074 2520921 2528401 2528531 "SDPOL" 2528536 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1073 2519514 2519780 2520099 "SCPKG" 2520636 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1072 2518650 2518830 2519030 "SCOPE" 2519336 T SCOPE (NIL) -8 NIL NIL NIL) (-1071 2517871 2518004 2518183 "SCACHE" 2518505 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1070 2517543 2517703 2517733 "SASTCAT" 2517738 T SASTCAT (NIL) -9 NIL 2517751 NIL) (-1069 2517057 2517378 2517454 "SAOS" 2517489 T SAOS (NIL) -8 NIL NIL NIL) (-1068 2516622 2516657 2516830 "SAERFFC" 2517016 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1067 2510596 2516519 2516599 "SAE" 2516604 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1066 2510189 2510224 2510383 "SAEFACT" 2510555 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1065 2508510 2508824 2509225 "RURPK" 2509855 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1064 2507146 2507425 2507737 "RULESET" 2508344 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1063 2504333 2504836 2505301 "RULE" 2506827 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1062 2503972 2504127 2504210 "RULECOLD" 2504285 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1061 2503470 2503689 2503783 "RSTRCAST" 2503900 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1060 2498319 2499113 2500033 "RSETGCD" 2502669 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1059 2487576 2492628 2492725 "RSETCAT" 2496844 NIL RSETCAT (NIL T T T T) -9 NIL 2497941 NIL) (-1058 2485503 2486042 2486866 "RSETCAT-" 2486871 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1057 2477890 2479265 2480785 "RSDCMPK" 2484102 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2475895 2476336 2476410 "RRCC" 2477496 NIL RRCC (NIL T T) -9 NIL 2477840 NIL) (-1055 2475246 2475420 2475699 "RRCC-" 2475704 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1054 2474716 2474942 2475043 "RPTAST" 2475167 T RPTAST (NIL) -8 NIL NIL NIL) (-1053 2448722 2458309 2458376 "RPOLCAT" 2469040 NIL RPOLCAT (NIL T T T) -9 NIL 2472199 NIL) (-1052 2440222 2442560 2445682 "RPOLCAT-" 2445687 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1051 2431269 2438433 2438915 "ROUTINE" 2439762 T ROUTINE (NIL) -8 NIL NIL NIL) (-1050 2428102 2430895 2431035 "ROMAN" 2431151 T ROMAN (NIL) -8 NIL NIL NIL) (-1049 2426377 2426962 2427222 "ROIRC" 2427907 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1048 2422770 2425013 2425043 "RNS" 2425347 T RNS (NIL) -9 NIL 2425620 NIL) (-1047 2421279 2421662 2422196 "RNS-" 2422271 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1046 2420728 2421110 2421140 "RNG" 2421145 T RNG (NIL) -9 NIL 2421166 NIL) (-1045 2420120 2420482 2420525 "RMODULE" 2420587 NIL RMODULE (NIL T) -9 NIL 2420629 NIL) (-1044 2418956 2419050 2419386 "RMCAT2" 2420021 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1043 2415833 2418302 2418599 "RMATRIX" 2418718 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1042 2408775 2411009 2411124 "RMATCAT" 2414483 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2415465 NIL) (-1041 2408150 2408297 2408604 "RMATCAT-" 2408609 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1040 2407717 2407792 2407920 "RINTERP" 2408069 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1039 2406850 2407370 2407400 "RING" 2407456 T RING (NIL) -9 NIL 2407542 NIL) (-1038 2406642 2406686 2406783 "RING-" 2406788 NIL RING- (NIL T) -8 NIL NIL NIL) (-1037 2405483 2405720 2405978 "RIDIST" 2406406 T RIDIST (NIL) -7 NIL NIL NIL) (-1036 2396799 2404951 2405157 "RGCHAIN" 2405331 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1035 2396175 2396555 2396596 "RGBCSPC" 2396654 NIL RGBCSPC (NIL T) -9 NIL 2396706 NIL) (-1034 2395359 2395714 2395755 "RGBCMDL" 2395987 NIL RGBCMDL (NIL T) -9 NIL 2396101 NIL) (-1033 2392353 2392967 2393637 "RF" 2394723 NIL RF (NIL T) -7 NIL NIL NIL) (-1032 2391999 2392062 2392165 "RFFACTOR" 2392284 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1031 2391724 2391759 2391856 "RFFACT" 2391958 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1030 2389841 2390205 2390587 "RFDIST" 2391364 T RFDIST (NIL) -7 NIL NIL NIL) (-1029 2389294 2389386 2389549 "RETSOL" 2389743 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1028 2388930 2389010 2389053 "RETRACT" 2389186 NIL RETRACT (NIL T) -9 NIL 2389273 NIL) (-1027 2388779 2388804 2388891 "RETRACT-" 2388896 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1026 2388408 2388601 2388671 "RETAST" 2388731 T RETAST (NIL) -8 NIL NIL NIL) (-1025 2381262 2388061 2388188 "RESULT" 2388303 T RESULT (NIL) -8 NIL NIL NIL) (-1024 2379888 2380531 2380730 "RESRING" 2381165 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1023 2379524 2379573 2379671 "RESLATC" 2379825 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1022 2379230 2379264 2379371 "REPSQ" 2379483 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1021 2376652 2377232 2377834 "REP" 2378650 T REP (NIL) -7 NIL NIL NIL) (-1020 2376350 2376384 2376495 "REPDB" 2376611 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1019 2370260 2371639 2372862 "REP2" 2375162 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1018 2366637 2367318 2368126 "REP1" 2369487 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1017 2359363 2364778 2365234 "REGSET" 2366267 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2358176 2358511 2358761 "REF" 2359148 NIL REF (NIL T) -8 NIL NIL NIL) (-1015 2357553 2357656 2357823 "REDORDER" 2358060 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1014 2353558 2356766 2356993 "RECLOS" 2357381 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1013 2352610 2352791 2353006 "REALSOLV" 2353365 T REALSOLV (NIL) -7 NIL NIL NIL) (-1012 2352456 2352497 2352527 "REAL" 2352532 T REAL (NIL) -9 NIL 2352567 NIL) (-1011 2348939 2349741 2350625 "REAL0Q" 2351621 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1010 2344540 2345528 2346589 "REAL0" 2347920 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1009 2344038 2344257 2344351 "RDUCEAST" 2344468 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1008 2343443 2343515 2343722 "RDIV" 2343960 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1007 2342511 2342685 2342898 "RDIST" 2343265 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1006 2341108 2341395 2341767 "RDETRS" 2342219 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1005 2338920 2339374 2339912 "RDETR" 2340650 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1004 2337531 2337809 2338213 "RDEEFS" 2338636 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1003 2336026 2336332 2336764 "RDEEF" 2337219 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1002 2330287 2333162 2333192 "RCFIELD" 2334487 T RCFIELD (NIL) -9 NIL 2335217 NIL) (-1001 2328351 2328855 2329551 "RCFIELD-" 2329626 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1000 2324667 2326452 2326495 "RCAGG" 2327579 NIL RCAGG (NIL T) -9 NIL 2328044 NIL) (-999 2324297 2324391 2324552 "RCAGG-" 2324557 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-998 2323637 2323749 2323912 "RATRET" 2324181 NIL RATRET (NIL T) -7 NIL NIL NIL) (-997 2323194 2323261 2323380 "RATFACT" 2323565 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-996 2322509 2322629 2322779 "RANDSRC" 2323064 T RANDSRC (NIL) -7 NIL NIL NIL) (-995 2322246 2322290 2322361 "RADUTIL" 2322458 T RADUTIL (NIL) -7 NIL NIL NIL) (-994 2315408 2321088 2321396 "RADIX" 2321970 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-993 2307065 2315252 2315380 "RADFF" 2315385 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-992 2306717 2306792 2306820 "RADCAT" 2306977 T RADCAT (NIL) -9 NIL NIL NIL) (-991 2306502 2306550 2306647 "RADCAT-" 2306652 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-990 2304653 2306277 2306366 "QUEUE" 2306446 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-989 2301229 2304590 2304635 "QUAT" 2304640 NIL QUAT (NIL T) -8 NIL NIL NIL) (-988 2300867 2300910 2301037 "QUATCT2" 2301180 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2294614 2297916 2297956 "QUATCAT" 2298736 NIL QUATCAT (NIL T) -9 NIL 2299502 NIL) (-986 2290758 2291795 2293182 "QUATCAT-" 2293276 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-985 2288278 2289842 2289883 "QUAGG" 2290258 NIL QUAGG (NIL T) -9 NIL 2290433 NIL) (-984 2287910 2288103 2288171 "QQUTAST" 2288230 T QQUTAST (NIL) -8 NIL NIL NIL) (-983 2286835 2287308 2287480 "QFORM" 2287782 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-982 2278047 2283252 2283292 "QFCAT" 2283950 NIL QFCAT (NIL T) -9 NIL 2284951 NIL) (-981 2273619 2274820 2276411 "QFCAT-" 2276505 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-980 2273257 2273300 2273427 "QFCAT2" 2273570 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-979 2272717 2272827 2272957 "QEQUAT" 2273147 T QEQUAT (NIL) -8 NIL NIL NIL) (-978 2265865 2266936 2268120 "QCMPACK" 2271650 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-977 2263441 2263862 2264290 "QALGSET" 2265520 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-976 2262686 2262860 2263092 "QALGSET2" 2263261 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-975 2261377 2261600 2261917 "PWFFINTB" 2262459 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-974 2259559 2259727 2260081 "PUSHVAR" 2261191 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-973 2255477 2256531 2256572 "PTRANFN" 2258456 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-972 2253879 2254170 2254492 "PTPACK" 2255188 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-971 2253511 2253568 2253677 "PTFUNC2" 2253816 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-970 2248038 2252383 2252424 "PTCAT" 2252720 NIL PTCAT (NIL T) -9 NIL 2252873 NIL) (-969 2247696 2247731 2247855 "PSQFR" 2247997 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-968 2246291 2246589 2246923 "PSEUDLIN" 2247394 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-967 2233061 2235425 2237749 "PSETPK" 2244051 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-966 2226105 2228819 2228915 "PSETCAT" 2231936 NIL PSETCAT (NIL T T T T) -9 NIL 2232750 NIL) (-965 2223941 2224575 2225396 "PSETCAT-" 2225401 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-964 2223290 2223455 2223483 "PSCURVE" 2223751 T PSCURVE (NIL) -9 NIL 2223918 NIL) (-963 2219646 2221128 2221193 "PSCAT" 2222037 NIL PSCAT (NIL T T T) -9 NIL 2222277 NIL) (-962 2218709 2218925 2219325 "PSCAT-" 2219330 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-961 2217441 2218074 2218279 "PRTITION" 2218524 T PRTITION (NIL) -8 NIL NIL NIL) (-960 2216943 2217162 2217254 "PRTDAST" 2217369 T PRTDAST (NIL) -8 NIL NIL NIL) (-959 2206041 2208247 2210435 "PRS" 2214805 NIL PRS (NIL T T) -7 NIL NIL NIL) (-958 2203899 2205391 2205431 "PRQAGG" 2205614 NIL PRQAGG (NIL T) -9 NIL 2205716 NIL) (-957 2203285 2203514 2203542 "PROPLOG" 2203727 T PROPLOG (NIL) -9 NIL 2203849 NIL) (-956 2200455 2201099 2201563 "PROPFRML" 2202853 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-955 2199915 2200025 2200155 "PROPERTY" 2200345 T PROPERTY (NIL) -8 NIL NIL NIL) (-954 2194000 2198081 2198901 "PRODUCT" 2199141 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-953 2191313 2193458 2193692 "PR" 2193811 NIL PR (NIL T T) -8 NIL NIL NIL) (-952 2191109 2191141 2191200 "PRINT" 2191274 T PRINT (NIL) -7 NIL NIL NIL) (-951 2190449 2190566 2190718 "PRIMES" 2190989 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-950 2188514 2188915 2189381 "PRIMELT" 2190028 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-949 2188243 2188292 2188320 "PRIMCAT" 2188444 T PRIMCAT (NIL) -9 NIL NIL NIL) (-948 2184404 2188181 2188226 "PRIMARR" 2188231 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-947 2183411 2183589 2183817 "PRIMARR2" 2184222 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-946 2183054 2183110 2183221 "PREASSOC" 2183349 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-945 2182529 2182662 2182690 "PPCURVE" 2182895 T PPCURVE (NIL) -9 NIL 2183031 NIL) (-944 2182151 2182324 2182407 "PORTNUM" 2182466 T PORTNUM (NIL) -8 NIL NIL NIL) (-943 2179510 2179909 2180501 "POLYROOT" 2181732 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-942 2173455 2179114 2179274 "POLY" 2179383 NIL POLY (NIL T) -8 NIL NIL NIL) (-941 2172838 2172896 2173130 "POLYLIFT" 2173391 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-940 2169113 2169562 2170191 "POLYCATQ" 2172383 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-939 2155930 2161288 2161353 "POLYCAT" 2164867 NIL POLYCAT (NIL T T T) -9 NIL 2166795 NIL) (-938 2149380 2151241 2153625 "POLYCAT-" 2153630 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-937 2148967 2149035 2149155 "POLY2UP" 2149306 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-936 2148599 2148656 2148765 "POLY2" 2148904 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-935 2147284 2147523 2147799 "POLUTIL" 2148373 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-934 2145639 2145916 2146247 "POLTOPOL" 2147006 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-933 2141157 2145575 2145621 "POINT" 2145626 NIL POINT (NIL T) -8 NIL NIL NIL) (-932 2139344 2139701 2140076 "PNTHEORY" 2140802 T PNTHEORY (NIL) -7 NIL NIL NIL) (-931 2137763 2138060 2138472 "PMTOOLS" 2139042 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-930 2137356 2137434 2137551 "PMSYM" 2137679 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-929 2136866 2136935 2137109 "PMQFCAT" 2137281 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-928 2136221 2136331 2136487 "PMPRED" 2136743 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-927 2135617 2135703 2135864 "PMPREDFS" 2136122 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-926 2134260 2134468 2134853 "PMPLCAT" 2135379 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-925 2133792 2133871 2134023 "PMLSAGG" 2134175 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-924 2133267 2133343 2133524 "PMKERNEL" 2133710 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-923 2132884 2132959 2133072 "PMINS" 2133186 NIL PMINS (NIL T) -7 NIL NIL NIL) (-922 2132312 2132381 2132597 "PMFS" 2132809 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-921 2131540 2131658 2131863 "PMDOWN" 2132189 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-920 2130703 2130862 2131044 "PMASS" 2131378 T PMASS (NIL) -7 NIL NIL NIL) (-919 2129977 2130088 2130251 "PMASSFS" 2130589 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-918 2129632 2129700 2129794 "PLOTTOOL" 2129903 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-917 2124254 2125443 2126591 "PLOT" 2128504 T PLOT (NIL) -8 NIL NIL NIL) (-916 2120068 2121102 2122023 "PLOT3D" 2123353 T PLOT3D (NIL) -8 NIL NIL NIL) (-915 2118980 2119157 2119392 "PLOT1" 2119872 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-914 2094374 2099046 2103897 "PLEQN" 2114246 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-913 2093692 2093814 2093994 "PINTERP" 2094239 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-912 2093385 2093432 2093535 "PINTERPA" 2093639 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-911 2092633 2093154 2093241 "PI" 2093281 T PI (NIL) -8 NIL NIL 2093348) (-910 2091030 2091971 2091999 "PID" 2092181 T PID (NIL) -9 NIL 2092315 NIL) (-909 2090755 2090792 2090880 "PICOERCE" 2090987 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-908 2090075 2090214 2090390 "PGROEB" 2090611 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-907 2085662 2086476 2087381 "PGE" 2089190 T PGE (NIL) -7 NIL NIL NIL) (-906 2083786 2084032 2084398 "PGCD" 2085379 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-905 2083124 2083227 2083388 "PFRPAC" 2083670 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-904 2079804 2081672 2082025 "PFR" 2082803 NIL PFR (NIL T) -8 NIL NIL NIL) (-903 2078193 2078437 2078762 "PFOTOOLS" 2079551 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-902 2076726 2076965 2077316 "PFOQ" 2077950 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-901 2075199 2075411 2075774 "PFO" 2076510 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-900 2071787 2075088 2075157 "PF" 2075162 NIL PF (NIL NIL) -8 NIL NIL NIL) (-899 2069221 2070458 2070486 "PFECAT" 2071071 T PFECAT (NIL) -9 NIL 2071455 NIL) (-898 2068666 2068820 2069034 "PFECAT-" 2069039 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-897 2067270 2067521 2067822 "PFBRU" 2068415 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-896 2065137 2065488 2065920 "PFBR" 2066921 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-895 2061053 2062513 2063189 "PERM" 2064494 NIL PERM (NIL T) -8 NIL NIL NIL) (-894 2056319 2057260 2058130 "PERMGRP" 2060216 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-893 2054451 2055382 2055423 "PERMCAT" 2055869 NIL PERMCAT (NIL T) -9 NIL 2056174 NIL) (-892 2054104 2054145 2054269 "PERMAN" 2054404 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-891 2051640 2053769 2053891 "PENDTREE" 2054015 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-890 2049733 2050467 2050508 "PDRING" 2051165 NIL PDRING (NIL T) -9 NIL 2051451 NIL) (-889 2048836 2049054 2049416 "PDRING-" 2049421 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-888 2046078 2046829 2047497 "PDEPROB" 2048188 T PDEPROB (NIL) -8 NIL NIL NIL) (-887 2043625 2044127 2044682 "PDEPACK" 2045543 T PDEPACK (NIL) -7 NIL NIL NIL) (-886 2042537 2042727 2042978 "PDECOMP" 2043424 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-885 2040142 2040959 2040987 "PDECAT" 2041774 T PDECAT (NIL) -9 NIL 2042487 NIL) (-884 2039893 2039926 2040016 "PCOMP" 2040103 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-883 2038098 2038694 2038991 "PBWLB" 2039622 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-882 2030603 2032171 2033509 "PATTERN" 2036781 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-881 2030235 2030292 2030401 "PATTERN2" 2030540 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-880 2027992 2028380 2028837 "PATTERN1" 2029824 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-879 2025387 2025941 2026422 "PATRES" 2027557 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-878 2024951 2025018 2025150 "PATRES2" 2025314 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-877 2022834 2023239 2023646 "PATMATCH" 2024618 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-876 2022370 2022553 2022594 "PATMAB" 2022701 NIL PATMAB (NIL T) -9 NIL 2022784 NIL) (-875 2020915 2021224 2021482 "PATLRES" 2022175 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-874 2020461 2020584 2020625 "PATAB" 2020630 NIL PATAB (NIL T) -9 NIL 2020802 NIL) (-873 2017942 2018474 2019047 "PARTPERM" 2019908 T PARTPERM (NIL) -7 NIL NIL NIL) (-872 2017563 2017626 2017728 "PARSURF" 2017873 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-871 2017195 2017252 2017361 "PARSU2" 2017500 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-870 2016959 2016999 2017066 "PARSER" 2017148 T PARSER (NIL) -7 NIL NIL NIL) (-869 2016580 2016643 2016745 "PARSCURV" 2016890 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-868 2016212 2016269 2016378 "PARSC2" 2016517 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-867 2015851 2015909 2016006 "PARPCURV" 2016148 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-866 2015483 2015540 2015649 "PARPC2" 2015788 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-865 2015003 2015089 2015208 "PAN2EXPR" 2015384 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-864 2013809 2014124 2014352 "PALETTE" 2014795 T PALETTE (NIL) -8 NIL NIL NIL) (-863 2012277 2012814 2013174 "PAIR" 2013495 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-862 2006183 2011536 2011730 "PADICRC" 2012132 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-861 1999447 2005529 2005713 "PADICRAT" 2006031 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-860 1997797 1999384 1999429 "PADIC" 1999434 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-859 1995007 1996537 1996577 "PADICCT" 1997158 NIL PADICCT (NIL NIL) -9 NIL 1997440 NIL) (-858 1993964 1994164 1994432 "PADEPAC" 1994794 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-857 1993176 1993309 1993515 "PADE" 1993826 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-856 1991598 1992384 1992664 "OWP" 1992980 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-855 1990671 1991203 1991375 "OVAR" 1991466 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-854 1989935 1990056 1990217 "OUT" 1990530 T OUT (NIL) -7 NIL NIL NIL) (-853 1978842 1981044 1983244 "OUTFORM" 1987755 T OUTFORM (NIL) -8 NIL NIL NIL) (-852 1978263 1978439 1978566 "OUTBFILE" 1978735 T OUTBFILE (NIL) -8 NIL NIL NIL) (-851 1977900 1977983 1978011 "OUTBCON" 1978162 T OUTBCON (NIL) -9 NIL 1978247 NIL) (-850 1977740 1977775 1977851 "OUTBCON-" 1977856 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-849 1977148 1977469 1977558 "OSI" 1977671 T OSI (NIL) -8 NIL NIL NIL) (-848 1976704 1977016 1977044 "OSGROUP" 1977049 T OSGROUP (NIL) -9 NIL 1977071 NIL) (-847 1975449 1975676 1975961 "ORTHPOL" 1976451 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-846 1973035 1975284 1975405 "OREUP" 1975410 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-845 1970473 1972726 1972853 "ORESUP" 1972977 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-844 1968001 1968501 1969062 "OREPCTO" 1969962 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-843 1961825 1963992 1964033 "OREPCAT" 1966381 NIL OREPCAT (NIL T) -9 NIL 1967485 NIL) (-842 1958972 1959754 1960812 "OREPCAT-" 1960817 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-841 1958149 1958421 1958449 "ORDSET" 1958758 T ORDSET (NIL) -9 NIL 1958922 NIL) (-840 1957668 1957790 1957983 "ORDSET-" 1957988 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-839 1956302 1957059 1957087 "ORDRING" 1957289 T ORDRING (NIL) -9 NIL 1957414 NIL) (-838 1955947 1956041 1956185 "ORDRING-" 1956190 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-837 1955353 1955790 1955818 "ORDMON" 1955823 T ORDMON (NIL) -9 NIL 1955844 NIL) (-836 1954515 1954662 1954857 "ORDFUNS" 1955202 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-835 1953879 1954272 1954300 "ORDFIN" 1954365 T ORDFIN (NIL) -9 NIL 1954439 NIL) (-834 1950471 1952465 1952874 "ORDCOMP" 1953503 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-833 1949737 1949864 1950050 "ORDCOMP2" 1950331 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1946345 1947228 1948042 "OPTPROB" 1948943 T OPTPROB (NIL) -8 NIL NIL NIL) (-831 1943147 1943786 1944490 "OPTPACK" 1945661 T OPTPACK (NIL) -7 NIL NIL NIL) (-830 1940860 1941600 1941628 "OPTCAT" 1942447 T OPTCAT (NIL) -9 NIL 1943097 NIL) (-829 1940303 1940537 1940642 "OPSIG" 1940775 T OPSIG (NIL) -8 NIL NIL NIL) (-828 1940071 1940110 1940176 "OPQUERY" 1940257 T OPQUERY (NIL) -7 NIL NIL NIL) (-827 1937237 1938382 1938886 "OP" 1939600 NIL OP (NIL T) -8 NIL NIL NIL) (-826 1936772 1936943 1936984 "OPERCAT" 1937119 NIL OPERCAT (NIL T) -9 NIL 1937187 NIL) (-825 1936618 1936645 1936731 "OPERCAT-" 1936736 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-824 1933463 1935415 1935784 "ONECOMP" 1936282 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-823 1932768 1932883 1933057 "ONECOMP2" 1933335 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-822 1932187 1932293 1932423 "OMSERVER" 1932658 T OMSERVER (NIL) -7 NIL NIL NIL) (-821 1929075 1931627 1931667 "OMSAGG" 1931728 NIL OMSAGG (NIL T) -9 NIL 1931792 NIL) (-820 1927698 1927961 1928243 "OMPKG" 1928813 T OMPKG (NIL) -7 NIL NIL NIL) (-819 1927128 1927231 1927259 "OM" 1927558 T OM (NIL) -9 NIL NIL NIL) (-818 1925710 1926677 1926846 "OMLO" 1927009 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-817 1924635 1924782 1925009 "OMEXPR" 1925536 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-816 1923953 1924181 1924317 "OMERR" 1924519 T OMERR (NIL) -8 NIL NIL NIL) (-815 1923131 1923374 1923534 "OMERRK" 1923813 T OMERRK (NIL) -8 NIL NIL NIL) (-814 1922609 1922808 1922916 "OMENC" 1923043 T OMENC (NIL) -8 NIL NIL NIL) (-813 1916504 1917689 1918860 "OMDEV" 1921458 T OMDEV (NIL) -8 NIL NIL NIL) (-812 1915573 1915744 1915938 "OMCONN" 1916330 T OMCONN (NIL) -8 NIL NIL NIL) (-811 1914194 1915136 1915164 "OINTDOM" 1915169 T OINTDOM (NIL) -9 NIL 1915190 NIL) (-810 1910000 1911184 1911900 "OFMONOID" 1913510 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-809 1909438 1909937 1909982 "ODVAR" 1909987 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-808 1906896 1909183 1909338 "ODR" 1909343 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-807 1899240 1906672 1906798 "ODPOL" 1906803 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-806 1893116 1899112 1899217 "ODP" 1899222 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-805 1891882 1892097 1892372 "ODETOOLS" 1892890 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-804 1888851 1889507 1890223 "ODESYS" 1891215 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-803 1883733 1884641 1885666 "ODERTRIC" 1887926 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-802 1883159 1883241 1883435 "ODERED" 1883645 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-801 1880047 1880595 1881272 "ODERAT" 1882582 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-800 1877007 1877471 1878068 "ODEPRRIC" 1879576 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-799 1874977 1875546 1876032 "ODEPROB" 1876541 T ODEPROB (NIL) -8 NIL NIL NIL) (-798 1871499 1871982 1872629 "ODEPRIM" 1874456 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-797 1870748 1870850 1871110 "ODEPAL" 1871391 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-796 1866910 1867701 1868565 "ODEPACK" 1869904 T ODEPACK (NIL) -7 NIL NIL NIL) (-795 1865943 1866050 1866279 "ODEINT" 1866799 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-794 1860044 1861469 1862916 "ODEIFTBL" 1864516 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-793 1855379 1856165 1857124 "ODEEF" 1859203 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-792 1854714 1854803 1855033 "ODECONST" 1855284 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-791 1852865 1853500 1853528 "ODECAT" 1854133 T ODECAT (NIL) -9 NIL 1854664 NIL) (-790 1849772 1852577 1852696 "OCT" 1852778 NIL OCT (NIL T) -8 NIL NIL NIL) (-789 1849410 1849453 1849580 "OCTCT2" 1849723 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-788 1844184 1846584 1846624 "OC" 1847721 NIL OC (NIL T) -9 NIL 1848579 NIL) (-787 1841411 1842159 1843149 "OC-" 1843243 NIL OC- (NIL T T) -8 NIL NIL NIL) (-786 1840789 1841231 1841259 "OCAMON" 1841264 T OCAMON (NIL) -9 NIL 1841285 NIL) (-785 1840346 1840661 1840689 "OASGP" 1840694 T OASGP (NIL) -9 NIL 1840714 NIL) (-784 1839633 1840096 1840124 "OAMONS" 1840164 T OAMONS (NIL) -9 NIL 1840207 NIL) (-783 1839073 1839480 1839508 "OAMON" 1839513 T OAMON (NIL) -9 NIL 1839533 NIL) (-782 1838377 1838869 1838897 "OAGROUP" 1838902 T OAGROUP (NIL) -9 NIL 1838922 NIL) (-781 1838067 1838117 1838205 "NUMTUBE" 1838321 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-780 1831640 1833158 1834694 "NUMQUAD" 1836551 T NUMQUAD (NIL) -7 NIL NIL NIL) (-779 1827396 1828384 1829409 "NUMODE" 1830635 T NUMODE (NIL) -7 NIL NIL NIL) (-778 1824777 1825631 1825659 "NUMINT" 1826582 T NUMINT (NIL) -9 NIL 1827346 NIL) (-777 1823725 1823922 1824140 "NUMFMT" 1824579 T NUMFMT (NIL) -7 NIL NIL NIL) (-776 1810084 1813029 1815561 "NUMERIC" 1821232 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-775 1804481 1809533 1809628 "NTSCAT" 1809633 NIL NTSCAT (NIL T T T T) -9 NIL 1809672 NIL) (-774 1803675 1803840 1804033 "NTPOLFN" 1804320 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-773 1791515 1800500 1801312 "NSUP" 1802896 NIL NSUP (NIL T) -8 NIL NIL NIL) (-772 1791147 1791204 1791313 "NSUP2" 1791452 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-771 1781144 1790921 1791054 "NSMP" 1791059 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-770 1779576 1779877 1780234 "NREP" 1780832 NIL NREP (NIL T) -7 NIL NIL NIL) (-769 1778167 1778419 1778777 "NPCOEF" 1779319 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-768 1777233 1777348 1777564 "NORMRETR" 1778048 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-767 1775274 1775564 1775973 "NORMPK" 1776941 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-766 1774959 1774987 1775111 "NORMMA" 1775240 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-765 1774786 1774916 1774945 "NONE" 1774950 T NONE (NIL) -8 NIL NIL NIL) (-764 1774575 1774604 1774673 "NONE1" 1774750 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-763 1774058 1774120 1774306 "NODE1" 1774507 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-762 1772329 1773152 1773407 "NNI" 1773754 T NNI (NIL) -8 NIL NIL 1773989) (-761 1770749 1771062 1771426 "NLINSOL" 1771997 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-760 1767017 1767985 1768884 "NIPROB" 1769870 T NIPROB (NIL) -8 NIL NIL NIL) (-759 1765774 1766008 1766310 "NFINTBAS" 1766779 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-758 1765218 1765425 1765466 "NETCLT" 1765630 NIL NETCLT (NIL T) -9 NIL 1765719 NIL) (-757 1763926 1764157 1764438 "NCODIV" 1764986 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-756 1763688 1763725 1763800 "NCNTFRAC" 1763883 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-755 1761868 1762232 1762652 "NCEP" 1763313 NIL NCEP (NIL T) -7 NIL NIL NIL) (-754 1760779 1761518 1761546 "NASRING" 1761656 T NASRING (NIL) -9 NIL 1761730 NIL) (-753 1760574 1760618 1760712 "NASRING-" 1760717 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-752 1759727 1760226 1760254 "NARNG" 1760371 T NARNG (NIL) -9 NIL 1760462 NIL) (-751 1759419 1759486 1759620 "NARNG-" 1759625 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-750 1758298 1758505 1758740 "NAGSP" 1759204 T NAGSP (NIL) -7 NIL NIL NIL) (-749 1749570 1751254 1752927 "NAGS" 1756645 T NAGS (NIL) -7 NIL NIL NIL) (-748 1748118 1748426 1748757 "NAGF07" 1749259 T NAGF07 (NIL) -7 NIL NIL NIL) (-747 1742656 1743947 1745254 "NAGF04" 1746831 T NAGF04 (NIL) -7 NIL NIL NIL) (-746 1735624 1737238 1738871 "NAGF02" 1741043 T NAGF02 (NIL) -7 NIL NIL NIL) (-745 1730848 1731948 1733065 "NAGF01" 1734527 T NAGF01 (NIL) -7 NIL NIL NIL) (-744 1724476 1726042 1727627 "NAGE04" 1729283 T NAGE04 (NIL) -7 NIL NIL NIL) (-743 1715645 1717766 1719896 "NAGE02" 1722366 T NAGE02 (NIL) -7 NIL NIL NIL) (-742 1711598 1712545 1713509 "NAGE01" 1714701 T NAGE01 (NIL) -7 NIL NIL NIL) (-741 1709393 1709927 1710485 "NAGD03" 1711060 T NAGD03 (NIL) -7 NIL NIL NIL) (-740 1701143 1703071 1705025 "NAGD02" 1707459 T NAGD02 (NIL) -7 NIL NIL NIL) (-739 1694954 1696379 1697819 "NAGD01" 1699723 T NAGD01 (NIL) -7 NIL NIL NIL) (-738 1691163 1691985 1692822 "NAGC06" 1694137 T NAGC06 (NIL) -7 NIL NIL NIL) (-737 1689628 1689960 1690316 "NAGC05" 1690827 T NAGC05 (NIL) -7 NIL NIL NIL) (-736 1689004 1689123 1689267 "NAGC02" 1689504 T NAGC02 (NIL) -7 NIL NIL NIL) (-735 1688064 1688621 1688661 "NAALG" 1688740 NIL NAALG (NIL T) -9 NIL 1688801 NIL) (-734 1687899 1687928 1688018 "NAALG-" 1688023 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-733 1681849 1682957 1684144 "MULTSQFR" 1686795 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-732 1681168 1681243 1681427 "MULTFACT" 1681761 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-731 1674261 1678131 1678184 "MTSCAT" 1679254 NIL MTSCAT (NIL T T) -9 NIL 1679768 NIL) (-730 1673973 1674027 1674119 "MTHING" 1674201 NIL MTHING (NIL T) -7 NIL NIL NIL) (-729 1673765 1673798 1673858 "MSYSCMD" 1673933 T MSYSCMD (NIL) -7 NIL NIL NIL) (-728 1669877 1672520 1672840 "MSET" 1673478 NIL MSET (NIL T) -8 NIL NIL NIL) (-727 1666972 1669438 1669479 "MSETAGG" 1669484 NIL MSETAGG (NIL T) -9 NIL 1669518 NIL) (-726 1662855 1664351 1665096 "MRING" 1666272 NIL MRING (NIL T T) -8 NIL NIL NIL) (-725 1662421 1662488 1662619 "MRF2" 1662782 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-724 1662039 1662074 1662218 "MRATFAC" 1662380 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-723 1659651 1659946 1660377 "MPRFF" 1661744 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-722 1653711 1659505 1659602 "MPOLY" 1659607 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-721 1653201 1653236 1653444 "MPCPF" 1653670 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-720 1652715 1652758 1652942 "MPC3" 1653152 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-719 1651910 1651991 1652212 "MPC2" 1652630 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-718 1650211 1650548 1650938 "MONOTOOL" 1651570 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-717 1649462 1649753 1649781 "MONOID" 1650000 T MONOID (NIL) -9 NIL 1650147 NIL) (-716 1649008 1649127 1649308 "MONOID-" 1649313 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-715 1639867 1645775 1645834 "MONOGEN" 1646508 NIL MONOGEN (NIL T T) -9 NIL 1646964 NIL) (-714 1637085 1637820 1638820 "MONOGEN-" 1638939 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-713 1635944 1636364 1636392 "MONADWU" 1636784 T MONADWU (NIL) -9 NIL 1637022 NIL) (-712 1635316 1635475 1635723 "MONADWU-" 1635728 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-711 1634701 1634919 1634947 "MONAD" 1635154 T MONAD (NIL) -9 NIL 1635266 NIL) (-710 1634386 1634464 1634596 "MONAD-" 1634601 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-709 1632702 1633299 1633578 "MOEBIUS" 1634139 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-708 1632094 1632472 1632512 "MODULE" 1632517 NIL MODULE (NIL T) -9 NIL 1632543 NIL) (-707 1631662 1631758 1631948 "MODULE-" 1631953 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-706 1629377 1630026 1630353 "MODRING" 1631486 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1626363 1627482 1628003 "MODOP" 1628906 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-704 1624978 1625430 1625707 "MODMONOM" 1626226 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-703 1614785 1623269 1623683 "MODMON" 1624615 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-702 1611976 1613629 1613905 "MODFIELD" 1614660 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-701 1610980 1611257 1611447 "MMLFORM" 1611806 T MMLFORM (NIL) -8 NIL NIL NIL) (-700 1610506 1610549 1610728 "MMAP" 1610931 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-699 1608723 1609456 1609497 "MLO" 1609920 NIL MLO (NIL T) -9 NIL 1610162 NIL) (-698 1606090 1606605 1607207 "MLIFT" 1608204 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-697 1605481 1605565 1605719 "MKUCFUNC" 1606001 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-696 1605080 1605150 1605273 "MKRECORD" 1605404 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-695 1604128 1604289 1604517 "MKFUNC" 1604891 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-694 1603516 1603620 1603776 "MKFLCFN" 1604011 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-693 1603059 1603426 1603485 "MKCHSET" 1603490 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-692 1602336 1602438 1602623 "MKBCFUNC" 1602952 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-691 1599078 1601890 1602026 "MINT" 1602220 T MINT (NIL) -8 NIL NIL NIL) (-690 1597890 1598133 1598410 "MHROWRED" 1598833 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-689 1593316 1596425 1596830 "MFLOAT" 1597505 T MFLOAT (NIL) -8 NIL NIL NIL) (-688 1592673 1592749 1592920 "MFINFACT" 1593228 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-687 1588988 1589836 1590720 "MESH" 1591809 T MESH (NIL) -7 NIL NIL NIL) (-686 1587378 1587690 1588043 "MDDFACT" 1588675 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-685 1584220 1586537 1586578 "MDAGG" 1586833 NIL MDAGG (NIL T) -9 NIL 1586976 NIL) (-684 1573998 1583513 1583720 "MCMPLX" 1584033 T MCMPLX (NIL) -8 NIL NIL NIL) (-683 1573139 1573285 1573485 "MCDEN" 1573847 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-682 1571029 1571299 1571679 "MCALCFN" 1572869 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-681 1569954 1570194 1570427 "MAYBE" 1570835 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-680 1567566 1568089 1568651 "MATSTOR" 1569425 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-679 1563572 1566938 1567186 "MATRIX" 1567351 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-678 1559341 1560045 1560781 "MATLIN" 1562929 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-677 1549495 1552633 1552710 "MATCAT" 1557590 NIL MATCAT (NIL T T T) -9 NIL 1559007 NIL) (-676 1545859 1546872 1548228 "MATCAT-" 1548233 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-675 1544453 1544606 1544939 "MATCAT2" 1545694 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-674 1542565 1542889 1543273 "MAPPKG3" 1544128 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-673 1541546 1541719 1541941 "MAPPKG2" 1542389 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-672 1540045 1540329 1540656 "MAPPKG1" 1541252 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-671 1539151 1539451 1539628 "MAPPAST" 1539888 T MAPPAST (NIL) -8 NIL NIL NIL) (-670 1538762 1538820 1538943 "MAPHACK3" 1539087 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-669 1538354 1538415 1538529 "MAPHACK2" 1538694 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-668 1537792 1537895 1538037 "MAPHACK1" 1538245 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-667 1535898 1536492 1536796 "MAGMA" 1537520 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-666 1535404 1535622 1535713 "MACROAST" 1535827 T MACROAST (NIL) -8 NIL NIL NIL) (-665 1531871 1533643 1534104 "M3D" 1534976 NIL M3D (NIL T) -8 NIL NIL NIL) (-664 1526025 1530240 1530281 "LZSTAGG" 1531063 NIL LZSTAGG (NIL T) -9 NIL 1531358 NIL) (-663 1521999 1523156 1524613 "LZSTAGG-" 1524618 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-662 1519113 1519890 1520377 "LWORD" 1521544 NIL LWORD (NIL T) -8 NIL NIL NIL) (-661 1518716 1518917 1518992 "LSTAST" 1519058 T LSTAST (NIL) -8 NIL NIL NIL) (-660 1511917 1518487 1518621 "LSQM" 1518626 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-659 1511141 1511280 1511508 "LSPP" 1511772 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-658 1508953 1509254 1509710 "LSMP" 1510830 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-657 1505732 1506406 1507136 "LSMP1" 1508255 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-656 1499657 1504899 1504940 "LSAGG" 1505002 NIL LSAGG (NIL T) -9 NIL 1505080 NIL) (-655 1496352 1497276 1498489 "LSAGG-" 1498494 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-654 1493978 1495496 1495745 "LPOLY" 1496147 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-653 1493560 1493645 1493768 "LPEFRAC" 1493887 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-652 1491907 1492654 1492907 "LO" 1493392 NIL LO (NIL T T T) -8 NIL NIL NIL) (-651 1491559 1491671 1491699 "LOGIC" 1491810 T LOGIC (NIL) -9 NIL 1491891 NIL) (-650 1491421 1491444 1491515 "LOGIC-" 1491520 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-649 1490614 1490754 1490947 "LODOOPS" 1491277 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-648 1488072 1490530 1490596 "LODO" 1490601 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-647 1486610 1486845 1487198 "LODOF" 1487819 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-646 1482966 1485363 1485404 "LODOCAT" 1485842 NIL LODOCAT (NIL T) -9 NIL 1486053 NIL) (-645 1482699 1482757 1482884 "LODOCAT-" 1482889 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-644 1480054 1482540 1482658 "LODO2" 1482663 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-643 1477524 1479991 1480036 "LODO1" 1480041 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-642 1476384 1476549 1476861 "LODEEF" 1477347 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-641 1471670 1474514 1474555 "LNAGG" 1475502 NIL LNAGG (NIL T) -9 NIL 1475946 NIL) (-640 1470817 1471031 1471373 "LNAGG-" 1471378 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-639 1466980 1467742 1468381 "LMOPS" 1470232 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-638 1466375 1466737 1466778 "LMODULE" 1466839 NIL LMODULE (NIL T) -9 NIL 1466881 NIL) (-637 1463621 1466020 1466143 "LMDICT" 1466285 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-636 1463347 1463529 1463589 "LITERAL" 1463594 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-635 1456574 1462293 1462591 "LIST" 1463082 NIL LIST (NIL T) -8 NIL NIL NIL) (-634 1456099 1456173 1456312 "LIST3" 1456494 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-633 1455106 1455284 1455512 "LIST2" 1455917 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-632 1453240 1453552 1453951 "LIST2MAP" 1454753 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-631 1451970 1452606 1452647 "LINEXP" 1452902 NIL LINEXP (NIL T) -9 NIL 1453051 NIL) (-630 1450617 1450877 1451174 "LINDEP" 1451722 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-629 1447384 1448103 1448880 "LIMITRF" 1449872 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-628 1445660 1445955 1446371 "LIMITPS" 1447079 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-627 1440115 1445171 1445399 "LIE" 1445481 NIL LIE (NIL T T) -8 NIL NIL NIL) (-626 1439164 1439607 1439647 "LIECAT" 1439787 NIL LIECAT (NIL T) -9 NIL 1439938 NIL) (-625 1439005 1439032 1439120 "LIECAT-" 1439125 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-624 1431617 1438454 1438619 "LIB" 1438860 T LIB (NIL) -8 NIL NIL NIL) (-623 1427254 1428135 1429070 "LGROBP" 1430734 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-622 1425120 1425394 1425756 "LF" 1426975 NIL LF (NIL T T) -7 NIL NIL NIL) (-621 1423960 1424652 1424680 "LFCAT" 1424887 T LFCAT (NIL) -9 NIL 1425026 NIL) (-620 1420864 1421492 1422180 "LEXTRIPK" 1423324 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-619 1417635 1418434 1418937 "LEXP" 1420444 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-618 1417138 1417356 1417448 "LETAST" 1417563 T LETAST (NIL) -8 NIL NIL NIL) (-617 1415536 1415849 1416250 "LEADCDET" 1416820 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-616 1414726 1414800 1415029 "LAZM3PK" 1415457 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-615 1409681 1412803 1413341 "LAUPOL" 1414238 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-614 1409246 1409290 1409458 "LAPLACE" 1409631 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-613 1407220 1408347 1408598 "LA" 1409079 NIL LA (NIL T T T) -8 NIL NIL NIL) (-612 1406301 1406851 1406892 "LALG" 1406954 NIL LALG (NIL T) -9 NIL 1407013 NIL) (-611 1406015 1406074 1406210 "LALG-" 1406215 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-610 1405850 1405874 1405915 "KVTFROM" 1405977 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-609 1404650 1405067 1405296 "KTVLOGIC" 1405641 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-608 1404485 1404509 1404550 "KRCFROM" 1404612 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-607 1403389 1403576 1403875 "KOVACIC" 1404285 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-606 1403224 1403248 1403289 "KONVERT" 1403351 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-605 1403059 1403083 1403124 "KOERCE" 1403186 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-604 1400793 1401553 1401946 "KERNEL" 1402698 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-603 1400295 1400376 1400506 "KERNEL2" 1400707 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-602 1394146 1398834 1398888 "KDAGG" 1399265 NIL KDAGG (NIL T T) -9 NIL 1399471 NIL) (-601 1393675 1393799 1394004 "KDAGG-" 1394009 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386850 1393336 1393491 "KAFILE" 1393553 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-599 1381305 1386361 1386589 "JORDAN" 1386671 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-598 1380711 1380954 1381075 "JOINAST" 1381204 T JOINAST (NIL) -8 NIL NIL NIL) (-597 1380557 1380616 1380671 "JAVACODE" 1380676 T JAVACODE (NIL) -8 NIL NIL NIL) (-596 1376856 1378762 1378816 "IXAGG" 1379745 NIL IXAGG (NIL T T) -9 NIL 1380204 NIL) (-595 1375775 1376081 1376500 "IXAGG-" 1376505 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-594 1371355 1375697 1375756 "IVECTOR" 1375761 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-593 1370121 1370358 1370624 "ITUPLE" 1371122 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-592 1368557 1368734 1369040 "ITRIGMNP" 1369943 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-591 1367302 1367506 1367789 "ITFUN3" 1368333 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-590 1366934 1366991 1367100 "ITFUN2" 1367239 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-589 1364771 1365796 1366095 "ITAYLOR" 1366668 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-588 1353754 1358908 1360071 "ISUPS" 1363641 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-587 1352858 1352998 1353234 "ISUMP" 1353601 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-586 1348122 1352659 1352738 "ISTRING" 1352811 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-585 1347625 1347843 1347935 "ISAST" 1348050 T ISAST (NIL) -8 NIL NIL NIL) (-584 1346835 1346916 1347132 "IRURPK" 1347539 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-583 1345771 1345972 1346212 "IRSN" 1346615 T IRSN (NIL) -7 NIL NIL NIL) (-582 1343800 1344155 1344591 "IRRF2F" 1345409 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-581 1343547 1343585 1343661 "IRREDFFX" 1343756 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-580 1342162 1342421 1342720 "IROOT" 1343280 NIL IROOT (NIL T) -7 NIL NIL NIL) (-579 1338794 1339846 1340538 "IR" 1341502 NIL IR (NIL T) -8 NIL NIL NIL) (-578 1336407 1336902 1337468 "IR2" 1338272 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-577 1335479 1335592 1335813 "IR2F" 1336290 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-576 1335270 1335304 1335364 "IPRNTPK" 1335439 T IPRNTPK (NIL) -7 NIL NIL NIL) (-575 1331889 1335159 1335228 "IPF" 1335233 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-574 1330252 1331814 1331871 "IPADIC" 1331876 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-573 1329583 1329810 1329947 "IP4ADDR" 1330135 T IP4ADDR (NIL) -8 NIL NIL NIL) (-572 1329083 1329287 1329397 "IOMODE" 1329493 T IOMODE (NIL) -8 NIL NIL NIL) (-571 1328441 1328680 1328807 "IOBFILE" 1328976 T IOBFILE (NIL) -8 NIL NIL NIL) (-570 1328205 1328345 1328373 "IOBCON" 1328378 T IOBCON (NIL) -9 NIL 1328399 NIL) (-569 1327702 1327760 1327950 "INVLAPLA" 1328141 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-568 1317351 1319704 1322090 "INTTR" 1325366 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-567 1313695 1314437 1315301 "INTTOOLS" 1316536 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-566 1313281 1313372 1313489 "INTSLPE" 1313598 T INTSLPE (NIL) -7 NIL NIL NIL) (-565 1311276 1313204 1313263 "INTRVL" 1313268 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-564 1308878 1309390 1309965 "INTRF" 1310761 NIL INTRF (NIL T) -7 NIL NIL NIL) (-563 1308289 1308386 1308528 "INTRET" 1308776 NIL INTRET (NIL T) -7 NIL NIL NIL) (-562 1306286 1306675 1307145 "INTRAT" 1307897 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-561 1303514 1304097 1304723 "INTPM" 1305771 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-560 1300217 1300816 1301561 "INTPAF" 1302900 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-559 1295396 1296358 1297409 "INTPACK" 1299186 T INTPACK (NIL) -7 NIL NIL NIL) (-558 1292308 1295125 1295252 "INT" 1295289 T INT (NIL) -8 NIL NIL NIL) (-557 1291560 1291712 1291920 "INTHERTR" 1292150 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-556 1290999 1291079 1291267 "INTHERAL" 1291474 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-555 1288845 1289288 1289745 "INTHEORY" 1290562 T INTHEORY (NIL) -7 NIL NIL NIL) (-554 1280153 1281774 1283553 "INTG0" 1287197 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-553 1260726 1265516 1270326 "INTFTBL" 1275363 T INTFTBL (NIL) -8 NIL NIL NIL) (-552 1259975 1260113 1260286 "INTFACT" 1260585 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-551 1257360 1257806 1258370 "INTEF" 1259529 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-550 1255827 1256532 1256560 "INTDOM" 1256861 T INTDOM (NIL) -9 NIL 1257068 NIL) (-549 1255196 1255370 1255612 "INTDOM-" 1255617 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-548 1251691 1253580 1253634 "INTCAT" 1254433 NIL INTCAT (NIL T) -9 NIL 1254753 NIL) (-547 1251164 1251266 1251394 "INTBIT" 1251583 T INTBIT (NIL) -7 NIL NIL NIL) (-546 1249835 1249989 1250303 "INTALG" 1251009 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-545 1249292 1249382 1249552 "INTAF" 1249739 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-544 1242746 1249102 1249242 "INTABL" 1249247 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-543 1237761 1240435 1240463 "INS" 1241397 T INS (NIL) -9 NIL 1242062 NIL) (-542 1235001 1235772 1236746 "INS-" 1236819 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1233776 1234003 1234301 "INPSIGN" 1234754 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1232894 1233011 1233208 "INPRODPF" 1233656 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1231788 1231905 1232142 "INPRODFF" 1232774 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1230788 1230940 1231200 "INNMFACT" 1231624 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1229985 1230082 1230270 "INMODGCD" 1230687 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1228494 1228738 1229062 "INFSP" 1229730 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1227678 1227795 1227978 "INFPROD0" 1228374 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1224560 1225743 1226258 "INFORM" 1227171 T INFORM (NIL) -8 NIL NIL NIL) (-533 1224170 1224230 1224328 "INFORM1" 1224495 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1223693 1223782 1223896 "INFINITY" 1224076 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1223138 1223411 1223519 "INETCLTS" 1223605 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1221755 1222004 1222325 "INEP" 1222886 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1221031 1221652 1221717 "INDE" 1221722 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1220595 1220663 1220780 "INCRMAPS" 1220958 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1219613 1219864 1220070 "INBFILE" 1220409 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1214924 1215849 1216793 "INBFF" 1218701 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1214593 1214669 1214697 "INBCON" 1214830 T INBCON (NIL) -9 NIL 1214908 NIL) (-524 1214433 1214468 1214544 "INBCON-" 1214549 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1213935 1214154 1214246 "INAST" 1214361 T INAST (NIL) -8 NIL NIL NIL) (-522 1213389 1213614 1213720 "IMPTAST" 1213849 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1209883 1213233 1213337 "IMATRIX" 1213342 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208595 1208718 1209033 "IMATQF" 1209739 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206815 1207042 1207379 "IMATLIN" 1208351 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201441 1206739 1206797 "ILIST" 1206802 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199394 1201301 1201414 "IIARRAY2" 1201419 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194827 1199305 1199369 "IFF" 1199374 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194201 1194444 1194560 "IFAST" 1194731 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189244 1193493 1193681 "IFARRAY" 1194058 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188451 1189148 1189221 "IFAMON" 1189226 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188035 1188100 1188154 "IEVALAB" 1188361 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187710 1187778 1187938 "IEVALAB-" 1187943 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187368 1187624 1187687 "IDPO" 1187692 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186645 1187257 1187332 "IDPOAMS" 1187337 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1185979 1186534 1186609 "IDPOAM" 1186614 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185064 1185314 1185367 "IDPC" 1185780 NIL IDPC (NIL T T) -9 NIL 1185929 NIL) (-506 1184560 1184956 1185029 "IDPAM" 1185034 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1183963 1184452 1184525 "IDPAG" 1184530 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183731 1183878 1183928 "IDENT" 1183933 T IDENT (NIL) -8 NIL NIL NIL) (-503 1179986 1180834 1181729 "IDECOMP" 1182888 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172860 1173909 1174956 "IDEAL" 1179022 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172024 1172136 1172335 "ICDEN" 1172744 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171123 1171504 1171651 "ICARD" 1171897 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169183 1169496 1169901 "IBPTOOLS" 1170800 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164817 1168803 1168916 "IBITS" 1169102 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161540 1162116 1162811 "IBATOOL" 1164234 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159320 1159781 1160314 "IBACHIN" 1161075 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157197 1159166 1159269 "IARRAY2" 1159274 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153350 1157123 1157180 "IARRAY1" 1157185 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147344 1151762 1152243 "IAN" 1152889 T IAN (NIL) -8 NIL NIL NIL) (-492 1146855 1146912 1147085 "IALGFACT" 1147281 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146383 1146496 1146524 "HYPCAT" 1146731 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1145921 1146038 1146224 "HYPCAT-" 1146229 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145543 1145716 1145799 "HOSTNAME" 1145858 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145388 1145425 1145466 "HOMOTOP" 1145471 NIL HOMOTOP (NIL T) -9 NIL 1145504 NIL) (-487 1142067 1143398 1143439 "HOAGG" 1144420 NIL HOAGG (NIL T) -9 NIL 1145099 NIL) (-486 1140661 1141060 1141586 "HOAGG-" 1141591 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134703 1140258 1140406 "HEXADEC" 1140533 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133451 1133673 1133936 "HEUGCD" 1134480 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132554 1133288 1133418 "HELLFDIV" 1133423 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130782 1132331 1132419 "HEAP" 1132498 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130073 1130334 1130468 "HEADAST" 1130668 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1123993 1129988 1130050 "HDP" 1130055 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117744 1123628 1123780 "HDMP" 1123894 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117069 1117208 1117372 "HB" 1117600 T HB (NIL) -7 NIL NIL NIL) (-477 1110566 1116915 1117019 "HASHTBL" 1117024 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110069 1110287 1110379 "HASAST" 1110494 T HASAST (NIL) -8 NIL NIL NIL) (-475 1107881 1109691 1109873 "HACKPI" 1109907 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103576 1107734 1107847 "GTSET" 1107852 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097102 1103454 1103552 "GSTBL" 1103557 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089415 1096133 1096398 "GSERIES" 1096893 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088582 1088973 1089001 "GROUP" 1089204 T GROUP (NIL) -9 NIL 1089338 NIL) (-470 1087948 1088107 1088358 "GROUP-" 1088363 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086317 1086636 1087023 "GROEBSOL" 1087625 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085257 1085519 1085570 "GRMOD" 1086099 NIL GRMOD (NIL T T) -9 NIL 1086267 NIL) (-467 1085025 1085061 1085189 "GRMOD-" 1085194 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080351 1081379 1082379 "GRIMAGE" 1084045 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078818 1079078 1079402 "GRDEF" 1080047 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078262 1078378 1078519 "GRAY" 1078697 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077475 1077855 1077906 "GRALG" 1078059 NIL GRALG (NIL T T) -9 NIL 1078152 NIL) (-462 1077136 1077209 1077372 "GRALG-" 1077377 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1073940 1076721 1076899 "GPOLSET" 1077043 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073294 1073351 1073609 "GOSPER" 1073877 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069053 1069732 1070258 "GMODPOL" 1072993 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068058 1068242 1068480 "GHENSEL" 1068865 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062109 1062952 1063979 "GENUPS" 1067142 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061806 1061857 1061946 "GENUFACT" 1062052 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061218 1061295 1061460 "GENPGCD" 1061724 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060692 1060727 1060940 "GENMFACT" 1061177 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059260 1059515 1059822 "GENEEZ" 1060435 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053173 1058871 1059033 "GDMP" 1059183 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042550 1046944 1048050 "GCNAALG" 1052156 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1040977 1041805 1041833 "GCDDOM" 1042088 T GCDDOM (NIL) -9 NIL 1042245 NIL) (-449 1040447 1040574 1040789 "GCDDOM-" 1040794 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039119 1039304 1039608 "GB" 1040226 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027739 1030065 1032457 "GBINTERN" 1036810 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025576 1025868 1026289 "GBF" 1027414 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024357 1024522 1024789 "GBEUCLID" 1025392 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023706 1023831 1023980 "GAUSSFAC" 1024228 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022073 1022375 1022689 "GALUTIL" 1023425 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020381 1020655 1020979 "GALPOLYU" 1021800 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017746 1018036 1018443 "GALFACTU" 1020078 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009552 1011051 1012659 "GALFACT" 1016178 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1006940 1007598 1007626 "FVFUN" 1008782 T FVFUN (NIL) -9 NIL 1009502 NIL) (-438 1006206 1006388 1006416 "FVC" 1006707 T FVC (NIL) -9 NIL 1006890 NIL) (-437 1005848 1006003 1006084 "FUNCTION" 1006158 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003619 1004170 1004636 "FT" 1005402 T FT (NIL) -8 NIL NIL NIL) (-435 1002437 1002920 1003123 "FTEM" 1003436 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000693 1000982 1001386 "FSUPFACT" 1002128 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999090 999379 999711 "FST" 1000381 T FST (NIL) -8 NIL NIL NIL) (-432 998261 998367 998562 "FSRED" 998972 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 996940 997195 997549 "FSPRMELT" 997976 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994025 994463 994962 "FSPECF" 996503 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976085 984528 984568 "FS" 988416 NIL FS (NIL T) -9 NIL 990705 NIL) (-428 964735 967725 971781 "FS-" 972078 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964249 964303 964480 "FSINT" 964676 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962576 963242 963545 "FSERIES" 964028 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961590 961706 961937 "FSCINT" 962456 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957824 960534 960575 "FSAGG" 960945 NIL FSAGG (NIL T) -9 NIL 961204 NIL) (-423 955586 956187 956983 "FSAGG-" 957078 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954628 954771 954998 "FSAGG2" 955439 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952283 952562 953116 "FS2UPS" 954346 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951865 951908 952063 "FS2" 952234 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950722 950893 951202 "FS2EXPXP" 951690 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950148 950263 950415 "FRUTIL" 950602 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941603 945643 947001 "FR" 948822 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936678 939321 939361 "FRNAALG" 940757 NIL FRNAALG (NIL T) -9 NIL 941364 NIL) (-415 932356 933427 934702 "FRNAALG-" 935452 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 931994 932037 932164 "FRNAAF2" 932307 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930401 930848 931143 "FRMOD" 931806 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928180 928784 929101 "FRIDEAL" 930192 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927375 927462 927751 "FRIDEAL2" 928087 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926508 926922 926963 "FRETRCT" 926968 NIL FRETRCT (NIL T) -9 NIL 927144 NIL) (-409 925620 925851 926202 "FRETRCT-" 926207 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922832 924008 924067 "FRAMALG" 924949 NIL FRAMALG (NIL T T) -9 NIL 925241 NIL) (-407 920966 921421 922051 "FRAMALG-" 922274 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 914924 920441 920717 "FRAC" 920722 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914560 914617 914724 "FRAC2" 914861 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914196 914253 914360 "FR2" 914497 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908869 911721 911749 "FPS" 912868 T FPS (NIL) -9 NIL 913425 NIL) (-402 908318 908427 908591 "FPS-" 908737 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905772 907407 907435 "FPC" 907660 T FPC (NIL) -9 NIL 907802 NIL) (-400 905565 905605 905702 "FPC-" 905707 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904443 905053 905094 "FPATMAB" 905099 NIL FPATMAB (NIL T) -9 NIL 905251 NIL) (-398 902143 902619 903045 "FPARFRAC" 904080 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897537 898035 898717 "FORTRAN" 901575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895253 895753 896292 "FORT" 897018 T FORT (NIL) -7 NIL NIL NIL) (-395 892929 893491 893519 "FORTFN" 894579 T FORTFN (NIL) -9 NIL 895203 NIL) (-394 892693 892743 892771 "FORTCAT" 892830 T FORTCAT (NIL) -9 NIL 892892 NIL) (-393 890826 891309 891699 "FORMULA" 892323 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890614 890644 890713 "FORMULA1" 890790 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890137 890189 890362 "FORDER" 890556 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889233 889397 889590 "FOP" 889964 T FOP (NIL) -7 NIL NIL NIL) (-389 887841 888513 888687 "FNLA" 889115 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886596 886985 887013 "FNCAT" 887473 T FNCAT (NIL) -9 NIL 887733 NIL) (-387 886162 886555 886583 "FNAME" 886588 T FNAME (NIL) -8 NIL NIL NIL) (-386 884825 885754 885782 "FMTC" 885787 T FMTC (NIL) -9 NIL 885823 NIL) (-385 881187 882348 882977 "FMONOID" 884229 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880406 880929 881078 "FM" 881083 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877830 878476 878504 "FMFUN" 879648 T FMFUN (NIL) -9 NIL 880356 NIL) (-382 877099 877280 877308 "FMC" 877598 T FMC (NIL) -9 NIL 877780 NIL) (-381 874293 875127 875181 "FMCAT" 876376 NIL FMCAT (NIL T T) -9 NIL 876871 NIL) (-380 873186 874059 874159 "FM1" 874238 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 870960 871376 871870 "FLOATRP" 872737 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864584 868689 869310 "FLOAT" 870359 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862022 862522 863100 "FLOATCP" 864051 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860831 861635 861676 "FLINEXP" 861681 NIL FLINEXP (NIL T) -9 NIL 861774 NIL) (-375 859985 860220 860548 "FLINEXP-" 860553 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859061 859205 859429 "FLASORT" 859837 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856278 857120 857172 "FLALG" 858399 NIL FLALG (NIL T T) -9 NIL 858866 NIL) (-372 850062 853764 853805 "FLAGG" 855067 NIL FLAGG (NIL T) -9 NIL 855719 NIL) (-371 848788 849127 849617 "FLAGG-" 849622 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847830 847973 848200 "FLAGG2" 848641 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844805 845779 845838 "FINRALG" 846966 NIL FINRALG (NIL T T) -9 NIL 847474 NIL) (-368 843965 844194 844533 "FINRALG-" 844538 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843371 843584 843612 "FINITE" 843808 T FINITE (NIL) -9 NIL 843915 NIL) (-366 835829 837990 838030 "FINAALG" 841697 NIL FINAALG (NIL T) -9 NIL 843150 NIL) (-365 831170 832211 833355 "FINAALG-" 834734 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830565 830925 831028 "FILE" 831100 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829249 829561 829615 "FILECAT" 830299 NIL FILECAT (NIL T T) -9 NIL 830515 NIL) (-362 827117 828611 828639 "FIELD" 828679 T FIELD (NIL) -9 NIL 828759 NIL) (-361 825737 826122 826633 "FIELD-" 826638 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823615 824372 824719 "FGROUP" 825423 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822705 822869 823089 "FGLMICPK" 823447 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818572 822630 822687 "FFX" 822692 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818173 818234 818369 "FFSLPE" 818505 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814166 814945 815741 "FFPOLY" 817409 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813670 813706 813915 "FFPOLY2" 814124 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809556 813589 813652 "FFP" 813657 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 804989 809467 809531 "FF" 809536 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800150 804332 804522 "FFNBX" 804843 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795124 799285 799543 "FFNBP" 800004 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789792 794408 794619 "FFNB" 794957 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788624 788822 789137 "FFINTBAS" 789589 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784852 787031 787059 "FFIELDC" 787679 T FFIELDC (NIL) -9 NIL 788055 NIL) (-347 783515 783885 784382 "FFIELDC-" 784387 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783085 783130 783254 "FFHOM" 783457 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780783 781267 781784 "FFF" 782600 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776436 780525 780626 "FFCGX" 780726 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772103 776168 776275 "FFCGP" 776379 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767321 771830 771938 "FFCG" 772039 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749154 758192 758278 "FFCAT" 763443 NIL FFCAT (NIL T T T) -9 NIL 764894 NIL) (-340 744352 745399 746713 "FFCAT-" 747943 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743763 743806 744041 "FFCAT2" 744303 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 732975 736735 737955 "FEXPR" 742615 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 731975 732410 732451 "FEVALAB" 732535 NIL FEVALAB (NIL T) -9 NIL 732796 NIL) (-336 731134 731344 731682 "FEVALAB-" 731687 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729727 730517 730720 "FDIV" 731033 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726793 727508 727623 "FDIVCAT" 729191 NIL FDIVCAT (NIL T T T T) -9 NIL 729628 NIL) (-333 726555 726582 726752 "FDIVCAT-" 726757 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725775 725862 726139 "FDIV2" 726462 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724461 724720 725009 "FCPAK1" 725506 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723589 723961 724102 "FCOMP" 724352 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707326 710739 714277 "FC" 720071 T FC (NIL) -8 NIL NIL NIL) (-328 699905 703890 703930 "FAXF" 705732 NIL FAXF (NIL T) -9 NIL 706424 NIL) (-327 697184 697839 698664 "FAXF-" 699129 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692284 696560 696736 "FARRAY" 697041 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687537 689569 689622 "FAMR" 690645 NIL FAMR (NIL T T) -9 NIL 691105 NIL) (-324 686427 686729 687164 "FAMR-" 687169 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685623 686349 686402 "FAMONOID" 686407 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683435 684119 684172 "FAMONC" 685113 NIL FAMONC (NIL T T) -9 NIL 685499 NIL) (-321 682127 683189 683326 "FAGROUP" 683331 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 679922 680241 680644 "FACUTIL" 681808 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679021 679206 679428 "FACTFUNC" 679732 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671426 678272 678484 "EXPUPXS" 678877 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 668909 669449 670035 "EXPRTUBE" 670860 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665103 665695 666432 "EXPRODE" 668248 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650477 663758 664186 "EXPR" 664707 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 644884 645471 646284 "EXPR2UPS" 649775 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644520 644577 644684 "EXPR2" 644821 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 635925 643652 643949 "EXPEXPAN" 644357 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635752 635882 635911 "EXIT" 635916 T EXIT (NIL) -8 NIL NIL NIL) (-310 635259 635476 635567 "EXITAST" 635681 T EXITAST (NIL) -8 NIL NIL NIL) (-309 634886 634948 635061 "EVALCYC" 635191 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634427 634545 634586 "EVALAB" 634756 NIL EVALAB (NIL T) -9 NIL 634860 NIL) (-307 633908 634030 634251 "EVALAB-" 634256 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631376 632644 632672 "EUCDOM" 633227 T EUCDOM (NIL) -9 NIL 633577 NIL) (-305 629781 630223 630813 "EUCDOM-" 630818 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617321 620079 622829 "ESTOOLS" 627051 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 616953 617010 617119 "ESTOOLS2" 617258 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616704 616746 616826 "ESTOOLS1" 616905 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610609 612337 612365 "ES" 615133 T ES (NIL) -9 NIL 616542 NIL) (-300 605557 606843 608660 "ES-" 608824 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 601932 602692 603472 "ESCONT" 604797 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601677 601709 601791 "ESCONT1" 601894 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601352 601402 601502 "ES2" 601621 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 600982 601040 601149 "ES1" 601288 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600198 600327 600503 "ERROR" 600826 T ERROR (NIL) -7 NIL NIL NIL) (-294 593701 600057 600148 "EQTBL" 600153 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586258 589015 590464 "EQ" 592285 NIL -3320 (NIL T) -8 NIL NIL NIL) (-292 585890 585947 586056 "EQ2" 586195 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581182 582228 583321 "EP" 584829 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579764 580065 580382 "ENV" 580885 T ENV (NIL) -8 NIL NIL NIL) (-289 578943 579463 579491 "ENTIRER" 579496 T ENTIRER (NIL) -9 NIL 579542 NIL) (-288 575445 576898 577268 "EMR" 578742 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574589 574774 574828 "ELTAGG" 575208 NIL ELTAGG (NIL T T) -9 NIL 575419 NIL) (-286 574308 574370 574511 "ELTAGG-" 574516 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574097 574126 574180 "ELTAB" 574264 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573223 573369 573568 "ELFUTS" 573948 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 572965 573021 573049 "ELEMFUN" 573154 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572835 572856 572924 "ELEMFUN-" 572929 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567726 570935 570976 "ELAGG" 571916 NIL ELAGG (NIL T) -9 NIL 572379 NIL) (-280 566011 566445 567108 "ELAGG-" 567113 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564668 564948 565243 "ELABEXPR" 565736 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557534 559335 560162 "EFUPXS" 563944 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 550984 552785 553595 "EFULS" 556810 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548406 548764 549243 "EFSTRUC" 550616 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537478 539043 540603 "EF" 546921 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536579 536963 537112 "EAB" 537349 T EAB (NIL) -8 NIL NIL NIL) (-273 535788 536538 536566 "E04UCFA" 536571 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 534997 535747 535775 "E04NAFA" 535780 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534206 534956 534984 "E04MBFA" 534989 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533415 534165 534193 "E04JAFA" 534198 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532626 533374 533402 "E04GCFA" 533407 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531837 532585 532613 "E04FDFA" 532618 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531046 531796 531824 "E04DGFA" 531829 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525224 526571 527935 "E04AGNT" 529702 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 523930 524410 524450 "DVARCAT" 524925 NIL DVARCAT (NIL T) -9 NIL 525124 NIL) (-264 523134 523346 523660 "DVARCAT-" 523665 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516034 522933 523062 "DSMP" 523067 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510844 511979 513047 "DROPT" 514986 T DROPT (NIL) -8 NIL NIL NIL) (-261 510509 510568 510666 "DROPT1" 510779 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505624 506750 507887 "DROPT0" 509392 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 503969 504294 504680 "DRAWPT" 505258 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498556 499479 500558 "DRAW" 502943 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498189 498242 498360 "DRAWHACK" 498497 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 496920 497189 497480 "DRAWCX" 497918 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496436 496504 496655 "DRAWCURV" 496846 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 486907 488866 490981 "DRAWCFUN" 494341 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483720 485602 485643 "DQAGG" 486272 NIL DQAGG (NIL T) -9 NIL 486545 NIL) (-252 471999 478698 478781 "DPOLCAT" 480633 NIL DPOLCAT (NIL T T T T) -9 NIL 481178 NIL) (-251 466838 468184 470142 "DPOLCAT-" 470147 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 459993 466699 466797 "DPMO" 466802 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453051 459773 459940 "DPMM" 459945 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452715 452970 453018 "DOMCTOR" 453023 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452010 452237 452374 "DOMAIN" 452598 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445761 451645 451797 "DMP" 451911 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445361 445417 445561 "DLP" 445699 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439231 444688 444878 "DLIST" 445203 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436075 438084 438125 "DLAGG" 438675 NIL DLAGG (NIL T) -9 NIL 438905 NIL) (-242 434888 435518 435546 "DIVRING" 435638 T DIVRING (NIL) -9 NIL 435721 NIL) (-241 434125 434315 434615 "DIVRING-" 434620 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432227 432584 432990 "DISPLAY" 433739 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426169 432141 432204 "DIRPROD" 432209 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425017 425220 425485 "DIRPROD2" 425962 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414280 420232 420285 "DIRPCAT" 420695 NIL DIRPCAT (NIL NIL T) -9 NIL 421535 NIL) (-236 411606 412248 413129 "DIRPCAT-" 413466 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 410893 411053 411239 "DIOSP" 411440 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407595 409805 409846 "DIOPS" 410280 NIL DIOPS (NIL T) -9 NIL 410509 NIL) (-233 407144 407258 407449 "DIOPS-" 407454 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406036 406630 406658 "DIFRING" 406845 T DIFRING (NIL) -9 NIL 406955 NIL) (-231 405682 405759 405911 "DIFRING-" 405916 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403487 404725 404766 "DIFEXT" 405129 NIL DIFEXT (NIL T) -9 NIL 405423 NIL) (-229 401772 402200 402866 "DIFEXT-" 402871 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399094 401304 401345 "DIAGG" 401350 NIL DIAGG (NIL T) -9 NIL 401370 NIL) (-227 398478 398635 398887 "DIAGG-" 398892 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 393943 397437 397714 "DHMATRIX" 398247 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389555 390464 391474 "DFSFUN" 392953 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384671 388486 388798 "DFLOAT" 389263 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 382899 383180 383576 "DFINTTLS" 384379 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 379964 380920 381320 "DERHAM" 382565 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377813 379739 379828 "DEQUEUE" 379908 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377028 377161 377357 "DEGRED" 377675 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373423 374168 375021 "DEFINTRF" 376256 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 370950 371419 372018 "DEFINTEF" 372942 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370327 370570 370685 "DEFAST" 370855 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364369 369924 370072 "DECIMAL" 370199 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 361881 362339 362845 "DDFACT" 363913 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361477 361520 361671 "DBLRESP" 361832 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359376 359710 360070 "DBASE" 361244 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358645 358856 359002 "DATAARY" 359275 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357778 358604 358632 "D03FAFA" 358637 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 356912 357737 357765 "D03EEFA" 357770 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354862 355328 355817 "D03AGNT" 356443 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354178 354821 354849 "D02EJFA" 354854 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353494 354137 354165 "D02CJFA" 354170 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352810 353453 353481 "D02BHFA" 353486 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352126 352769 352797 "D02BBFA" 352802 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345324 346912 348518 "D02AGNT" 350540 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343093 343615 344161 "D01WGTS" 344798 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342188 343052 343080 "D01TRNS" 343085 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341283 342147 342175 "D01GBFA" 342180 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340378 341242 341270 "D01FCFA" 341275 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339473 340337 340365 "D01ASFA" 340370 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338568 339432 339460 "D01AQFA" 339465 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337663 338527 338555 "D01APFA" 338560 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336758 337622 337650 "D01ANFA" 337655 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335853 336717 336745 "D01AMFA" 336750 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 334948 335812 335840 "D01ALFA" 335845 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334043 334907 334935 "D01AKFA" 334940 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333138 334002 334030 "D01AJFA" 334035 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326435 327986 329547 "D01AGNT" 331597 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 325772 325900 326052 "CYCLOTOM" 326303 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322507 323220 323947 "CYCLES" 325065 T CYCLES (NIL) -7 NIL NIL NIL) (-188 321819 321953 322124 "CVMP" 322368 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319590 319848 320224 "CTRIGMNP" 321547 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319313 319549 319577 "CTOR" 319582 T CTOR (NIL) -8 NIL NIL NIL) (-185 318849 319044 319145 "CTORKIND" 319232 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318320 318548 318576 "CTORCAT" 318696 T CTORCAT (NIL) -9 NIL 318779 NIL) (-183 318015 318095 318221 "CTORCAT-" 318226 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317531 317718 317816 "CTORCALL" 317937 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 316905 317004 317157 "CSTTOOLS" 317428 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312704 313361 314119 "CRFP" 316217 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312206 312425 312517 "CRCEAST" 312632 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311253 311438 311666 "CRAPACK" 312010 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310637 310738 310942 "CPMATCH" 311129 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310362 310390 310496 "CPIMA" 310603 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306726 307398 308116 "COORDSYS" 309697 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306110 306239 306389 "CONTOUR" 306596 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302036 304113 304605 "CONTFRAC" 305650 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 301916 301937 301965 "CONDUIT" 302002 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301089 301609 301637 "COMRING" 301642 T COMRING (NIL) -9 NIL 301694 NIL) (-170 300170 300447 300631 "COMPPROP" 300925 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299831 299866 299994 "COMPLPAT" 300129 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 289888 299640 299749 "COMPLEX" 299754 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289524 289581 289688 "COMPLEX2" 289825 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289242 289277 289375 "COMPFACT" 289483 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273415 283635 283675 "COMPCAT" 284679 NIL COMPCAT (NIL T) -9 NIL 286064 NIL) (-164 262931 265854 269481 "COMPCAT-" 269837 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262660 262688 262791 "COMMUPC" 262897 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262455 262488 262547 "COMMONOP" 262621 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262038 262206 262293 "COMM" 262388 T COMM (NIL) -8 NIL NIL NIL) (-160 261642 261842 261917 "COMMAAST" 261983 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 260891 261085 261113 "COMBOPC" 261451 T COMBOPC (NIL) -9 NIL 261626 NIL) (-158 259787 259997 260239 "COMBINAT" 260681 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 255985 256558 257198 "COMBF" 259209 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254771 255101 255336 "COLOR" 255770 T COLOR (NIL) -8 NIL NIL NIL) (-155 254274 254492 254584 "COLONAST" 254699 T COLONAST (NIL) -8 NIL NIL NIL) (-154 253914 253961 254086 "CMPLXRT" 254221 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253389 253614 253713 "CLLCTAST" 253835 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 248891 249919 250999 "CLIP" 252329 T CLIP (NIL) -7 NIL NIL NIL) (-151 247273 247997 248236 "CLIF" 248718 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243495 245419 245460 "CLAGG" 246389 NIL CLAGG (NIL T) -9 NIL 246925 NIL) (-149 241917 242374 242957 "CLAGG-" 242962 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241461 241546 241686 "CINTSLPE" 241826 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 238962 239433 239981 "CHVAR" 240989 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238205 238725 238753 "CHARZ" 238758 T CHARZ (NIL) -9 NIL 238773 NIL) (-145 237959 237999 238077 "CHARPOL" 238159 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237086 237639 237667 "CHARNZ" 237714 T CHARNZ (NIL) -9 NIL 237770 NIL) (-143 235075 235776 236111 "CHAR" 236771 T CHAR (NIL) -8 NIL NIL NIL) (-142 234801 234862 234890 "CFCAT" 235001 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234046 234157 234339 "CDEN" 234685 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230038 233199 233479 "CCLASS" 233786 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229345 229488 229651 "CATEGORY" 229895 T -10 (NIL) -8 NIL NIL NIL) (-138 229009 229264 229312 "CATCTOR" 229317 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228483 228709 228808 "CATAST" 228930 T CATAST (NIL) -8 NIL NIL NIL) (-136 227986 228204 228296 "CASEAST" 228411 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223038 224015 224768 "CARTEN" 227289 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222146 222294 222515 "CARTEN2" 222885 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220488 221296 221553 "CARD" 221909 T CARD (NIL) -8 NIL NIL NIL) (-132 220091 220292 220367 "CAPSLAST" 220433 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219463 219791 219819 "CACHSET" 219951 T CACHSET (NIL) -9 NIL 220028 NIL) (-130 218959 219255 219283 "CABMON" 219333 T CABMON (NIL) -9 NIL 219389 NIL) (-129 218107 218505 218641 "BYTE" 218804 T BYTE (NIL) -8 NIL NIL 218920) (-128 213516 217575 217738 "BYTEBUF" 217964 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211073 213208 213315 "BTREE" 213442 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208571 210721 210843 "BTOURN" 210983 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205988 208041 208082 "BTCAT" 208150 NIL BTCAT (NIL T) -9 NIL 208227 NIL) (-124 205655 205735 205884 "BTCAT-" 205889 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200947 204798 204826 "BTAGG" 205048 T BTAGG (NIL) -9 NIL 205209 NIL) (-122 200437 200562 200768 "BTAGG-" 200773 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197481 199715 199930 "BSTREE" 200254 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196619 196745 196929 "BRILL" 197337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193318 195345 195386 "BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293 NIL) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861 NIL) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127098 127712 127823 "ASP24" 127934 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126175 126900 127012 "ASP20" 127017 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125263 125876 125986 "ASP1" 126096 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124207 124937 125056 "ASP19" 125175 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 123944 124011 124087 "ASP12" 124162 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122796 123543 123687 "ASP10" 123831 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120695 122640 122731 "ARRAY2" 122736 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116511 120343 120457 "ARRAY1" 120612 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115543 115716 115937 "ARRAY12" 116334 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109902 111773 111848 "ARR2CAT" 114478 NIL ARR2CAT (NIL T T T) -9 NIL 115236 NIL) (-56 107336 108080 109034 "ARR2CAT-" 109039 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106930 107163 107242 "ARITY" 107275 T ARITY (NIL) -8 NIL NIL NIL) (-54 105678 105830 106136 "APPRULE" 106766 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105329 105377 105496 "APPLYORE" 105624 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104303 104594 104789 "ANY" 105152 T ANY (NIL) -8 NIL NIL NIL) (-51 103581 103704 103861 "ANY1" 104177 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101146 102018 102345 "ANTISYM" 103305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100661 100850 100947 "ANON" 101067 T ANON (NIL) -8 NIL NIL NIL) (-48 94793 99200 99654 "AN" 100225 T AN (NIL) -8 NIL NIL NIL) (-47 91049 92403 92454 "AMR" 93202 NIL AMR (NIL T T) -9 NIL 93802 NIL) (-46 90161 90382 90745 "AMR-" 90750 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74711 90078 90139 "ALIST" 90144 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71548 74305 74474 "ALGSC" 74629 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68104 68658 69265 "ALGPKG" 70988 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67381 67482 67666 "ALGMFACT" 67990 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63120 63805 64460 "ALGMANIP" 66904 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437 NIL) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856 NIL) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283 NIL) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332 NIL) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
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continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1143 (-224))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1540 + (-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 (-553))))) +(((*1 *2 *2) + (-12 (-5 *2 (-635 *6)) (-4 *6 (-939 *3 *4 *5)) (-4 *3 (-306)) + (-4 *4 (-784)) (-4 *5 (-841)) (-5 *1 (-445 *3 *4 *5 *6)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-635 *7)) (-5 *3 (-1145)) (-4 *7 (-939 *4 *5 *6)) + (-4 *4 (-306)) (-4 *5 (-784)) (-4 *6 (-841)) + (-5 *1 (-445 *4 *5 *6 *7)))) + ((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-635 *7)) (-5 *3 (-1145)) (-4 *7 (-939 *4 *5 *6)) + (-4 *4 (-306)) (-4 *5 (-784)) (-4 *6 (-841)) + (-5 *1 (-445 *4 *5 *6 *7))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-841) (-550))) (-5 *1 (-275 *3 *2)) + (-4 *2 (-13 (-429 *3) (-992)))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-1165 (-406 (-558)))) (-5 *2 (-406 (-558))) + (-5 *1 (-189))))) (((*1 *2 *2) (|partial| -12 (-4 *3 (-362)) (-4 *4 (-372 *3)) (-4 *5 (-372 *3)) (-5 *1 (-519 *3 *4 *5 *2)) (-4 *2 (-677 *3 *4 *5)))) @@ -3970,10 +4735,44 @@ (|partial| -12 (-4 *1 (-1110 *2 *3 *4 *5)) (-4 *3 (-1039)) (-4 *4 (-237 *2 *3)) (-4 *5 (-237 *2 *3)) (-4 *3 (-362)))) ((*1 *2 *2) (-12 (-5 *2 (-635 *3)) (-4 *3 (-841)) (-5 *1 (-1171 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-558)) (-5 *1 (-310)))) - ((*1 *2 *1) - (-12 (-5 *2 (-762)) (-5 *1 (-1151 *3 *4)) (-14 *3 (-911)) - (-4 *4 (-1039))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-1143 *3)) (-4 *3 (-362)) (-4 *3 (-1039)) + (-5 *1 (-1147 *3))))) +(((*1 *1 *1) (-5 *1 (-224))) ((*1 *1 *1) (-5 *1 (-378))) + ((*1 *1) (-5 *1 (-378)))) +(((*1 *1 *2 *2 *3) + (-12 (-5 *3 (-635 (-1163))) (-4 *4 (-1087)) + (-4 *5 (-13 (-1039) (-876 *4) (-841) (-606 (-882 *4)))) + (-5 *1 (-1063 *4 *5 *2)) + (-4 *2 (-13 (-429 *5) (-876 *4) (-606 (-882 *4)))))) + ((*1 *1 *2 *2) + (-12 (-4 *3 (-1087)) + (-4 *4 (-13 (-1039) (-876 *3) (-841) (-606 (-882 *3)))) + (-5 *1 (-1063 *3 *4 *2)) + (-4 *2 (-13 (-429 *4) (-876 *3) (-606 (-882 *3))))))) +(((*1 *1 *2) + (-12 (-5 *2 (-635 *3)) (-4 *3 (-1200)) (-5 *1 (-1143 *3))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-13 (-839) (-362))) (-5 *2 (-112)) (-5 *1 (-1049 *4 *3)) + (-4 *3 (-1222 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-387)) (-5 *2 (-1251)) (-5 *1 (-390)))) + ((*1 *2 *3) (-12 (-5 *3 (-1145)) (-5 *2 (-1251)) (-5 *1 (-390))))) +(((*1 *2 *3) (-12 (-5 *3 (-1145)) (-5 *2 (-1251)) (-5 *1 (-240)))) + ((*1 *2 *3) + (-12 (-5 *3 (-635 (-1145))) (-5 *2 (-1251)) (-5 *1 (-240))))) +(((*1 *1 *2) (-12 (-5 *2 (-406 (-558))) (-5 *1 (-216))))) +(((*1 *2) + (-12 (-4 *3 (-550)) (-5 *2 (-635 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-416 *3))))) +(((*1 *1 *2 *3 *3 *4 *4) + (-12 (-5 *2 (-942 (-558))) (-5 *3 (-1163)) + (-5 *4 (-1081 (-406 (-558)))) (-5 *1 (-30))))) +(((*1 *1 *2 *1) + (-12 (-5 *1 (-639 *2 *3 *4)) (-4 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"void"))) (-14 *5 (-635 (-1163))) (-14 *6 (-1167)))) ((*1 *1 *2) (-12 (-5 *2 (-329)) (-5 *1 (-397 *3 *4 *5 *6)) (-14 *3 (-1163)) - (-14 *4 (-3 (|:| |fst| (-433)) (|:| -1647 "void"))) + (-14 *4 (-3 (|:| |fst| (-433)) (|:| -3587 "void"))) (-14 *5 (-635 (-1163))) (-14 *6 (-1167)))) ((*1 *1 *2) (-12 (-5 *2 (-330 *4)) (-4 *4 (-13 (-841) (-21))) @@ -10985,14 +9590,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-433)) (-5 *1 (-436)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1167)) (|:| -3268 (-635 (-329))))) + (-5 *2 (-2 (|:| |localSymbols| (-1167)) (|:| -3331 (-635 (-329))))) (-4 *1 (-438)))) ((*1 *1 *2) (-12 (-5 *2 (-329)) (-4 *1 (-438)))) ((*1 *1 *2) (-12 (-5 *2 (-635 (-329))) (-4 *1 (-438)))) ((*1 *1 *2) (-12 (-5 *2 (-1246 (-689))) (-4 *1 (-438)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1167)) (|:| -3268 (-635 (-329))))) + (-5 *2 (-2 (|:| |localSymbols| (-1167)) (|:| -3331 (-635 (-329))))) (-4 *1 (-439)))) ((*1 *1 *2) (-12 (-5 *2 (-329)) (-4 *1 (-439)))) ((*1 *1 *2) (-12 (-5 *2 (-635 (-329))) (-4 *1 (-439)))) @@ -11042,8 +9647,6 @@ ((*1 *1 *2) (-12 (-4 *3 (-1039)) (-4 *1 (-677 *3 *4 *2)) (-4 *4 (-372 *3)) (-4 *2 (-372 *3)))) - ((*1 *2 *1) (-12 (-5 *1 (-681 *2)) (-4 *2 (-605 (-853))))) - ((*1 *1 *2) (-12 (-5 *1 (-681 *2)) (-4 *2 (-605 (-853))))) ((*1 *2 *1) (-12 (-5 *2 (-168 (-378))) (-5 *1 (-684)))) ((*1 *1 *2) (-12 (-5 *2 (-168 (-691))) (-5 *1 (-684)))) ((*1 *1 *2) (-12 (-5 *2 (-168 (-689))) (-5 *1 (-684)))) @@ -11063,7 +9666,7 @@ (-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 (-635 (-2 (|:| -3201 *3) (|:| -2074 *4)))) + (-12 (-5 *2 (-635 (-2 (|:| -2313 *3) (|:| -4017 *4)))) (-4 *3 (-1039)) (-4 *4 (-717)) (-5 *1 (-726 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-754)))) ((*1 *1 *2) @@ -11072,25 +9675,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1163)) (|:| |fn| (-315 (-224))) - (|:| -3951 (-1081 (-834 (-224)))) (|:| |abserr| (-224)) + (|:| -1540 (-1081 (-834 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (|:| |mdnia| (-2 (|:| |fn| (-315 (-224))) - (|:| -3951 (-635 (-1081 (-834 (-224))))) + (|:| -1540 (-635 (-1081 (-834 (-224))))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))))) (-5 *1 (-760)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-315 (-224))) - (|:| -3951 (-635 (-1081 (-834 (-224))))) (|:| |abserr| (-224)) + (|:| -1540 (-635 (-1081 (-834 (-224))))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *1 (-760)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1163)) (|:| |fn| (-315 (-224))) - (|:| -3951 (-1081 (-834 (-224)))) (|:| |abserr| (-224)) + (|:| -1540 (-1081 (-834 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *1 (-760)))) ((*1 *2 *3) (-12 (-5 *2 (-765)) (-5 *1 (-764 *3)) (-4 *3 (-1200)))) @@ -11108,23 +9711,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-315 (-224))) (|:| -2320 (-635 (-224))) + (-2 (|:| |fn| (-315 (-224))) (|:| -3636 (-635 (-224))) (|:| |lb| (-635 (-834 (-224)))) (|:| |cf| (-635 (-315 (-224)))) (|:| |ub| (-635 (-834 (-224)))))) (|:| |lsa| (-2 (|:| |lfn| (-635 (-315 (-224)))) - (|:| -2320 (-635 (-224))))))) + (|:| -3636 (-635 (-224))))))) (-5 *1 (-832)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-635 (-315 (-224)))) (|:| -2320 (-635 (-224))))) + (-2 (|:| |lfn| (-635 (-315 (-224)))) (|:| -3636 (-635 (-224))))) (-5 *1 (-832)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-315 (-224))) (|:| -2320 (-635 (-224))) + (-2 (|:| |fn| (-315 (-224))) (|:| -3636 (-635 (-224))) (|:| |lb| (-635 (-834 (-224)))) (|:| |cf| (-635 (-315 (-224)))) (|:| |ub| (-635 (-834 (-224)))))) (-5 *1 (-832)))) @@ -11227,469 +9830,358 @@ ((*1 *1 *2) (-12 (-5 *2 (-654 *3 *4)) (-4 *3 (-841)) (-4 *4 (-171)) (-5 *1 (-1266 *3 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-832)) (-5 *2 (-1025)) (-5 *1 (-831)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-635 (-315 (-378)))) (-5 *4 (-635 (-378))) + (-5 *2 (-1025)) (-5 *1 (-831))))) (((*1 *2 *3) - (-12 (-5 *3 (-679 (-315 (-224)))) (-5 *2 (-378)) (-5 *1 (-204))))) -(((*1 *2 *3) - (-12 (-5 *3 (-911)) (-5 *2 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76748) + (-4047 . 76094) (-4048 . 75838) (-4049 . 75647) (-4050 . 75581) + (-4051 . 75500) (-4052 . 74926) (-4053 . 74723) (-4054 . 74664) + (-4055 . 72401) (-4056 . 72257) (-4057 . 71875) (-4058 . 70017) + (-4059 . 69919) (-4060 . 69853) (-4061 . 69780) (-4062 . 69562) + (-4063 . 69496) (-4064 . 69408) (-4065 . 68721) (-4066 . 68618) + (-4067 . 68186) (-4068 . 67811) (-4069 . 67756) (-4070 . 67682) + (-4071 . 67614) (-4072 . 67512) (-4073 . 67375) (-4074 . 67274) + (-4075 . 67172) (-4076 . 67098) (-4077 . 66411) (-4078 . 65890) + (-4079 . 65768) (-4080 . 65670) (-4081 . 65599) (-4082 . 64841) + (-4083 . 64786) (-4084 . 64689) (-4085 . 64480) (-4086 . 64342) + (-4087 . 64132) (-4088 . 64001) (-4089 . 63314) (-4090 . 63243) + (-4091 . 63063) (-4092 . 63012) (-4093 . 62894) (-4094 . 62151) + (-4095 . 61991) (-4096 . 61875) (-4097 . 61745) (-4098 . 61648) + (-4099 . 61580) (-4100 . 61444) (-4101 . 61237) (-4102 . 61030) + (-4103 . 60750) (-4104 . 60175) (-4105 . 59953) (-4106 . 59835) + (-4107 . 59723) (-4108 . 59658) (-4109 . 59455) (-4110 . 59346) + (-4111 . 59153) (-4112 . 59084) (-4113 . 58830) (-4114 . 58627) + (-4115 . 58052) (-4116 . 58020) (-4117 . 57960) (-4118 . 57777) + (* . 53231) (-4120 . 53113) (-4121 . 53058) (-4122 . 52988) + (-4123 . 52904) (-4124 . 52696) (-4125 . 52622) (-4126 . 52503) + (-4127 . 52433) (-4128 . 52206) (-4129 . 51631) (-4130 . 51503) + (-4131 . 51405) (-4132 . 50901) (-4133 . 50729) (-4134 . 50569) + (-4135 . 50426) (-4136 . 50356) (-4137 . 50286) (-4138 . 50212) + (-4139 . 49723) (-4140 . 49112) (-4141 . 49055) (-4142 . 48823) + (-4143 . 48249) (-4144 . 48197) (-4145 . 47005) (-4146 . 46774) + (-4147 . 46606) (-4148 . 46434) (-4149 . 46281) (-4150 . 46048) + (-4151 . 45939) (-4152 . 45811) (-4153 . 45692) (-4154 . 45579) + (-4155 . 45547) (-4156 . 45389) (-4157 . 44815) (-4158 . 44708) + (-4159 . 44069) (-4160 . 43779) (-4161 . 43607) (-4162 . 43163) + (-4163 . 42846) (-4164 . 42775) (-4165 . 42719) (-4166 . 42467) + (-4167 . 42373) (-4168 . 41799) (-4169 . 41432) (-4170 . 41274) + (-4171 . 40923) (-4172 . 40849) (-4173 . 40677) (-4174 . 40538) + (-4175 . 40410) (-4176 . 39957) (-4177 . 39781) (-4178 . 39695) + (-4179 . 39591) (-4180 . 39017) (-4181 . 38961) (-4182 . 38767) + (-4183 . 38672) (-4184 . 38577) (-4185 . 38246) (-4186 . 38149) + (-4187 . 38093) (-4188 . 37867) (-4189 . 37795) (-4190 . 37697) + (-4191 . 37541) (-4192 . 37401) (-4193 . 37193) (-4194 . 36323) + (-4195 . 36188) (-4196 . 35959) (-4197 . 35880) (-4198 . 35752) + (-4199 . 35682) (-4200 . 35581) (-4201 . 35159) (-4202 . 34585) + (-4203 . 34470) (-4204 . 34389) (-4205 . 34334) (-4206 . 34205) + (-4207 . 34047) (-4208 . 33856) (-4209 . 33803) (-4210 . 33662) + (-4211 . 33558) (-4212 . 33286) (-4213 . 33230) (-4214 . 33111) + (-4215 . 33004) (-4216 . 32918) (-4217 . 32700) (-4218 . 32671) + (-4219 . 30703) (-4220 . 30206) (-4221 . 29342) (-4222 . 29253) + (-4223 . 28917) (-4224 . 28759) (-4225 . 28696) (-4226 . 28089) + (-4227 . 27816) (-4228 . 27757) (-4229 . 27533) (-4230 . 27311) + (-4231 . 27136) (-4232 . 26968) (-4233 . 26781) (-4234 . 25964) + (-4235 . 25877) (-4236 . 25453) (-4237 . 25298) (-4238 . 25153) + (-4239 . 25124) (-4240 . 25045) (-4241 . 24889) (-4242 . 24643) + (-4243 . 24528) (-4244 . 24426) (-4245 . 24261) (-4246 . 24179) + (-4247 . 24033) (-4248 . 23929) (-4249 . 23863) (-4250 . 23807) + (-4251 . 23680) (-4252 . 23600) (-4253 . 23416) (-4254 . 23310) + (-4255 . 23200) (-4256 . 23091) (-4257 . 22996) (-4258 . 22912) + (-4259 . 22813) (-4260 . 22689) (-4261 . 22630) (-4262 . 22574) + (-4263 . 22547) (-4264 . 22440) (-4265 . 22221) (-4266 . 22023) + (-4267 . 21910) (-4268 . 21472) (-4269 . 21420) (-4270 . 21275) + (-4271 . 21065) (-4272 . 20855) (-4273 . 20632) (-4274 . 20544) + (-4275 . 20438) (-4276 . 20301) (-4277 . 20189) (-4278 . 19703) + (-4279 . 19573) (-4280 . 19301) (-4281 . 19143) (-4282 . 18998) + (-4283 . 18886) (-4284 . 18290) (-4285 . 18112) (-4286 . 18024) + (-4287 . 17971) (-4288 . 17655) (-4289 . 17329) (-4290 . 17171) + (-4291 . 16956) (-4292 . 16904) (-4293 . 16608) (-4294 . 16538) + (-4295 . 14123) (-4296 . 13864) (-4297 . 13583) (-4298 . 13502) + (-4299 . 13329) (-4300 . 13185) (-4301 . 12933) (-4302 . 12880) + (-4303 . 12679) (-4304 . 12554) (-4305 . 12481) (-4306 . 12276) + (-4307 . 12245) (-4308 . 12167) (-4309 . 11857) (-4310 . 11758) + (-4311 . 11708) (-4312 . 11636) (-4313 . 11532) (-4314 . 11443) + (-4315 . 11183) (-4316 . 11130) (-4317 . 11014) (-4318 . 10945) + (-4319 . 10764) (-4320 . 10569) (-4321 . 10496) (-4322 . 10050) + (-4323 . 9873) (-4324 . 9783) (-4325 . 9566) (-4326 . 9447) + (-4327 . 9364) (-4328 . 9173) (-4329 . 9021) (-4330 . 8884) + (-4331 . 8817) (-4332 . 8740) (-4333 . 8683) (-4334 . 8507) + (-4335 . 8445) (-4336 . 8246) (-4337 . 8189) (-4338 . 8161) + (-4339 . 8034) (-4340 . 7978) (-4341 . 7882) (-4342 . 7529) + (-4343 . 7429) (-4344 . 6191) (-4345 . 6097) (-4346 . 2099) + (-4347 . 1777) (-4348 . 1703) (-4349 . 1605) (-4350 . 1438) + (-4351 . 1272) (-4352 . 1220) (-4353 . 1164) (-4354 . 1008) + (-4355 . 925) (-4356 . 851) (-4357 . 638) (-4358 . 586) (-4359 . 490) + (-4360 . 353) (-4361 . 321) (-4362 . 118) (-4363 . 30))
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