diff options
| author | dos-reis <gdr@axiomatics.org> | 2008-01-17 14:27:29 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2008-01-17 14:27:29 +0000 |
| commit | 15dcc4936996a27019112ff58e9202a81d792047 (patch) | |
| tree | 1e49da404b12b46c30989feac07e26f87f4810ba /src | |
| parent | f5ba07e55ec584939b62a3887c2ff7ebf8083759 (diff) | |
| download | open-axiom-15dcc4936996a27019112ff58e9202a81d792047.tar.gz | |
Fix SF/1849734
* interp/i-spec1.boot (upand): Don't insist on having operands of
type Boolean.
(upor): Likewise.
* algebra/mkrecord.spad.pamphlet (Pair): New domain constructor.
* algebra/exposed.lsp.pamphlet: Expose Pair, PropositionalLogic,
PropositionalFormula.
* algebra/boolean.spad.pamphlet (PropositionalFormula): New domain
constructor.
* algebra/Makefile.pamphlet (axiom_algebra_layer_4): Include
PAIR.o.
(axiom_algebra_layer_19): Include PROPFRML.o
* share/algebra: Update databases.
* testsuite/interpreter/1849734.input: New.
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 17 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 8 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/boolean.spad.pamphlet | 230 | ||||
| -rw-r--r-- | src/algebra/exposed.lsp.pamphlet | 3 | ||||
| -rw-r--r-- | src/algebra/mkrecord.spad.pamphlet | 57 | ||||
| -rw-r--r-- | src/interp/i-spec1.boot | 12 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2126 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 2225 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1277 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9310 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 29804 | ||||
| -rw-r--r-- | src/testsuite/interpreter/1849734.input | 6 |
13 files changed, 22706 insertions, 22377 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 1d9d9d9a..bd454cb0 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,20 @@ +2008-01-17 Gabriel Dos Reis <gdr@cs.tamu.edu> + + Fix SF/1849734 + * interp/i-spec1.boot (upand): Don't insist on having operands of + type Boolean. + (upor): Likewise. + * algebra/mkrecord.spad.pamphlet (Pair): New domain constructor. + * algebra/exposed.lsp.pamphlet: Expose Pair, PropositionalLogic, + PropositionalFormula. + * algebra/boolean.spad.pamphlet (PropositionalFormula): New domain + constructor. + * algebra/Makefile.pamphlet (axiom_algebra_layer_4): Include + PAIR.o. + (axiom_algebra_layer_19): Include PROPFRML.o + * share/algebra: Update databases. + * testsuite/interpreter/1849734.input: New. + 2008-01-16 Gabriel Dos Reis <gdr@cs.tamu.edu> Fix SF/1848975 diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 7fe8dd8f..4a806873 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -391,7 +391,7 @@ axiom_algebra_layer_1 = \ PATAB.o PLOT1.o PPCURVE.o PSCURVE.o \ REAL.o RESLATC.o RETRACT.o RETRACT-.o \ SEGBIND2.o SEGCAT.o STREAM1.o STREAM2.o \ - STREAM3.o + STREAM3.o axiom_algebra_layer_1_nrlibs = \ $(axiom_algebra_layer_1:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) @@ -433,7 +433,7 @@ axiom_algebra_layer_4 = \ REPDB.o RFDIST.o RIDIST.o RMODULE.o \ SEXCAT.o SGROUP.o SGROUP-.o SPACEC.o \ SPLNODE.o STEP.o SUCH.o TEX1.o \ - UDVO.o YSTREAM.o + UDVO.o YSTREAM.o PAIR.o axiom_algebra_layer_4_nrlibs = \ $(axiom_algebra_layer_4:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) @@ -453,7 +453,7 @@ axiom_algebra_layer_5 = \ ODVAR.o OPQUERY.o ORDFIN.o ORDMON.o \ PATMATCH.o PERMCAT.o PDRING.o PDRING-.o \ SDVAR.o SUP2.o TRIGCAT.o TRIGCAT-.o \ - ULS2.o UP2.o + ULS2.o UP2.o axiom_algebra_layer_5_nrlibs = \ $(axiom_algebra_layer_5:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) @@ -732,7 +732,7 @@ axiom_algebra_layer_19 = \ SET.o SPECOUT.o SQMATRIX.o SWITCH.o \ SYMS.o SYMTAB.o SYSSOLP.o UTSCAT.o \ UTSCAT-.o VARIABLE.o WFFINTBS.o SPADPRSR.o \ - PARSER.o + PARSER.o PROPFRML.o axiom_algebra_layer_19_nrlibs = \ $(axiom_algebra_layer_19:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 70a3f05c..2e8dc2be 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -233,7 +233,7 @@ axiom_algebra_layer_1 = \ PATAB.o PLOT1.o PPCURVE.o PSCURVE.o \ REAL.o RESLATC.o RETRACT.o RETRACT-.o \ SEGBIND2.o SEGCAT.o STREAM1.o STREAM2.o \ - STREAM3.o + STREAM3.o axiom_algebra_layer_1_nrlibs = \ $(axiom_algebra_layer_1:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) @@ -308,7 +308,7 @@ axiom_algebra_layer_4 = \ REPDB.o RFDIST.o RIDIST.o RMODULE.o \ SEXCAT.o SGROUP.o SGROUP-.o SPACEC.o \ SPLNODE.o STEP.o SUCH.o TEX1.o \ - UDVO.o YSTREAM.o + UDVO.o YSTREAM.o PAIR.o axiom_algebra_layer_4_nrlibs = \ $(axiom_algebra_layer_4:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) @@ -339,7 +339,7 @@ axiom_algebra_layer_5 = \ ODVAR.o OPQUERY.o ORDFIN.o ORDMON.o \ PATMATCH.o PERMCAT.o PDRING.o PDRING-.o \ SDVAR.o SUP2.o TRIGCAT.o TRIGCAT-.o \ - ULS2.o UP2.o + ULS2.o UP2.o axiom_algebra_layer_5_nrlibs = \ $(axiom_algebra_layer_5:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) @@ -997,7 +997,7 @@ axiom_algebra_layer_19 = \ SET.o SPECOUT.o SQMATRIX.o SWITCH.o \ SYMS.o SYMTAB.o SYSSOLP.o UTSCAT.o \ UTSCAT-.o VARIABLE.o WFFINTBS.o SPADPRSR.o \ - PARSER.o + PARSER.o PROPFRML.o axiom_algebra_layer_19_nrlibs = \ $(axiom_algebra_layer_19:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet index 85b2c056..4fe76ef3 100644 --- a/src/algebra/boolean.spad.pamphlet +++ b/src/algebra/boolean.spad.pamphlet @@ -1,4 +1,4 @@ -\documentclass{article} +documentclass{article} \usepackage{axiom} \title{src/algebra boolean.spad} @@ -33,6 +33,233 @@ PropositionalLogic(): Category == with ++ equiv(p,q) returns the logical equivalence of `p', `q'. @ +\section{domain PROPFRML PropositionalFormula} +<<domain PROPFRML PropositionalFormula>>= +)set mess autoload on +)abbrev domain PROPFRML PropositionalFormula +++ Author: Gabriel Dos Reis +++ Date Created: Januray 14, 2008 +++ Date Last Modified: January 16, 2008 +++ Description: This domain implements propositional formula build +++ over a term domain, that itself belongs to PropositionalLogic +PropositionalFormula(T: PropositionalLogic): PropositionalLogic with + if T has CoercibleTo OutputForm then CoercibleTo OutputForm + coerce: T -> % + ++ coerce(t) turns the term `t' into a propositional formula + coerce: Symbol -> % + ++ coerce(t) turns the term `t' into a propositional variable. +-- variables: % -> Set Symbol + ++ variables(p) returns the set of propositional variables + ++ appearing in the proposition `p'. + + term?: % -> Boolean + term: % -> T + + variable?: % -> Boolean + variable: % -> Symbol + + not?: % -> Boolean + notOperand: % -> % + + and?: % -> Boolean + andOperands: % -> Pair(%, %) + + or?: % -> Boolean + orOperands: % -> Pair(%,%) + + implies?: % -> Boolean + impliesOperands: % -> Pair(%,%) + + equiv?: % -> Boolean + equivOperands: % -> Pair(%,%) + + == add + FORMULA ==> Union(base: T, var: Symbol, unForm: %, + binForm: Record(op: Symbol, lhs: %, rhs: %)) + + per(f: FORMULA): % == + f pretend % + + rep(p: %): FORMULA == + p pretend FORMULA + + coerce(t: T): % == + per [t]$FORMULA + + coerce(s: Symbol): % == + per [s]$FORMULA + + not p == + per [p]$FORMULA + + binaryForm(o: Symbol, l: %, r: %): % == + per [[o, l, r]$Record(op: Symbol, lhs: %, rhs: %)]$FORMULA + + p and q == + binaryForm('_and, p, q) + + p or q == + binaryForm('_or, p, q) + + implies(p,q) == + binaryForm('implies, p, q) + + equiv(p,q) == + binaryForm('equiv, p, q) + +-- variables p == +-- p' := rep p +-- p' case base => empty()$Set(Symbol) +-- p' case var => { p'.var } +-- p' case unForm => variables(p'.unForm) +-- p'' := p'.binForm +-- union(variables(p''.lhs), variables(p''.rhs))$Set(Symbol) + + -- returns true if the proposition `p' is a formula of kind + -- indicated by `o'. + isBinaryNode?(p: %, o: Symbol): Boolean == + p' := rep p + p' case binForm and p'.binForm.op = o + + -- returns the operands of a binary formula node + binaryOperands(p: %): Pair(%,%) == + p' := (rep p).binForm + pair(p'.lhs,p'.rhs)$Pair(%,%) + + term? p == + rep p case base + + term p == + term? p => (rep p).base + userError "formula is not a term" + + variable? p == + rep p case var + + variable p == + variable? p => (rep p).var + userError "formula is not a variable" + + not? p == + rep p case unForm + + notOperand p == + not? p => (rep p).unForm + userError "formula is not a logical negation" + + and? p == + isBinaryNode?(p,'_and) + + andOperands p == + and? p => binaryOperands p + userError "formula is not a conjunction formula" + + or? p == + isBinaryNode?(p,'_or) + + orOperands p == + or? p => binaryOperands p + userError "formula is not a disjunction formula" + + implies? p == + isBinaryNode?(p, 'implies) + + impliesOperands p == + implies? p => binaryOperands p + userError "formula is not an implication formula" + + equiv? p == + isBinaryNode?(p,'equiv) + + equivOperands p == + equiv? p => binaryOperands p + userError "formula is not an equivalence equivalence" + + -- Unparsing grammar. + -- + -- Ideally, the following syntax would the external form + -- Formula: + -- EquivFormula + -- + -- EquivFormula: + -- ImpliesFormula + -- ImpliesFormula <=> EquivFormula + -- + -- ImpliesFormula: + -- OrFormula + -- OrFormula => ImpliesFormula + -- + -- OrFormula: + -- AndFormula + -- AndFormula or OrFormula + -- + -- AndFormula + -- NotFormula + -- NotFormula and AndFormula + -- + -- NotFormula: + -- PrimaryFormula + -- not NotFormula + -- + -- PrimaryFormula: + -- Term + -- ( Formula ) + -- + -- Note: Since the token '=>' already means a construct different + -- from what we would like to have as a notation for + -- propositional logic, we will output the formula `p => q' + -- as implies(p,q), which looks like a function call. + -- Similarly, we do not have the token `<=>' for logical + -- equivalence; so we unparser `p <=> q' as equiv(p,q). + -- + -- So, we modify the nonterminal PrimaryFormula to read + -- PrimaryFormula: + -- Term + -- implies(Formula, Formula) + -- equiv(Formula, Formula) + if T has CoercibleTo OutputForm then + formula: % -> OutputForm + coerce(p: %): OutputForm == + formula p + + primaryFormula(p: %): OutputForm == + term? p => term(p)::OutputForm + variable? p => variable(p)::OutputForm + if rep p case binForm then + p' := (rep p).binForm + p'.op = 'implies or p'.op = 'equiv => + return elt(outputForm p'.op, + [formula p'.lhs, formula p'.rhs])$OutputForm + paren(formula p)$OutputForm + + notFormula(p: %): OutputForm == + not? p => + elt(outputForm '_not, [notFormula((rep p).'unForm)])$OutputForm + primaryFormula p + + andFormula(p: %): OutputForm == + and? p => + p' := (rep p).binForm + -- ??? idealy, we should be using `and$OutputForm' but + -- ??? a bug in the compiler currently prevents that. + infix(outputForm '_and, notFormula p'.lhs, + andFormula p'.rhs)$OutputForm + notFormula p + + orFormula(p: %): OutputForm == + or? p => + p' := (rep p).binForm + -- ??? idealy, we should be using `or$OutputForm' but + -- ??? a bug in the compiler currently prevents that. + infix(outputForm '_or, andFormula p'.lhs, + orFormula p'.rhs)$OutputForm + andFormula p + + formula p == + -- Note: this should be equivFormula, but see the explanation above. + orFormula p + +@ \section{domain REF Reference} <<domain REF Reference>>= @@ -503,6 +730,7 @@ Bits(): Exports == Implementation where <<domain IBITS IndexedBits>> <<domain BITS Bits>> <<category PROPLOG PropositionalLogic>> +<<domain PROPFRML PropositionalFormula>> @ \eject \begin{thebibliography}{99} diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index 94b05ddb..be4f8464 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -254,6 +254,7 @@ (|OrthogonalPolynomialFunctions| . ORTHPOL) (|OutputPackage| . OUT) (|PadeApproximantPackage| . PADEPAC) + (|Pair| . PAIR) (|Palette| . PALETTE) (|PartialFraction| . PFR) (|PatternFunctions2| . PATTERN2) @@ -289,6 +290,7 @@ (|PrimeField| . PF) (|PrimitiveArrayFunctions2| . PRIMARR2) (|PrintPackage| . PRINT) + (|PropositionalFormula| . PROPFRML) (|QuadraticForm| . QFORM) (|QuasiComponentPackage| . QCMPACK) (|Quaternion| . QUAT) @@ -663,6 +665,7 @@ (|PrimitiveFunctionCategory| . PRIMCAT) (|PrincipalIdealDomain| . PID) (|PriorityQueueAggregate| . PRQAGG) + (|PropositionalLogic| . PROPLOG) (|QuaternionCategory| . QUATCAT) (|QueueAggregate| . QUAGG) (|QuotientFieldCategory| . QFCAT) diff --git a/src/algebra/mkrecord.spad.pamphlet b/src/algebra/mkrecord.spad.pamphlet index 2fe15855..0087800c 100644 --- a/src/algebra/mkrecord.spad.pamphlet +++ b/src/algebra/mkrecord.spad.pamphlet @@ -25,10 +25,64 @@ MakeRecord(S: Type, T: Type): public == private where [s,t]$Record(part1: S, part2: T) @ + +\section{domain PAIR Pair} +<<domain PAIR Pair>>= +)abbrev domain PAIR Pair +++ Author: Gabriel Dos Reis +++ Date Created: January 16, 2008 +++ Date Last Modified: January 16, 2008 +++ Description: This domain provides a very simple representation +++ of the notion of `pair of objects'. It does not try to achieve +++ all possible imaginable things. +Pair(S: Type, T: Type): Public == Private where + Public ==> Type with + + if S has CoercibleTo OutputForm and T has CoercibleTo OutputForm then + CoercibleTo OutputForm + + if S has SetCategory and T has SetCategory then SetCategory + + pair: (S,T) -> % + ++ pair(s,t) returns a pair object composed of `s' and `t'. + construct: (S,T) -> % + ++ construct(s,t) is same as pair(s,t), with syntactic sugar. + first: % -> S + ++ first(p) extracts the first component of `p'. + second: % -> T + ++ second(p) extracts the second components of `p'. + + Private ==> add + Rep := Record(fst: S, snd: T) + + pair(s,t) == + [s,t]$Rep + + construct(s,t) == + pair(s,t) + + first x == + x.fst + + second x == + x.snd + + if S has CoercibleTo OutputForm and T has CoercibleTo OutputForm then + coerce x == + paren([first(x)::OutputForm, second(x)::OutputForm])$OutputForm + + if S has SetCategory and T has SetCategory then + x = y == + first(x) = first(y) and second(x) = second(y) +@ + + \section{License} <<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. +--Copyright (c) 1991-2002, The Numerical Algorithms Group Ltd. --All rights reserved. +-- Copyright (C) 2007-2008, Gabriel Dos Reis. +-- All rights reserved. -- --Redistribution and use in source and binary forms, with or without --modification, are permitted provided that the following conditions are @@ -62,6 +116,7 @@ MakeRecord(S: Type, T: Type): public == private where <<license>> <<package MKRECORD MakeRecord>> +<<domain PAIR Pair>> @ \eject \begin{thebibliography}{99} diff --git a/src/interp/i-spec1.boot b/src/interp/i-spec1.boot index 574d5b75..064c7e58 100644 --- a/src/interp/i-spec1.boot +++ b/src/interp/i-spec1.boot @@ -246,7 +246,7 @@ upand x == putTarget(term1,$Boolean) putTarget(term2,$Boolean) ms := bottomUp term1 - ms isnt [=$Boolean] => throwKeyedMsgSP("S2IS0054",[1,'"_"and_""],term1) + ms isnt [=$Boolean] => nil $genValue => BooleanEquality(objValUnwrap(getValue term1), getConstantFromDomain('(false),$Boolean)) => @@ -254,12 +254,12 @@ upand x == putModeSet(x,ms) -- first term is true, so look at the second one ms := bottomUp term2 - ms isnt [=$Boolean] => throwKeyedMsgSP("S2IS0054",[2,'"_"and_""],term2) + ms isnt [=$Boolean] => nil putValue(x,getValue term2) putModeSet(x,ms) ms := bottomUp term2 - ms isnt [=$Boolean] => throwKeyedMsgSP("S2IS0054",[2,'"_"and_""],term2) + ms isnt [=$Boolean] => nil -- generate an IF expression and let the rest of the code handle it cond := [mkAtreeNode "=",mkAtree "false",term1] putTarget(cond,$Boolean) @@ -276,7 +276,7 @@ upor x == putTarget(term1,$Boolean) putTarget(term2,$Boolean) ms := bottomUp term1 - ms isnt [=$Boolean] => throwKeyedMsgSP("S2IS0054",[1,'"_"or_""],term1) + ms isnt [=$Boolean] => nil $genValue => BooleanEquality(objValUnwrap(getValue term1), getConstantFromDomain('(true),$Boolean)) => @@ -284,12 +284,12 @@ upor x == putModeSet(x,ms) -- first term is false, so look at the second one ms := bottomUp term2 - ms isnt [=$Boolean] => throwKeyedMsgSP("S2IS0054",[2,'"_"or_""],term2) + ms isnt [=$Boolean] => nil putValue(x,getValue term2) putModeSet(x,ms) ms := bottomUp term2 - ms isnt [=$Boolean] => throwKeyedMsgSP("S2IS0054",[2,'"_"or_""],term2) + ms isnt [=$Boolean] => nil -- generate an IF expression and let the rest of the code handle it cond := [mkAtreeNode "=",mkAtree "true",term1] putTarget(cond,$Boolean) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index d64b8402..cab36da4 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2225717 . 3409435990) +(2226437 . 3409486832) (-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."))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . 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}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . 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}."))) @@ -46,23 +46,23 @@ 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4189 . T) (-4187 . T) (-4186 . T) ((-4194 "*") . T) (-4185 . T) (-4190 . T) (-4184 . T) (-2181 . T)) +((-4192 . T) (-4190 . T) (-4189 . T) ((-4197 "*") . T) (-4188 . T) (-4193 . T) (-4187 . T) (-2169 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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."))) NIL NIL -(-31 R -1725) +(-31 R -4057) ((|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 -954) (QUOTE (-517))))) +((|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517))))) (-32 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 -4192))) +((|HasAttribute| |#1| (QUOTE -4195))) (-33) ((|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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2181 . T)) +((-2169 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -70,7 +70,7 @@ NIL NIL (-35 |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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4192 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4196 . T) (-2169 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -78,20 +78,20 @@ NIL NIL (-37 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) NIL (-38 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 -(-39 -1725 UP UPUP -1673) +(-39 -4057 UP UPUP -2263) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4185 |has| (-377 |#2|) (-333)) (-4190 |has| (-377 |#2|) (-333)) (-4184 |has| (-377 |#2|) (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3747 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3747 (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) -(-40 R -1725) +((-4188 |has| (-377 |#2|) (-333)) (-4193 |has| (-377 |#2|) (-333)) (-4187 |has| (-377 |#2|) (-333)) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3786 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3786 (|HasCategory| (-377 |#2|) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3786 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3786 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) +(-40 R -4057) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -400) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -400) (|devaluate| |#1|))))) (-41 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -102,31 +102,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-278)))) (-43 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4189 |has| |#1| (-509)) (-4187 . T) (-4186 . T)) +((-4192 |has| |#1| (-509)) (-4190 . T) (-4189 . T)) ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-44 |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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (-3747 (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|))))))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1006))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|)))))) (-3786 (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|))))))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) (-45 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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333)))) (-46 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-47) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (LIST (QUOTE -954) (QUOTE (-517))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| $ (QUOTE (-964))) (|HasCategory| $ (LIST (QUOTE -955) (QUOTE (-517))))) (-48) ((|constructor| (NIL "This domain implements anonymous functions"))) NIL NIL (-49 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}."))) -((-4189 . T)) +((-4192 . T)) NIL (-50 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}."))) @@ -140,7 +140,7 @@ 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 -(-53 |Base| R -1725) +(-53 |Base| R -4057) ((|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 @@ -150,7 +150,7 @@ NIL NIL (-55 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"))) -((-4192 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4196 . T) (-2169 . T)) NIL (-56 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),{}...]}."))) @@ -158,65 +158,65 @@ NIL NIL (-57 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-58 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}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-59 -2989) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-59 -2981) ((|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 -(-60 -2989) +(-60 -2981) ((|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 -(-61 -2989) +(-61 -2981) ((|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 -(-62 -2989) +(-62 -2981) ((|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 -(-63 -2989) +(-63 -2981) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2989) +(-64 -2981) ((|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 -(-65 -2989) +(-65 -2981) ((|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 -(-66 -2989) +(-66 -2981) ((|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 -(-67 -2989) +(-67 -2981) ((|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 -(-68 -2989) +(-68 -2981) ((|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 -(-69 -2989) +(-69 -2981) ((|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 -(-70 -2989) +(-70 -2981) ((|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 -(-71 -2989) +(-71 -2981) ((|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 -(-72 -2989) +(-72 -2981) ((|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 @@ -228,55 +228,55 @@ 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 -(-75 -2989) +(-75 -2981) ((|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 -(-76 -2989) +(-76 -2981) ((|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 -(-77 -2989) +(-77 -2981) ((|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 -(-78 -2989) +(-78 -2981) ((|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 -(-79 -2989) +(-79 -2981) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2989) +(-80 -2981) ((|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 -(-81 -2989) +(-81 -2981) ((|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 -(-82 -2989) +(-82 -2981) ((|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 -(-83 -2989) +(-83 -2981) ((|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 -(-84 -2989) +(-84 -2981) ((|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 -(-85 -2989) +(-85 -2981) ((|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 -(-86 -2989) +(-86 -2981) ((|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 -(-87 -2989) +(-87 -2981) ((|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 @@ -286,8 +286,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-333)))) (-89 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}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-90 S) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) NIL @@ -298,15 +298,15 @@ NIL NIL (-92) ((|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\"."))) -((-4192 . T)) +((-4195 . T)) NIL (-93) ((|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."))) -((-4192 . T) ((-4194 "*") . T) (-4193 . T) (-4189 . T) (-4187 . T) (-4186 . T) (-4185 . T) (-4190 . T) (-4184 . T) (-4183 . T) (-4182 . T) (-4181 . T) (-4180 . T) (-4188 . T) (-4191 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4179 . T)) +((-4195 . T) ((-4197 "*") . T) (-4196 . T) (-4192 . T) (-4190 . T) (-4189 . T) (-4188 . T) (-4193 . T) (-4187 . T) (-4186 . T) (-4185 . T) (-4184 . T) (-4183 . T) (-4191 . T) (-4194 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4182 . T)) NIL (-94 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}."))) -((-4189 . T)) +((-4192 . T)) NIL (-95 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}."))) @@ -322,15 +322,15 @@ NIL NIL (-98 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}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-99 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 (-4194 "*")))) +((|HasAttribute| |#1| (QUOTE (-4197 "*")))) (-100) ((|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"))) -((-4192 . T)) +((-4195 . T)) NIL (-101 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."))) @@ -338,26 +338,26 @@ NIL NIL (-102 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."))) -((-4193 . T) (-2181 . T)) +((-4196 . T) (-2169 . T)) NIL (-103) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-939))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1052))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3747 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-517) (QUOTE (-833))) (|HasCategory| (-517) (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-940))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1053))) (|HasCategory| (-517) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1077)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3786 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-833)))) (|HasCategory| (-517) (QUOTE (-132))))) (-104) ((|constructor| (NIL "This domain provides an implementation of binary files. Data is accessed one byte at a time as a small integer.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "\\spad{position!(f,{} i)} sets the current byte-position to \\spad{i}.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{f}.")) (|readIfCan!| (((|Union| (|SingleInteger|) "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL (-105) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4193 . T) (-4192 . T)) -((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1005))) (-12 (|HasCategory| (-107) (QUOTE (-1005))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107))))) (|HasCategory| (-107) (LIST (QUOTE -557) (QUOTE (-787))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1006))) (-12 (|HasCategory| (-107) (QUOTE (-1006))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107))))) (|HasCategory| (-107) (LIST (QUOTE -557) (QUOTE (-787))))) (-106 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}"))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) NIL (-107) -((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|implies| (($ $ $) "\\spad{implies(a,{}b)} returns the logical implication of Boolean \\spad{a} and \\spad{b}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical inclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of Boolean \\spad{a} and \\spad{b}.")) (|not| (($ $) "\\spad{not n} returns the negation of \\spad{n}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) +((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL (-108 A) @@ -368,25 +368,25 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-110 -1725 UP) +(-110 -4057 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 (-111 |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}."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-112 |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}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-111 |#1|) (QUOTE (-832))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-111 |#1|) (QUOTE (-939))) (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-1052))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-207))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -478) (QUOTE (-1076)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-278))) (|HasCategory| (-111 |#1|) (QUOTE (-502))) (|HasCategory| (-111 |#1|) (QUOTE (-779))) (-3747 (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-832)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-111 |#1|) (QUOTE (-833))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-111 |#1|) (QUOTE (-940))) (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-1053))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-207))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -478) (QUOTE (-1077)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-278))) (|HasCategory| (-111 |#1|) (QUOTE (-502))) (|HasCategory| (-111 |#1|) (QUOTE (-779))) (-3786 (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-833)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) (-113 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4193))) +((|HasAttribute| |#1| (QUOTE -4196))) (-114 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-2181 . T)) +((-2169 . T)) NIL (-115 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) @@ -394,15 +394,15 @@ NIL NIL (-116 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"))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-117 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-118) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL (-119 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -410,16 +410,16 @@ NIL NIL (-120 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4192 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4196 . T) (-2169 . T)) NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-122 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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-123) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL @@ -430,20 +430,20 @@ NIL NIL (-125) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4194 "*") . T)) +(((-4197 "*") . T)) NIL -(-126 |minix| -3136 S T$) +(-126 |minix| -3124 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-127 |minix| -3136 R) +(-127 |minix| -3124 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 (-128) ((|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}."))) -((-4192 . T) (-4182 . T) (-4193 . T)) -((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1005))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3747 (-12 (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787))))) +((-4195 . T) (-4185 . T) (-4196 . T)) +((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1006))) (-12 (|HasCategory| (-131) (QUOTE (-1006))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3786 (-12 (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1006))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787))))) (-129 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 @@ -458,7 +458,7 @@ NIL NIL (-132) ((|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."))) -((-4189 . T)) +((-4192 . T)) NIL (-133 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}."))) @@ -466,9 +466,9 @@ NIL NIL (-134) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4189 . T)) +((-4192 . T)) NIL -(-135 -1725 UP UPUP) +(-135 -4057 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 @@ -479,14 +479,14 @@ NIL (-137 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 -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasAttribute| |#1| (QUOTE -4192))) +((|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasAttribute| |#1| (QUOTE -4195))) (-138 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."))) -((-2181 . T)) +((-2169 . T)) NIL (-139 |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."))) -((-4187 . T) (-4186 . T) (-4189 . T)) +((-4190 . T) (-4189 . T) (-4192 . T)) NIL (-140) ((|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."))) @@ -500,7 +500,7 @@ 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 -(-143 R -1725) +(-143 R -4057) ((|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 @@ -527,10 +527,10 @@ NIL (-149 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-920))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasAttribute| |#2| (QUOTE -4188)) (|HasAttribute| |#2| (QUOTE -4191)) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-779)))) +((|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-921))) (|HasCategory| |#2| (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasAttribute| |#2| (QUOTE -4191)) (|HasAttribute| |#2| (QUOTE -4194)) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-779)))) (-150 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4185 -3747 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-832)))) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4188 |has| |#1| (-6 -4188)) (-4191 |has| |#1| (-6 -4191)) (-3883 . T) (-2181 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 -3786 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-833)))) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-4191 |has| |#1| (-6 -4191)) (-4194 |has| |#1| (-6 -4194)) (-3913 . T) (-2169 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-151 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."))) @@ -542,8 +542,8 @@ NIL NIL (-153 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}."))) -((-4185 -3747 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-832)))) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4188 |has| |#1| (-6 -4188)) (-4191 |has| |#1| (-6 -4191)) (-3883 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . 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T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (QUOTE (-921))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1077)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-502))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-278))) (-3786 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-3786 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-833))) 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(|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-779)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-1098)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-833))))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-833))))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-333)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasAttribute| |#1| (QUOTE -4191)) (|HasAttribute| |#1| (QUOTE -4194)) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077))))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-132)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-319))))) (-154 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 @@ -554,11 +554,11 @@ NIL NIL (-156) ((|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."))) -(((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-157 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}."))) -(((-4194 "*") . T) (-4185 . T) (-4190 . T) (-4184 . T) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") . T) (-4188 . T) (-4193 . T) (-4187 . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-158 R) ((|constructor| (NIL "CoordinateSystems provides coordinate transformation functions for plotting. Functions in this package return conversion functions which take points expressed in other coordinate systems and return points with the corresponding Cartesian coordinates.")) (|conical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|) "\\spad{conical(a,{}b)} transforms from conical coordinates to Cartesian coordinates: \\spad{conical(a,{}b)} is a function which will map the point \\spad{(lambda,{}mu,{}nu)} to \\spad{x = lambda*mu*nu/(a*b)},{} \\spad{y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2))},{} \\spad{z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2))}.")) (|toroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{toroidal(a)} transforms from toroidal coordinates to Cartesian coordinates: \\spad{toroidal(a)} is a function which will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = a*sinh(v)*cos(phi)/(cosh(v)-cos(u))},{} \\spad{y = a*sinh(v)*sin(phi)/(cosh(v)-cos(u))},{} \\spad{z = a*sin(u)/(cosh(v)-cos(u))}.")) (|bipolarCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolarCylindrical(a)} transforms from bipolar cylindrical coordinates to Cartesian coordinates: \\spad{bipolarCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))},{} \\spad{z}.")) (|bipolar| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolar(a)} transforms from bipolar coordinates to Cartesian coordinates: \\spad{bipolar(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))}.")) (|oblateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{oblateSpheroidal(a)} transforms from oblate spheroidal coordinates to Cartesian coordinates: \\spad{oblateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|prolateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{prolateSpheroidal(a)} transforms from prolate spheroidal coordinates to Cartesian coordinates: \\spad{prolateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|ellipticCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{ellipticCylindrical(a)} transforms from elliptic cylindrical coordinates to Cartesian coordinates: \\spad{ellipticCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)},{} \\spad{z}.")) (|elliptic| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{elliptic(a)} transforms from elliptic coordinates to Cartesian coordinates: \\spad{elliptic(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)}.")) (|paraboloidal| (((|Point| |#1|) (|Point| |#1|)) "\\spad{paraboloidal(pt)} transforms \\spad{pt} from paraboloidal coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = u*v*cos(phi)},{} \\spad{y = u*v*sin(phi)},{} \\spad{z = 1/2 * (u**2 - v**2)}.")) (|parabolicCylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolicCylindrical(pt)} transforms \\spad{pt} from parabolic cylindrical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}z)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v},{} \\spad{z}.")) (|parabolic| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolic(pt)} transforms \\spad{pt} from parabolic coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v}.")) (|spherical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{spherical(pt)} transforms \\spad{pt} from spherical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}phi)} to \\spad{x = r*sin(phi)*cos(theta)},{} \\spad{y = r*sin(phi)*sin(theta)},{} \\spad{z = r*cos(phi)}.")) (|cylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cylindrical(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}z)} to \\spad{x = r * cos(theta)},{} \\spad{y = r * sin(theta)},{} \\spad{z}.")) (|polar| (((|Point| |#1|) (|Point| |#1|)) "\\spad{polar(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta)} to \\spad{x = r * cos(theta)} ,{} \\spad{y = r * sin(theta)}.")) (|cartesian| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cartesian(pt)} returns the Cartesian coordinates of point \\spad{pt}."))) @@ -571,7 +571,7 @@ NIL (-160 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-875 |#2|) (LIST (QUOTE -809) (|devaluate| |#1|)))) +((|HasCategory| (-876 |#2|) (LIST (QUOTE -810) (|devaluate| |#1|)))) (-161 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) NIL @@ -584,7 +584,7 @@ NIL ((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,{}cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic"))) NIL NIL -(-164 R -1725) +(-164 R -4057) ((|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 @@ -688,19 +688,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-190 -1725 UP UPUP R) +(-190 -4057 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 -(-191 -1725 FP) +(-191 -4057 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 (-192) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-939))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1052))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3747 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) -(-193 R -1725) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-517) (QUOTE (-833))) (|HasCategory| (-517) (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-940))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1053))) (|HasCategory| (-517) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1077)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3786 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-833)))) (|HasCategory| (-517) (QUOTE (-132))))) +(-193 R -4057) ((|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 @@ -714,19 +714,19 @@ NIL NIL (-196 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}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-197 |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}."))) -((-4189 . T)) +((-4192 . T)) NIL -(-198 R -1725) +(-198 R -4057) ((|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 (-199) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\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}."))) -((-2204 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-2194 . T) (-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-200) ((|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)}.}"))) @@ -734,23 +734,23 @@ NIL NIL (-201 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}"))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4194 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4197 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-202 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 (-203 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."))) -((-4193 . T) (-2181 . T)) +((-4196 . T) (-2169 . T)) NIL (-204 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}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207)))) +((|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#2| (QUOTE (-207)))) (-205 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}."))) -((-4189 . T)) +((-4192 . T)) NIL (-206 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -758,36 +758,36 @@ NIL NIL (-207) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4189 . T)) +((-4192 . T)) NIL (-208 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4192))) +((|HasAttribute| |#1| (QUOTE -4195))) (-209 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}."))) -((-4193 . T) (-2181 . T)) +((-4196 . T) (-2169 . T)) NIL (-210) ((|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 -(-211 S -3136 R) +(-211 S -3124 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 (-333))) (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777))) (|HasAttribute| |#3| (QUOTE -4189)) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-659))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-963))) (|HasCategory| |#3| (QUOTE (-1005)))) -(-212 -3136 R) +((|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777))) (|HasAttribute| |#3| (QUOTE -4192)) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-659))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-964))) (|HasCategory| |#3| (QUOTE (-1006)))) +(-212 -3124 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"))) -((-4186 |has| |#2| (-963)) (-4187 |has| |#2| (-963)) (-4189 |has| |#2| (-6 -4189)) ((-4194 "*") |has| |#2| (-156)) (-4192 . T) (-2181 . T)) +((-4189 |has| |#2| (-964)) (-4190 |has| |#2| (-964)) (-4192 |has| |#2| (-6 -4192)) ((-4197 "*") |has| |#2| (-156)) (-4195 . T) (-2169 . T)) NIL -(-213 -3136 A B) +(-213 -3124 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 -(-214 -3136 R) +(-214 -3124 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."))) -((-4186 |has| |#2| (-963)) (-4187 |has| |#2| (-963)) (-4189 |has| |#2| (-6 -4189)) ((-4194 "*") |has| |#2| (-156)) (-4192 . 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((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -798,47 +798,47 @@ NIL NIL (-217) ((|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}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4185 . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-218 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."))) -((-2181 . T)) +((-2169 . T)) NIL (-219 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})}.")) 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(|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-221 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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|#3| (QUOTE -4192)) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (QUOTE (-964)))) (-12 (|HasCategory| |#3| (QUOTE (-964))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-964))) (|HasCategory| |#3| (LIST (QUOTE -824) (QUOTE (-1077)))))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1006))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3786 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-964))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1006))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -824) (QUOTE (-1077)))))) (|HasCategory| |#3| (LIST (QUOTE -557) (QUOTE (-787))))) (-225 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 (-207)))) (-226 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."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) NIL (-227 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}."))) -((-4192 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4196 . T) (-2169 . T)) NIL (-228) ((|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."))) @@ -878,8 +878,8 @@ NIL NIL (-237 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"))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#3| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#3| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#1| (QUOTE (-421))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-132))))) (-238 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 @@ -924,11 +924,11 @@ 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 -(-249 R -1725) +(-249 R -4057) ((|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 -(-250 R -1725) +(-250 R -4057) ((|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 @@ -943,10 +943,10 @@ NIL (-253 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005)))) +((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1006)))) (-254 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}."))) -((-4193 . T) (-2181 . T)) +((-4196 . T) (-2169 . T)) NIL (-255 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}."))) @@ -967,18 +967,18 @@ NIL (-259 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 -4193))) +((|HasAttribute| |#1| (QUOTE -4196))) (-260 |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 -(-261 S R |Mod| -1769 -2662 |exactQuo|) +(-261 S R |Mod| -2563 -3824 |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"))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-262) ((|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."))) -((-4185 . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-263 R) ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,{}m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,{}m,{}k,{}g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,{}m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) @@ -990,21 +990,21 @@ NIL NIL (-265 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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1006))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) (-267) ((|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 -(-268 -1725 S) +(-268 -4057 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 -(-269 E -1725) +(-269 E -4057) ((|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 @@ -1019,7 +1019,7 @@ NIL (-272 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-963)))) +((|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-964)))) (-273) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL @@ -1042,7 +1042,7 @@ NIL NIL (-278) ((|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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-279 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1052,7 +1052,7 @@ 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 -(-281 -1725) +(-281 -4057) ((|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 @@ -1062,8 +1062,8 @@ NIL NIL (-283 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-207))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -478) (QUOTE (-1076)) (LIST (QUOTE -1143) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1143) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (LIST (QUOTE -258) (LIST (QUOTE -1143) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1143) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-278))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-502))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-779))) (-3747 (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-779)))) (-12 (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| $ (QUOTE (-132)))) (-3747 (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (-12 (|HasCategory| (-1143 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| $ (QUOTE (-132)))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . 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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 @@ -1074,9 +1074,9 @@ NIL NIL (-286 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) 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(|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 @@ -1086,8 +1086,8 @@ NIL NIL (-289 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."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2262) (LIST (|devaluate| |#1|) (QUOTE (-1077)))))) (-3786 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-882))) (|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1077))))) (|HasSignature| |#1| (LIST (QUOTE -2080) (LIST (LIST (QUOTE -583) (QUOTE (-1077))) (|devaluate| |#1|))))))) (-290 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 @@ -1098,7 +1098,7 @@ NIL NIL (-292 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."))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) ((|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-724)))) (-293 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1114,19 +1114,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156)))) (-296 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-297 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."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-298 S -1725) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-298 S -4057) ((|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 (-338)))) -(-299 -1725) +(-299 -4057) ((|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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-300) ((|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.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) @@ -1144,54 +1144,54 @@ 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 -(-304 S -1725 UP UPUP R) +(-304 S -4057 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 -(-305 -1725 UP UPUP R) +(-305 -4057 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 -(-306 -1725 UP UPUP R) +(-306 -4057 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-307 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1077)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|)))) (-308 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-309 |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.}"))) -((-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -954) (QUOTE (-349)))) (|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (LIST (QUOTE -954) (QUOTE (-517))))) +((-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#3| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -955) (QUOTE (-349)))) (|HasCategory| $ (QUOTE (-964))) (|HasCategory| $ (LIST (QUOTE -955) (QUOTE (-517))))) (-310 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 -(-311 S -1725 UP UPUP) +(-311 S -4057 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}.") (($ (|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 (-338))) (|HasCategory| |#2| (QUOTE (-333)))) -(-312 -1725 UP UPUP) +(-312 -4057 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}.") (($ (|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."))) -((-4185 |has| (-377 |#2|) (-333)) (-4190 |has| (-377 |#2|) (-333)) (-4184 |has| (-377 |#2|) (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 |has| (-377 |#2|) (-333)) (-4193 |has| (-377 |#2|) (-333)) (-4187 |has| (-377 |#2|) (-333)) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-313 |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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3747 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-834 |#1|) (QUOTE (-134))) (|HasCategory| (-834 |#1|) (QUOTE (-338))) (|HasCategory| (-834 |#1|) (QUOTE (-132))) (-3786 (|HasCategory| (-834 |#1|) (QUOTE (-132))) (|HasCategory| (-834 |#1|) (QUOTE (-338))))) (-314 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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3786 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-315 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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3786 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-316 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 @@ -1206,33 +1206,33 @@ NIL NIL (-319) ((|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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-320 R UP -1725) +(-320 R UP -4057) ((|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 (-321 |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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3747 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-834 |#1|) (QUOTE (-134))) (|HasCategory| (-834 |#1|) (QUOTE (-338))) (|HasCategory| (-834 |#1|) (QUOTE (-132))) (-3786 (|HasCategory| (-834 |#1|) (QUOTE (-132))) (|HasCategory| (-834 |#1|) (QUOTE (-338))))) (-322 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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3786 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-323 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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3786 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-324 |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}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-833 |#1|) (QUOTE (-134))) (|HasCategory| (-833 |#1|) (QUOTE (-338))) (|HasCategory| (-833 |#1|) (QUOTE (-132))) (-3747 (|HasCategory| (-833 |#1|) (QUOTE (-132))) (|HasCategory| (-833 |#1|) (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-834 |#1|) (QUOTE (-134))) (|HasCategory| (-834 |#1|) (QUOTE (-338))) (|HasCategory| (-834 |#1|) (QUOTE (-132))) (-3786 (|HasCategory| (-834 |#1|) (QUOTE (-132))) (|HasCategory| (-834 |#1|) (QUOTE (-338))))) (-325 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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) -(-326 -1725 GF) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3786 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +(-326 -4057 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 @@ -1240,21 +1240,21 @@ 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 -(-328 -1725 FP FPP) +(-328 -4057 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 (-329 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}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3747 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3786 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-330 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 (-331 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4189 . T)) +((-4192 . T)) NIL (-332 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1262,7 +1262,7 @@ NIL NIL (-333) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-334 |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."))) @@ -1278,7 +1278,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-509)))) (-337 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4189 |has| |#1| (-509)) (-4187 . T) (-4186 . T)) +((-4192 |has| |#1| (-509)) (-4190 . T) (-4189 . T)) NIL (-338) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1290,7 +1290,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-333)))) (-340 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) NIL (-341 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1299,14 +1299,14 @@ NIL (-342 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005)))) +((|HasAttribute| |#1| (QUOTE -4196)) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1006)))) (-343 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4192 . T) (-2181 . T)) +((-4195 . T) (-2169 . T)) NIL (-344 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4187 . T) (-4186 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4190 . T) (-4189 . T)) NIL (-345 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."))) @@ -1318,7 +1318,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-347 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}"))) -((-4189 . T)) +((-4192 . T)) NIL (-348 |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}."))) @@ -1326,7 +1326,7 @@ NIL NIL (-349) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\^= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4175 . T) (-4183 . T) (-2204 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4178 . T) (-4186 . T) (-2194 . T) (-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-350 |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}."))) @@ -1334,23 +1334,23 @@ NIL NIL (-351 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}"))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) ((|HasCategory| |#1| (QUOTE (-156)))) (-352 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}."))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) NIL (-353) ((|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}."))) -((-2181 . T)) +((-2169 . T)) NIL (-354) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2181 . T)) +((-2169 . T)) NIL (-355 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."))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) ((|HasCategory| |#1| (QUOTE (-156)))) (-356 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1358,7 +1358,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-779)))) (-357) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-358) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1370,13 +1370,13 @@ NIL NIL (-360 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) NIL (-361) ((|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 -(-362 -1725 UP UPUP R) +(-362 -4057 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 @@ -1390,27 +1390,27 @@ NIL NIL (-365) ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-2181 . T)) +((-2169 . T)) NIL (-366) ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2181 . T)) +((-2169 . T)) NIL (-367) ((|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 -(-368 -2989 |returnType| |arguments| |symbols|) +(-368 -2981 |returnType| |arguments| |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 -(-369 -1725 UP) +(-369 -4057 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-370 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2181 . T)) +((-2169 . T)) NIL (-371 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1418,15 +1418,15 @@ NIL NIL (-372) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-373 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4175)) (|HasAttribute| |#1| (QUOTE -4183))) +((|HasAttribute| |#1| (QUOTE -4178)) (|HasAttribute| |#1| (QUOTE -4186))) (-374) ((|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\"."))) -((-2204 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-2194 . T) (-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-375 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."))) @@ -1438,20 +1438,20 @@ NIL NIL (-377 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."))) -((-4179 -12 (|has| |#1| (-6 -4190)) (|has| |#1| (-421)) (|has| |#1| (-6 -4179))) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-502))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasAttribute| |#1| (QUOTE -4190)) (|HasAttribute| |#1| (QUOTE -4179)) (|HasCategory| |#1| (QUOTE (-421)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (-3747 (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) +((-4182 -12 (|has| |#1| (-6 -4193)) (|has| |#1| (-421)) (|has| |#1| (-6 -4182))) (-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1077)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-502))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasAttribute| |#1| (QUOTE -4193)) (|HasAttribute| |#1| (QUOTE -4182)) (|HasCategory| |#1| (QUOTE (-421)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (-3786 (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-132))))) (-378 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 (-379 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."))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) NIL (-380 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517))))) +((|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517))))) (-381 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL @@ -1460,14 +1460,14 @@ 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 -(-383 R -1725 UP A) +(-383 R -4057 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)}."))) -((-4189 . T)) +((-4192 . T)) NIL -(-384 R -1725 UP A |ibasis|) +(-384 R -4057 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -954) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -955) (|devaluate| |#2|)))) (-385 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1478,12 +1478,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-333)))) (-387 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) -((-4189 |has| |#1| (-509)) (-4187 . T) (-4186 . T)) +((-4192 |has| |#1| (-509)) (-4190 . T) (-4189 . T)) NIL (-388 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."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -258) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-1115))))) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1077)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -258) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1077)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-421))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-1116))))) (-389 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 @@ -1510,37 +1510,37 @@ NIL ((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) (-395 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4192 . T) (-4182 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4185 . T) (-4196 . T) (-2169 . T)) NIL -(-396 R -1725) +(-396 R -4057) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-397 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4179 -12 (|has| |#1| (-6 -4179)) (|has| |#2| (-6 -4179))) (-4186 . T) (-4187 . T) (-4189 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4179)) (|HasAttribute| |#2| (QUOTE -4179)))) -(-398 R -1725) +((-4182 -12 (|has| |#1| (-6 -4182)) (|has| |#2| (-6 -4182))) (-4189 . T) (-4190 . T) (-4192 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4182)) (|HasAttribute| |#2| (QUOTE -4182)))) +(-398 R -4057) ((|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 (-399 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) +((|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-964))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (-400 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}."))) -((-4189 -3747 (|has| |#1| (-963)) (|has| |#1| (-442))) (-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) ((-4194 "*") |has| |#1| (-509)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-509)) (-4184 |has| |#1| (-509)) (-2181 . T)) +((-4192 -3786 (|has| |#1| (-964)) (|has| |#1| (-442))) (-4190 |has| |#1| (-156)) (-4189 |has| |#1| (-156)) ((-4197 "*") |has| |#1| (-509)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-509)) (-4187 |has| |#1| (-509)) (-2169 . T)) NIL -(-401 R -1725) +(-401 R -4057) ((|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 -(-402 R -1725) +(-402 R -4057) ((|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)))) -(-403 R -1725) +(-403 R -4057) ((|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 @@ -1548,10 +1548,10 @@ 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 -(-405 R -1725 UP) +(-405 R -4057 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 -954) (QUOTE (-47))))) +((|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-47))))) (-406) ((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) NIL @@ -1566,17 +1566,17 @@ NIL NIL (-409) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2181 . T)) +((-2169 . T)) NIL (-410) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2181 . T)) +((-2169 . T)) NIL (-411 UP) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-412 R UP -1725) +(-412 R UP -4057) ((|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 @@ -1614,16 +1614,16 @@ NIL NIL (-421) ((|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}."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-422 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"))) -((-4189 |has| (-377 (-875 |#1|)) (-509)) (-4187 . T) (-4186 . T)) -((|HasCategory| (-377 (-875 |#1|)) (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-377 (-875 |#1|)) (QUOTE (-509)))) +((-4192 |has| (-377 (-876 |#1|)) (-509)) (-4190 . T) (-4189 . T)) +((|HasCategory| (-377 (-876 |#1|)) (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-377 (-876 |#1|)) (QUOTE (-509)))) (-423 |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"))) -(((-4194 "*") |has| |#2| (-156)) (-4185 |has| |#2| (-509)) (-4190 |has| |#2| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4190)) (|HasCategory| |#2| (QUOTE (-421))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) +(((-4197 "*") |has| |#2| (-156)) (-4188 |has| |#2| (-509)) (-4193 |has| |#2| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3786 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3786 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4193)) (|HasCategory| |#2| (QUOTE (-421))) (-3786 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-833)))) (|HasCategory| |#2| (QUOTE (-132))))) (-424 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 @@ -1650,7 +1650,7 @@ NIL NIL (-430 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) NIL (-431 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1658,8 +1658,8 @@ NIL NIL (-432 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1006))) (-12 (|HasCategory| |#4| (QUOTE (-1006))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) (-433 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1688,7 +1688,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-440 |lv| -1725 R) +(-440 |lv| -4057 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1698,45 +1698,45 @@ NIL NIL (-442) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4189 . T)) +((-4192 . T)) NIL (-443 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2262) (LIST (|devaluate| |#1|) (QUOTE (-1077)))))) (-3786 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-882))) (|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1077))))) (|HasSignature| |#1| (LIST (QUOTE -2080) (LIST (LIST (QUOTE -583) (QUOTE (-1077))) (|devaluate| |#1|))))))) (-444 |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."))) -((-4193 . T)) -((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4196 . T)) +((|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|)))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) (-445 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)}"))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1006))) (-12 (|HasCategory| |#4| (QUOTE (-1006))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) (-446) ((|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}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-447 |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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1006))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) (-448) ((|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. 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(|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-1006)))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-964)))) (-12 (|HasCategory| |#2| (QUOTE (-964))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-964))) (|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077))))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) (-451 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}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-452 -1725 UP UPUP R) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-452 -4057 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 @@ -1746,15 +1746,15 @@ NIL NIL (-454) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-939))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1052))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3747 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-517) (QUOTE (-833))) (|HasCategory| (-517) (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-940))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1053))) (|HasCategory| (-517) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1077)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3786 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-833)))) (|HasCategory| (-517) (QUOTE (-132))))) (-455 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 -4192)) (|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) +((|HasAttribute| |#1| (QUOTE -4195)) (|HasAttribute| |#1| (QUOTE -4196)) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-456 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2181 . T)) +((-2169 . T)) NIL (-457 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1764,34 +1764,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-459 -1725 UP |AlExt| |AlPol|) +(-459 -4057 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-460) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (LIST (QUOTE -954) (QUOTE (-517))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| $ (QUOTE (-964))) (|HasCategory| $ (LIST (QUOTE -955) (QUOTE (-517))))) (-461 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-462 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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-463 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 -(-464 R UP -1725) +(-464 R UP -4057) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-465 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1005))) (-12 (|HasCategory| (-107) (QUOTE (-1005))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107))))) (|HasCategory| (-107) (LIST (QUOTE -557) (QUOTE (-787))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1006))) (-12 (|HasCategory| (-107) (QUOTE (-1006))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107))))) (|HasCategory| (-107) (LIST (QUOTE -557) (QUOTE (-787))))) (-466 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1804,10 +1804,10 @@ 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 -(-469 -1725 |Expon| |VarSet| |DPoly|) +(-469 -4057 |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 -558) (QUOTE (-1076))))) +((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-1077))))) (-470 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,{}lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL @@ -1850,32 +1850,32 @@ NIL ((|HasCategory| |#2| (QUOTE (-724)))) (-480 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}"))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-481 |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}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-530 |#1|) (QUOTE (-134))) (|HasCategory| (-530 |#1|) (QUOTE (-338))) (|HasCategory| (-530 |#1|) (QUOTE (-132))) (-3747 (|HasCategory| (-530 |#1|) (QUOTE (-132))) (|HasCategory| (-530 |#1|) (QUOTE (-338))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-530 |#1|) (QUOTE (-134))) (|HasCategory| (-530 |#1|) (QUOTE (-338))) (|HasCategory| (-530 |#1|) (QUOTE (-132))) (-3786 (|HasCategory| (-530 |#1|) (QUOTE (-132))) (|HasCategory| (-530 |#1|) (QUOTE (-338))))) (-482 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}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-483 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."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-484 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 -4193))) +((|HasAttribute| |#3| (QUOTE -4196))) (-485 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 -4193))) +((|HasAttribute| |#7| (QUOTE -4196))) (-486 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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4194 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4197 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-487 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) NIL @@ -1888,7 +1888,7 @@ NIL ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-490 K -1725 |Par|) +(-490 K -4057 |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 @@ -1908,7 +1908,7 @@ 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 -(-495 K -1725 |Par|) +(-495 K -4057 |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 @@ -1938,17 +1938,17 @@ NIL NIL (-502) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|hash| (($ $) "\\spad{hash(n)} returns the hash code of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\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."))) -((-4190 . T) (-4191 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4193 . T) (-4194 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-503 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-504 R -1725) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1006))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-504 R -4057) ((|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 -(-505 R0 -1725 UP UPUP R) +(-505 R0 -4057 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 @@ -1958,7 +1958,7 @@ NIL NIL (-507 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."))) -((-2204 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-2194 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-508 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."))) @@ -1966,9 +1966,9 @@ NIL NIL (-509) ((|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."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-510 R -1725) +(-510 R -4057) ((|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 @@ -1980,7 +1980,7 @@ 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 -(-513 R -1725 L) +(-513 R -4057 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 -593) (|devaluate| |#2|)))) @@ -1988,31 +1988,31 @@ 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 -(-515 -1725 UP UPUP R) +(-515 -4057 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 -(-516 -1725 UP) +(-516 -4057 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 (-517) ((|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}."))) -((-4174 . T) (-4180 . T) (-4184 . T) (-4179 . T) (-4190 . T) (-4191 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4177 . T) (-4183 . T) (-4187 . T) (-4182 . T) (-4193 . T) (-4194 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-518) ((|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 -(-519 R -1725 L) +(-519 R -4057 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 -593) (|devaluate| |#2|)))) -(-520 R -1725) +(-520 R -4057) ((|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 -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1040)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-569))))) -(-521 -1725 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1041)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-569))))) +(-521 -4057 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 @@ -2020,54 +2020,54 @@ 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 -(-523 -1725) +(-523 -4057) ((|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 (-524 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."))) -((-2204 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-2194 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-525) ((|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 -(-526 R -1725) +(-526 R -4057) ((|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 -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-256))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076))))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-256)))) (|HasCategory| |#1| (QUOTE (-509)))) -(-527 -1725 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-256))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-1077))))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-256)))) (|HasCategory| |#1| (QUOTE (-509)))) +(-527 -4057 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 -(-528 R -1725) +(-528 R -4057) ((|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 (-529 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-530 |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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) ((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-338)))) (-531) ((|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 -(-532 R -1725) +(-532 R -4057) ((|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 -(-533 E -1725) +(-533 E -4057) ((|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 -(-534 -1725) +(-534 -4057) ((|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}."))) -((-4187 . T) (-4186 . T)) -((|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-1076))))) +((-4190 . T) (-4189 . T)) +((|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-1077))))) (-535 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL @@ -2090,19 +2090,19 @@ NIL NIL (-540 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4193 . T) (-4192 . T)) -((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1005))) (-3747 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1005)))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3747 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1006))) (-3786 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1006)))) (-12 (|HasCategory| (-131) (QUOTE (-1006))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3786 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1006))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-131) (QUOTE (-1006))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) (-541 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 (-542 |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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (|HasCategory| (-517) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076))))))) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (|HasCategory| (-517) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-333))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2262) (LIST (|devaluate| |#1|) (QUOTE (-1077))))))) (-543 |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.}"))) -((-4187 |has| |#1| (-509)) (-4186 |has| |#1| (-509)) ((-4194 "*") |has| |#1| (-509)) (-4185 |has| |#1| (-509)) (-4189 . T)) +((-4190 |has| |#1| (-509)) (-4189 |has| |#1| (-509)) ((-4197 "*") |has| |#1| (-509)) (-4188 |has| |#1| (-509)) (-4192 . T)) ((|HasCategory| |#1| (QUOTE (-509)))) (-544 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),{}..]}."))) @@ -2112,7 +2112,7 @@ 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 -(-546 R -1725 FG) +(-546 R -4057 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 @@ -2122,31 +2122,31 @@ NIL NIL (-548 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-964))) (-12 (|HasCategory| |#1| (QUOTE (-921))) (|HasCategory| |#1| (QUOTE (-964)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-549 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 -4193)) (|HasCategory| |#2| (QUOTE (-779))) (|HasAttribute| |#1| (QUOTE -4192)) (|HasCategory| |#3| (QUOTE (-1005)))) +((|HasAttribute| |#1| (QUOTE -4196)) (|HasCategory| |#2| (QUOTE (-779))) (|HasAttribute| |#1| (QUOTE -4195)) (|HasCategory| |#3| (QUOTE (-1006)))) (-550 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2181 . T)) +((-2169 . T)) NIL (-551 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4189 -3747 (-3993 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4187 . T) (-4186 . T)) -((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) +((-4192 -3786 (-4024 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4190 . T) (-4189 . T)) +((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3786 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) (-552 |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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| (-1059) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1059))) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -557) (QUOTE (-787))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| (-1060) (QUOTE (-779))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (QUOTE (-1060))) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (LIST (QUOTE -557) (QUOTE (-787))))) (-553 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 (-554 |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}."))) -((-4193 . T) (-2181 . T)) +((-4196 . T) (-2169 . T)) NIL (-555 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"))) @@ -2155,7 +2155,7 @@ NIL (-556 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-557 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL @@ -2164,7 +2164,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-559 -1725 UP) +(-559 -4057 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2174,20 +2174,20 @@ NIL NIL (-561 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."))) -((-4189 . T)) +((-4192 . T)) NIL (-562 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}."))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) ((|HasCategory| |#1| (QUOTE (-777)))) -(-563 R -1725) +(-563 R -4057) ((|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 (-564 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"))) -((-4187 . T) (-4186 . T) ((-4194 "*") . T) (-4185 . T) (-4189 . T)) -((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) +((-4190 . T) (-4189 . T) ((-4197 "*") . T) (-4188 . T) (-4192 . T)) +((|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517))))) (-565 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL @@ -2198,7 +2198,7 @@ NIL NIL (-567 |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}}."))) -((-4189 . T)) +((-4192 . T)) NIL (-568 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}}."))) @@ -2208,30 +2208,30 @@ 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 -(-570 R -1725) +(-570 R -4057) ((|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 -(-571 |lv| -1725) +(-571 |lv| -4057) ((|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 (-572) ((|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."))) -((-4193 . T)) -((|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1059) (QUOTE (-779))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1005))) (-12 (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1059))) (LIST (QUOTE |:|) (QUOTE -1859) (QUOTE (-51))))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-51) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4196 . T)) +((|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1060) (QUOTE (-779))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1006))) (-12 (|HasCategory| (-51) (QUOTE (-1006))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (QUOTE (-1060))) (LIST (QUOTE |:|) (QUOTE -1846) (QUOTE (-51))))))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-51) (QUOTE (-1006)))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1006))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) (-573 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-333)))) (-574 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4187 . T) (-4186 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4190 . T) (-4189 . T)) NIL (-575 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4189 -3747 (-3993 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4187 . T) (-4186 . T)) -((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) +((-4192 -3786 (-4024 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4190 . T) (-4189 . T)) +((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3786 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) (-576 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 @@ -2246,7 +2246,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-333))) (-2479 (|HasCategory| |#1| (QUOTE (-333))))) (-579 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}."))) -((-4189 . T)) +((-4192 . T)) NIL (-580 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}."))) @@ -2262,12 +2262,12 @@ NIL NIL (-583 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."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-584 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-585 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2279,39 +2279,39 @@ NIL (-587 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 -4193))) +((|HasAttribute| |#1| (QUOTE -4196))) (-588 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})}."))) -((-2181 . T)) +((-2169 . T)) NIL -(-589 R -1725 L) +(-589 R -4057 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 (-590 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}}"))) -((-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) +((-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) (-591 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) +((-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) (-592 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-333)))) (-593 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}."))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-594 -1725 UP) +(-594 -4057 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)))) -(-595 A -2669) +(-595 A -2903) ((|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}}"))) -((-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) +((-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) (-596 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL @@ -2326,7 +2326,7 @@ NIL NIL (-599 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}."))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) ((|HasCategory| |#1| (QUOTE (-723)))) (-600 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."))) @@ -2334,7 +2334,7 @@ NIL NIL (-601 |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) (-4187 . T) (-4186 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4190 . T) (-4189 . T)) ((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-156)))) (-602 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}."))) @@ -2342,13 +2342,13 @@ NIL NIL (-603 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}."))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-604 -1725) +(-604 -4057) ((|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 -(-605 -1725 |Row| |Col| M) +(-605 -4057 |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 @@ -2358,8 +2358,8 @@ NIL NIL (-607 |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."))) -((-4189 . T) (-4192 . T) (-4186 . T) (-4187 . T)) -((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509))) (-3747 (|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3747 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-156)))) +((-4192 . T) (-4195 . T) (-4189 . T) (-4190 . T)) +((|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4197 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509))) (-3786 (|HasAttribute| |#2| (QUOTE (-4197 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3786 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-156)))) (-608 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2370,12 +2370,12 @@ NIL NIL (-610 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) -((-2181 . T)) +((-2169 . T)) NIL (-611 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 -((|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (QUOTE (-964))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-964))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-612 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL @@ -2411,10 +2411,10 @@ NIL (-620 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 (-4194 "*"))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509)))) +((|HasAttribute| |#2| (QUOTE (-4197 "*"))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509)))) (-621 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"))) -((-4192 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4196 . T) (-2169 . T)) NIL (-622 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."))) @@ -2422,13 +2422,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509)))) (-623 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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4194 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4197 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-624 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 -(-625 S -1725 FLAF FLAS) +(-625 S -4057 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 @@ -2438,11 +2438,11 @@ NIL NIL (-627) ((|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"))) -((-4185 . T) (-4190 |has| (-632) (-333)) (-4184 |has| (-632) (-333)) (-3883 . T) (-4191 |has| (-632) (-6 -4191)) (-4188 |has| (-632) (-6 -4188)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-632) (QUOTE (-134))) (|HasCategory| (-632) (QUOTE (-132))) (|HasCategory| (-632) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-338))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-319))) (-3747 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (LIST (QUOTE -258) (QUOTE (-632)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -280) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-632) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-632) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-632) (QUOTE (-939))) (|HasCategory| (-632) (QUOTE (-1097))) (-12 (|HasCategory| (-632) (QUOTE (-920))) (|HasCategory| (-632) (QUOTE (-1097)))) (|HasCategory| (-632) (QUOTE (-502))) (|HasCategory| (-632) (QUOTE (-972))) (-12 (|HasCategory| (-632) (QUOTE (-972))) (|HasCategory| (-632) (QUOTE (-1097)))) (-3747 (|HasCategory| (-632) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (QUOTE (-278))) (-3747 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (QUOTE (-832))) (-12 (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-333)))) (-12 (|HasCategory| (-632) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-779))) (|HasCategory| (-632) (QUOTE (-509))) (|HasAttribute| (-632) (QUOTE -4191)) (|HasAttribute| (-632) (QUOTE -4188)) (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-333))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-832))))) (-3747 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (-12 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-832)))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-832))))) (-3747 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-509)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-132)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-832)))) (|HasCategory| (-632) (QUOTE (-319))))) +((-4188 . T) (-4193 |has| (-632) (-333)) (-4187 |has| (-632) (-333)) (-3913 . T) (-4194 |has| (-632) (-6 -4194)) (-4191 |has| (-632) (-6 -4191)) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-632) (QUOTE (-134))) (|HasCategory| (-632) (QUOTE (-132))) (|HasCategory| (-632) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-338))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-319))) (-3786 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (LIST (QUOTE -258) (QUOTE (-632)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -280) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -478) (QUOTE (-1077)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| (-632) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| (-632) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-632) (QUOTE (-940))) (|HasCategory| (-632) (QUOTE (-1098))) (-12 (|HasCategory| (-632) (QUOTE (-921))) (|HasCategory| (-632) (QUOTE (-1098)))) (|HasCategory| (-632) (QUOTE (-502))) (|HasCategory| (-632) (QUOTE (-973))) (-12 (|HasCategory| (-632) (QUOTE (-973))) (|HasCategory| (-632) (QUOTE (-1098)))) (-3786 (|HasCategory| (-632) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (QUOTE (-278))) (-3786 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (QUOTE (-833))) (-12 (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-333)))) (-12 (|HasCategory| (-632) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-779))) (|HasCategory| (-632) (QUOTE (-509))) (|HasAttribute| (-632) (QUOTE -4194)) (|HasAttribute| (-632) (QUOTE -4191)) (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-833)))) (-3786 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-833)))) (|HasCategory| (-632) (QUOTE (-333))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-833))))) (-3786 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-833)))) (-12 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-833)))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-833))))) (-3786 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-833)))) (|HasCategory| (-632) (QUOTE (-333)))) (-3786 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-833)))) (|HasCategory| (-632) (QUOTE (-509)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-833)))) (|HasCategory| (-632) (QUOTE (-132)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-833)))) (|HasCategory| (-632) (QUOTE (-319))))) (-628 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}."))) -((-4193 . T) (-2181 . T)) +((-4196 . T) (-2169 . T)) NIL (-629 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}."))) @@ -2452,13 +2452,13 @@ 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 -(-631 OV E -1725 PG) +(-631 OV E -4057 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 (-632) ((|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|)) "\\spad{base()} returns the base of the model") (((|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}"))) -((-2204 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-2194 . T) (-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-633 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."))) @@ -2466,7 +2466,7 @@ NIL NIL (-634) ((|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}"))) -((-4191 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4194 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-635 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"))) @@ -2488,7 +2488,7 @@ 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 -(-640 S -3342 I) +(-640 S -3348 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 @@ -2498,31 +2498,31 @@ NIL NIL (-642 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)}.}"))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) NIL (-643 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}."))) NIL NIL -(-644 R |Mod| -1769 -2662 |exactQuo|) +(-644 R |Mod| -2563 -3824 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-645 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-991) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-319))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4191 |has| |#1| (-333)) (-4193 |has| |#1| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-992) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-319))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#1| (QUOTE (-421))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-132))))) (-646 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-647 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) +((-4190 |has| |#1| (-156)) (-4189 |has| |#1| (-156)) (-4192 . T)) ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) -(-648 R |Mod| -1769 -2662 |exactQuo|) +(-648 R |Mod| -2563 -3824 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4189 . T)) +((-4192 . T)) NIL (-649 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2530,11 +2530,11 @@ NIL NIL (-650 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) NIL -(-651 -1725) +(-651 -4057) ((|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]]}."))) -((-4189 . T)) +((-4192 . T)) NIL (-652 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."))) @@ -2558,7 +2558,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-338)))) (-657 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."))) -((-4185 |has| |#1| (-333)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 |has| |#1| (-333)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-658 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.")) (** (($ $ (|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."))) @@ -2568,7 +2568,7 @@ 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.")) (** (($ $ (|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 -(-660 -1725 UP) +(-660 -4057 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 @@ -2586,8 +2586,8 @@ NIL NIL (-664 |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."))) -(((-4194 "*") |has| |#2| (-156)) (-4185 |has| |#2| (-509)) (-4190 |has| |#2| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3747 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4190)) (|HasCategory| |#2| (QUOTE (-421))) (-3747 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) +(((-4197 "*") |has| |#2| (-156)) (-4188 |has| |#2| (-509)) (-4193 |has| |#2| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3786 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3786 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4193)) (|HasCategory| |#2| (QUOTE (-421))) (-3786 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-833)))) (|HasCategory| |#2| (QUOTE (-132))))) (-665 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2602,16 +2602,16 @@ NIL NIL (-668 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) +((-4190 |has| |#1| (-156)) (-4189 |has| |#1| (-156)) (-4192 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-779)))) (-669 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4182 . T) (-4193 . T) (-2181 . T)) +((-4185 . T) (-4196 . T) (-2169 . T)) NIL (-670 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}."))) -((-4192 . T) (-4182 . T) (-4193 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) +((-4195 . T) (-4185 . T) (-4196 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) (-671) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL @@ -2622,7 +2622,7 @@ NIL NIL (-673 |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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4187 . T) (-4186 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4190 . T) (-4189 . T) (-4192 . T)) NIL (-674 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"))) @@ -2638,7 +2638,7 @@ NIL NIL (-677 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}."))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) NIL (-678) ((|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}."))) @@ -2720,15 +2720,15 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-698 -1725) +(-698 -4057) ((|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 -(-699 P -1725) +(-699 P -4057) ((|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 -(-700 UP -1725) +(-700 UP -4057) ((|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 @@ -2742,9 +2742,9 @@ NIL NIL (-703) ((|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."))) -(((-4194 "*") . T)) +(((-4197 "*") . T)) NIL -(-704 R -1725) +(-704 R -4057) ((|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 @@ -2764,7 +2764,7 @@ 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 -(-709 -1725 |ExtF| |SUEx| |ExtP| |n|) +(-709 -4057 |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 @@ -2778,28 +2778,28 @@ NIL NIL (-712 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."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . 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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 (-714 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . 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T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-992) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#1| (QUOTE (-421))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-132))))) (-715 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 -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-716 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.}"))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL (-717 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-509))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-156)))) +((|HasCategory| |#1| (QUOTE (-509))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (QUOTE (-964))) (|HasCategory| |#1| (QUOTE (-156)))) (-718) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL @@ -2843,28 +2843,28 @@ NIL (-728 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) +((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) (-729 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-730 -3747 R OS S) +(-730 -3786 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-731 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| (-917 |#1|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-917 |#1|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (-3747 (|HasCategory| (-917 |#1|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (-3747 (|HasCategory| (-917 |#1|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))))) +((-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1077)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| (-918 |#1|) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-918 |#1|) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (-3786 (|HasCategory| (-918 |#1|) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (-3786 (|HasCategory| (-918 |#1|) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))))) (-732) ((|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 -(-733 R -1725 L) +(-733 R -4057 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 -(-734 R -1725) +(-734 R -4057) ((|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 @@ -2872,7 +2872,7 @@ 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 -(-736 R -1725) +(-736 R -4057) ((|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 @@ -2880,11 +2880,11 @@ 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 -(-738 -1725 UP UPUP R) +(-738 -4057 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 -(-739 -1725 UP L LQ) +(-739 -4057 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 @@ -2892,41 +2892,41 @@ 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| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-741 -1725 UP L LQ) +(-741 -4057 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 -(-742 -1725 UP) +(-742 -4057 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 -(-743 -1725 L UP A LO) +(-743 -4057 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 -(-744 -1725 UP) +(-744 -4057 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)))) -(-745 -1725 LO) +(-745 -4057 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 -(-746 -1725 LODO) +(-746 -4057 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)]}."))) 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((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. 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(|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) -(((-4194 "*") |has| |#2| (-333)) (-4185 |has| |#2| (-333)) (-4190 |has| |#2| (-333)) (-4184 |has| |#2| (-333)) (-4189 . T) (-4187 . T) (-4186 . T)) +(((-4197 "*") |has| |#2| (-333)) (-4188 |has| |#2| (-333)) (-4193 |has| |#2| (-333)) (-4187 |has| |#2| (-333)) (-4192 . T) (-4190 . T) (-4189 . T)) ((|HasCategory| |#2| (QUOTE (-333)))) (-750 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}))."))) @@ -2938,7 +2938,7 @@ NIL NIL (-752) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-753) ((|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}"))) @@ -2966,7 +2966,7 @@ NIL NIL (-759 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}."))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) ((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-207)))) (-760) ((|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."))) @@ -2978,7 +2978,7 @@ NIL NIL (-762 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4192 . T) (-4182 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4185 . T) (-4196 . T) (-2169 . T)) NIL (-763) ((|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."))) @@ -2990,11 +2990,11 @@ NIL NIL (-765 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."))) -((-4189 |has| |#1| (-777))) -((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3747 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3747 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) +((-4192 |has| |#1| (-777))) +((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3786 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3786 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) (-766 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) +((-4190 |has| |#1| (-156)) (-4189 |has| |#1| (-156)) (-4192 . T)) ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) (-767) ((|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)."))) @@ -3018,13 +3018,13 @@ NIL NIL (-772 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."))) -((-4189 |has| |#1| (-777))) -((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3747 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3747 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) +((-4192 |has| |#1| (-777))) +((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3786 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3786 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) (-773) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-774 -3136 S) +(-774 -3124 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 @@ -3038,7 +3038,7 @@ NIL NIL (-777) ((|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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4189 . T)) +((-4192 . T)) NIL (-778 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3054,20 +3054,20 @@ NIL ((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156)))) (-781 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) NIL (-782 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 (-333))) (|HasCategory| |#1| (QUOTE (-509)))) -(-783 R |sigma| -1857) +(-783 R |sigma| -1844) ((|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."))) -((-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) -(-784 |x| R |sigma| -1857) +((-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) +(-784 |x| R |sigma| -1844) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) -((-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-333)))) +((-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-333)))) (-785 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) NIL @@ -3090,7 +3090,7 @@ NIL NIL (-790 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) -((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) +((-4190 |has| |#1| (-156)) (-4189 |has| |#1| (-156)) (-4192 . T)) ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) (-791 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3102,1567 +3102,1571 @@ NIL NIL (-793 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-794 |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)."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL (-795 |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)."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-794 |#1|) (QUOTE (-832))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-134))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-794 |#1|) (QUOTE (-939))) (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-1052))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-207))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -478) (QUOTE (-1076)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -794) (|devaluate| |#1|)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (QUOTE (-278))) (|HasCategory| (-794 |#1|) (QUOTE (-502))) (|HasCategory| (-794 |#1|) (QUOTE (-779))) (-3747 (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-832)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))))) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-794 |#1|) (QUOTE (-833))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-134))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-794 |#1|) (QUOTE (-940))) (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-1053))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-207))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -478) (QUOTE (-1077)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -794) (|devaluate| |#1|)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (QUOTE (-278))) (|HasCategory| (-794 |#1|) (QUOTE (-502))) (|HasCategory| (-794 |#1|) (QUOTE (-779))) (-3786 (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-833)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))))) (-796 |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)}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-779))) (-3747 (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-132))))) -(-797) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1077)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-779))) (-3786 (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-833)))) (|HasCategory| |#2| (QUOTE (-132))))) +(-797 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 (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))))) +(-798) ((|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 NIL -(-798) +(-799) ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-799 CF1 CF2) +(-800 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-800 |ComponentFunction|) +(-801 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,{}c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-801 CF1 CF2) +(-802 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-802 |ComponentFunction|) +(-803 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,{}c2,{}c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-803) +(-804) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) NIL NIL -(-804 CF1 CF2) +(-805 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-805 |ComponentFunction|) +(-806 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,{}i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,{}c2,{}c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-806) +(-807) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,{}2,{}3,{}...,{}n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,{}l1,{}l2,{}..,{}ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,{}l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,{}2,{}4],{}[2,{}3,{}5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,{}st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,{}l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l,{}n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}"))) NIL NIL -(-807 R) +(-808 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-808 R S L) +(-809 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,{}r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|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 -(-809 S) +(-810 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\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 (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-810 |Base| |Subject| |Pat|) +(-811 |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 -((|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076)))) (-12 (-2479 (|HasCategory| |#2| (QUOTE (-963)))) (-2479 (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076)))))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (-2479 (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076))))))) -(-811 R A B) +((|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-1077)))) (-12 (-2479 (|HasCategory| |#2| (QUOTE (-964)))) (-2479 (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-1077)))))) (-12 (|HasCategory| |#2| (QUOTE (-964))) (-2479 (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-1077))))))) +(-812 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-812 R S) +(-813 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-813 R -3342) +(-814 R -3348) ((|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 -(-814 R S) +(-815 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-815 R) +(-816 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-816 |VarSet|) +(-817 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-817 UP R) +(-818 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented"))) NIL NIL -(-818) +(-819) ((|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 -(-819 UP -1725) +(-820 UP -4057) ((|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 -(-820) +(-821) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|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 PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} 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 PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\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 PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} 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 PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\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 PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st,{}tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\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 PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,{}routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\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 PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) NIL NIL -(-821) +(-822) ((|retract| (((|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{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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{coerce(x)} \\undocumented{}"))) NIL NIL -(-822 A S) +(-823 A S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#2| (|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| |#2|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-823 S) +(-824 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}."))) -((-4189 . T)) +((-4192 . T)) NIL -(-824 S) +(-825 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-825 |n| R) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-826 |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 -(-826 S) +(-827 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."))) -((-4189 . T)) +((-4192 . T)) NIL -(-827 S) +(-828 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-828 S) +(-829 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4189 . T)) -((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))) (-3747 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))))) -(-829 R E |VarSet| S) +((-4192 . T)) +((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))) (-3786 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))))) +(-830 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-830 R S) +(-831 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-831 S) +(-832 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-132)))) -(-832) +(-833) ((|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}."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-833 |p|) +(-834 |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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) ((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-338)))) -(-834 R0 -1725 UP UPUP R) +(-835 R0 -4057 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 -(-835 UP UPUP R) +(-836 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| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-836 UP UPUP) +(-837 UP UPUP) ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-837 R) +(-838 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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-838 R) +(-839 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."))) NIL NIL -(-839 E OV R P) +(-840 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-840) +(-841) ((|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 -(-841 -1725) +(-842 -4057) ((|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 -(-842 R) +(-843 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-843) +(-844) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-844) +(-845) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4194 "*") . T)) +(((-4197 "*") . T)) NIL -(-845 -1725 P) +(-846 -4057 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-846 |xx| -1725) +(-847 |xx| -4057) ((|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 -(-847 R |Var| |Expon| GR) +(-848 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{^=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-848 S) +(-849 S) ((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-849) +(-850) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-850) +(-851) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) NIL NIL -(-851) +(-852) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-852 R -1725) +(-853 R -4057) ((|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 -(-853) +(-854) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-854 S A B) +(-855 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-855 S R -1725) +(-856 S R -4057) ((|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 -(-856 I) +(-857 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n,{} pat,{} res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-857 S E) +(-858 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,{}...,{}en),{} pat,{} res)} matches the pattern \\spad{pat} to \\spad{f(e1,{}...,{}en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-858 S R L) +(-859 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l,{} pat,{} res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-859 S E V R P) +(-860 S E V R P) ((|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 -809) (|devaluate| |#1|)))) -(-860 R -1725 -3342) +((|HasCategory| |#3| (LIST (QUOTE -810) (|devaluate| |#1|)))) +(-861 R -4057 -3348) ((|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 -(-861 -3342) +(-862 -3348) ((|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 -(-862 S R Q) +(-863 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b,{} pat,{} res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-863 S) +(-864 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\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 (necessary for recursion)."))) NIL NIL -(-864 S R P) +(-865 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj,{} lpat,{} res,{} match)} matches the product of patterns \\spad{reduce(*,{}lpat)} to the product of subjects \\spad{reduce(*,{}lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj,{} lpat,{} op,{} res,{} match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-865) +(-866) ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n,{} n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!,{} n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,{}[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,{}x)} computed by solving the differential equation \\spad{differentiate(E(n,{}x),{}x) = n E(n-1,{}x)} where \\spad{E(0,{}x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,{}1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,{}x)} computed by solving the differential equation \\spad{differentiate(B(n,{}x),{}x) = n B(n-1,{}x)} where \\spad{B(0,{}x) = 1} and initial condition comes from \\spad{B(n) = B(n,{}0)}."))) NIL NIL -(-866 R) +(-867 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-867 |lv| R) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-964))) (-12 (|HasCategory| |#1| (QUOTE (-921))) (|HasCategory| |#1| (QUOTE (-964)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-868 |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 NIL -(-868 |TheField| |ThePols|) +(-869 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL ((|HasCategory| |#1| (QUOTE (-777)))) -(-869 R S) +(-870 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-870 |x| R) +(-871 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-871 S R E |VarSet|) +(-872 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 (-832))) (|HasAttribute| |#2| (QUOTE -4190)) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#4| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779)))) -(-872 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-833))) (|HasAttribute| |#2| (QUOTE -4193)) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#4| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779)))) +(-873 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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) NIL -(-873 E V R P -1725) +(-874 E V R P -4057) ((|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 -(-874 E |Vars| R P S) +(-875 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-875 R) +(-876 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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . 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T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-1077) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| (-1077) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| (-1077) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| (-1077) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| (-1077) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#1| (QUOTE (-421))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-132))))) +(-877 E V R P -4057) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-421)))) -(-877) +(-878) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-878 R L) +(-879 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) NIL NIL -(-879 A B) +(-880 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) NIL NIL -(-880 S) +(-881 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"))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-881) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-882) ((|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 -(-882 -1725) +(-883 -4057) ((|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 -(-883 I) +(-884 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-884) +(-885) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-885 R E) +(-886 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}"))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-123)))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190))) -(-886 A B) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-6 -4193)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-123)))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4193))) +(-887 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"))) -((-4189 -12 (|has| |#2| (-442)) (|has| |#1| (-442)))) -((-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))))) -(-887) +((-4192 -12 (|has| |#2| (-442)) (|has| |#1| (-442)))) +((-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))))) +(-888) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}."))) NIL NIL -(-888 S) +(-889 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4192 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4196 . T) (-2169 . T)) NIL -(-889 R |polR|) +(-890 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}}"))) NIL ((|HasCategory| |#1| (QUOTE (-421)))) -(-890) +(-891) ((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|coerce| (((|List| (|Integer|)) $) "\\spad{coerce(p)} coerces a partition into a list of integers")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-891 S |Coef| |Expon| |Var|) +(-892 S |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| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) NIL NIL -(-892 |Coef| |Expon| |Var|) +(-893 |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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-893) +(-894) ((|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}."))) NIL NIL -(-894 S R E |VarSet| P) +(-895 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL ((|HasCategory| |#2| (QUOTE (-509)))) -(-895 R E |VarSet| P) +(-896 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."))) -((-4192 . T) (-2181 . T)) +((-4195 . T) (-2169 . T)) NIL -(-896 R E V P) +(-897 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."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-278)))) (|HasCategory| |#1| (QUOTE (-421)))) -(-897 K) +(-898 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m,{} v)} returns \\spad{[[C_1,{} g_1],{}...,{}[C_k,{} g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,{}...,{}C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M,{} A,{} sig,{} der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M,{} sig,{} der)} returns \\spad{[R,{} A,{} A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-898 |VarSet| E RC P) +(-899 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-899 R) +(-900 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-900 R1 R2) +(-901 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) NIL NIL -(-901 R) +(-902 R) ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-902 K) +(-903 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,{}n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-903 R E OV PPR) +(-904 R E OV PPR) ((|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 -(-904 K R UP -1725) +(-905 K R UP -4057) ((|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 -(-905 |vl| |nv|) +(-906 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL -(-906 R |Var| |Expon| |Dpoly|) +(-907 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{^=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-278))))) -(-907 R E V P TS) +(-908 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-908) +(-909) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation."))) NIL NIL -(-909 A B R S) +(-910 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL NIL -(-910 A S) +(-911 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1052)))) -(-911 S) +((|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1053)))) +(-912 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}."))) -((-2181 . T) (-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-2169 . T) (-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-912 |n| K) +(-913 |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}."))) NIL NIL -(-913 S) +(-914 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."))) -((-4192 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4196 . T) (-2169 . T)) NIL -(-914 S R) +(-915 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-262)))) -(-915 R) +((|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-262)))) +(-916 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}."))) -((-4185 |has| |#1| (-262)) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 |has| |#1| (-262)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-916 QR R QS S) +(-917 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-917 R) +(-918 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.}"))) -((-4185 |has| |#1| (-262)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-262))) (-3747 (|HasCategory| |#1| (QUOTE (-262))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1076)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-502))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))))) -(-918 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}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((-4188 |has| |#1| (-262)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-262))) (-3786 (|HasCategory| |#1| (QUOTE (-262))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1077)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-502))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))))) (-919 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}."))) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-920 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-920) +(-921) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-921 -1725 UP UPUP |radicnd| |n|) +(-922 -4057 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4185 |has| (-377 |#2|) (-333)) (-4190 |has| (-377 |#2|) (-333)) (-4184 |has| (-377 |#2|) (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3747 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3747 (|HasCategory| (-377 |#2|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3747 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) -(-922 |bb|) +((-4188 |has| (-377 |#2|) (-333)) (-4193 |has| (-377 |#2|) (-333)) (-4187 |has| (-377 |#2|) (-333)) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3786 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3786 (|HasCategory| (-377 |#2|) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3786 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3786 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) +(-923 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-517) (QUOTE (-832))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-1076)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-939))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1052))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1076)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3747 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-832)))) (|HasCategory| (-517) (QUOTE (-132))))) -(-923) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-517) (QUOTE (-833))) (|HasCategory| (-517) (LIST (QUOTE -955) (QUOTE (-1077)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-940))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1053))) (|HasCategory| (-517) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1077)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3786 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-833)))) (|HasCategory| (-517) (QUOTE (-132))))) +(-924) ((|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 NIL -(-924) +(-925) ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-925 RP) +(-926 RP) ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-926 S) +(-927 S) ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-927 A S) +(-928 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 -4193)) (|HasCategory| |#2| (QUOTE (-1005)))) -(-928 S) +((|HasAttribute| |#1| (QUOTE -4196)) (|HasCategory| |#2| (QUOTE (-1006)))) +(-929 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}."))) -((-2181 . T)) +((-2169 . T)) NIL -(-929 S) +(-930 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\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}}"))) NIL NIL -(-930) +(-931) ((|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)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\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}}"))) -((-4185 . T) (-4190 . T) (-4184 . T) (-4187 . T) (-4186 . T) ((-4194 "*") . T) (-4189 . T)) +((-4188 . T) (-4193 . T) (-4187 . T) (-4190 . T) (-4189 . T) ((-4197 "*") . T) (-4192 . T)) NIL -(-931 R -1725) +(-932 R -4057) ((|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 -(-932 R -1725) +(-933 R -4057) ((|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 -(-933 -1725 UP) +(-934 -4057 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 -(-934 -1725 UP) +(-935 -4057 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 -(-935 S) +(-936 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,{}u,{}n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-936 F1 UP UPUP R F2) +(-937 F1 UP UPUP R F2) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,{}u,{}g)} \\undocumented"))) NIL NIL -(-937 |Pol|) +(-938 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-938 |Pol|) +(-939 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-939) +(-940) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-940) +(-941) ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,{}lv,{}eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL NIL -(-941 |TheField|) +(-942 |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"))) -((-4185 . T) (-4190 . T) (-4184 . T) (-4187 . T) (-4186 . T) ((-4194 "*") . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -954) (QUOTE (-517)))) (-3747 (|HasCategory| (-377 (-517)) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))))) -(-942 -1725 L) +((-4188 . T) (-4193 . T) (-4187 . T) (-4190 . T) (-4189 . T) ((-4197 "*") . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -955) (QUOTE (-517)))) (-3786 (|HasCategory| (-377 (-517)) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))))) +(-943 -4057 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 -(-943 S) +(-944 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1005)))) -(-944 R E V P) +((|HasCategory| |#1| (QUOTE (-1006)))) +(-945 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."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) -(-945 R) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1006))) (-12 (|HasCategory| |#4| (QUOTE (-1006))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) +(-946 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 (-4194 "*")))) -(-946 R) +((|HasAttribute| |#1| (QUOTE (-4197 "*")))) +(-947 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 ((|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-278)))) -(-947 S) +(-948 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-948) +(-949) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-949 S) +(-950 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-950 S) +(-951 S) ((|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 -(-951 -1725 |Expon| |VarSet| |FPol| |LFPol|) +(-952 -4057 |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"))) -(((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-952) +(-953) ((|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.}"))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1076))) (LIST (QUOTE |:|) (QUOTE -1859) (QUOTE (-51))))))) (|HasCategory| (-1076) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-51) (QUOTE (-1005)))) (-12 (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) -(-953 A S) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (QUOTE (-1077))) (LIST (QUOTE |:|) (QUOTE -1846) (QUOTE (-51))))))) (|HasCategory| (-1077) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1006))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-51) (QUOTE (-1006)))) (-12 (|HasCategory| (-51) (QUOTE (-1006))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1006))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) +(-954 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL NIL -(-954 S) +(-955 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#1|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL NIL -(-955 Q R) +(-956 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-956) +(-957) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-957 UP) +(-958 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-958 R) +(-959 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL -(-959 R) +(-960 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-960 R |ls|) +(-961 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}."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1005))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -712) (|devaluate| |#1|) (LIST (QUOTE -789) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-789 |#2|) (QUOTE (-338))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -557) (QUOTE (-787))))) -(-961) +((-4196 . T) (-4195 . T)) +((|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1006))) (-12 (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1006))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -712) (|devaluate| |#1|) (LIST (QUOTE -789) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-789 |#2|) (QUOTE (-338))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -557) (QUOTE (-787))))) +(-962) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-962 S) +(-963 S) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL NIL -(-963) +(-964) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4189 . T)) +((-4192 . T)) NIL -(-964 |xx| -1725) +(-965 |xx| -4057) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-965 S |m| |n| R |Row| |Col|) +(-966 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL ((|HasCategory| |#4| (QUOTE (-278))) (|HasCategory| |#4| (QUOTE (-333))) (|HasCategory| |#4| (QUOTE (-509))) (|HasCategory| |#4| (QUOTE (-156)))) -(-966 |m| |n| R |Row| |Col|) +(-967 |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"))) -((-4192 . T) (-2181 . T) (-4187 . T) (-4186 . T)) +((-4195 . T) (-2169 . T) (-4190 . T) (-4189 . T)) NIL -(-967 |m| |n| R) +(-968 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4192 . T) (-4187 . T) (-4186 . T)) -((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (QUOTE (-278))) (|HasCategory| |#3| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-156))) (-3747 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (|HasCategory| |#3| (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3747 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))))) -(-968 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4195 . T) (-4190 . T) (-4189 . T)) +((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-1006))) (|HasCategory| |#3| (QUOTE (-278))) (|HasCategory| |#3| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-156))) (-3786 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (|HasCategory| |#3| (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| |#3| (QUOTE (-1006))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3786 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1006))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))))) +(-969 |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 NIL -(-969 R) +(-970 R) ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL NIL -(-970) +(-971) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) NIL NIL -(-971 S) +(-972 S) ((|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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-972) +(-973) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-973 |TheField| |ThePolDom|) +(-974 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-974) +(-975) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(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."))) -((-4180 . T) (-4184 . T) (-4179 . T) (-4190 . T) (-4191 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4183 . T) (-4187 . T) (-4182 . T) (-4193 . T) (-4194 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-975) +(-976) ((|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}"))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1076))) (LIST (QUOTE |:|) (QUOTE -1859) (QUOTE (-51))))))) (|HasCategory| (-1076) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-51) (QUOTE (-1005)))) (-12 (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1005))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1076)) (|:| -1859 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) -(-976 S R E V) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (QUOTE (-1077))) (LIST (QUOTE |:|) (QUOTE -1846) (QUOTE (-51))))))) (|HasCategory| (-1077) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1006))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-51) (QUOTE (-1006)))) (-12 (|HasCategory| (-51) (QUOTE (-1006))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (QUOTE (-1006))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1077)) (|:| -1846 (-51))) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-51) (LIST (QUOTE -557) (QUOTE (-787)))))) +(-977 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-1076))))) -(-977 R E V) +((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-1077))))) +(-978 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) NIL -(-978 S |TheField| |ThePols|) +(-979 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-979 |TheField| |ThePols|) +(-980 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-980 R E V P TS) +(-981 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 proposed: 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 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 \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} 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 \\axiom{\\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.}"))) NIL NIL -(-981 S R E V P) +(-982 S 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| |#5|) (|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| |#5|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\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| $) |#5| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#5| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\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| $) |#5| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#5| $) "\\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| $) |#5| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\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| $) |#5| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\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| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\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| |#5| (|List| $)) |#5| |#5| $) "\\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| $) |#5| $) "\\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|) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\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| $)) |#5| $) "\\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|) |#5| $) "\\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|) |#5| $) "\\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|) |#5| $) "\\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|) |#5| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-982 R E V P) +(-983 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}."))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-983 R E V P TS) +(-984 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."))) NIL NIL -(-984 |f|) +(-985 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-985 |Base| R -1725) +(-986 |Base| R -4057) ((|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 -(-986 |Base| R -1725) +(-987 |Base| R -4057) ((|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 -(-987 R |ls|) +(-988 R |ls|) ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-988 UP SAE UPA) +(-989 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-989 R UP M) +(-990 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."))) -((-4185 |has| |#1| (-333)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076))))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-319))))) -(-990 UP SAE UPA) +((-4188 |has| |#1| (-333)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077))))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-319))))) +(-991 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 NIL -(-991) +(-992) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-992 S) +(-993 S) ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(x,{} y)} to determine whether \\spad{x < y (f(x,{}y) < 0),{} x = y (f(x,{}y) = 0)},{} or \\spad{x > y (f(x,{}y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-993 R) +(-994 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-994 R) +(-995 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"))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| (-995 (-1076)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-995 S) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-996 (-1077)) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| (-996 (-1077)) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| (-996 (-1077)) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| (-996 (-1077)) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| (-996 (-1077)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#1| (QUOTE (-421))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-132))))) +(-996 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-996 R S) +(-997 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL ((|HasCategory| |#1| (QUOTE (-777)))) -(-997 R S) +(-998 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-998 S) +(-999 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1005)))) -(-999 S) +((|HasCategory| |#1| (QUOTE (-1006)))) +(-1000 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-2181 . T)) +((-2169 . T)) NIL -(-1000 S) +(-1001 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1005)))) -(-1001 S L) +((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1006)))) +(-1002 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2181 . T)) +((-2169 . T)) NIL -(-1002 A S) +(-1003 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1003 S) +(-1004 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4182 . T) (-2181 . T)) +((-4185 . T) (-2169 . T)) NIL -(-1004 S) +(-1005 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1005) +(-1006) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1006 |m| |n|) +(-1007 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1007 S) +(-1008 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)}}"))) -((-4192 . T) (-4182 . T) (-4193 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) -(-1008 |Str| |Sym| |Int| |Flt| |Expr|) +((-4195 . T) (-4185 . T) (-4196 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) +(-1009 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1009) +(-1010) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1010 |Str| |Sym| |Int| |Flt| |Expr|) +(-1011 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1011 R FS) +(-1012 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,{}ftype,{}body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) NIL NIL -(-1012 R E V P TS) +(-1013 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1013 R E V P TS) +(-1014 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\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.}"))) NIL NIL -(-1014 R E V P) +(-1015 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.}"))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-1015) +(-1016) ((|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."))) NIL NIL -(-1016 S) +(-1017 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) 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((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-421)))) -(-1020 R -1725) +(-1021 R -4057) ((|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 -(-1021 R) +(-1022 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1022) +(-1023) ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1023) +(-1024) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|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."))) -((-4180 . T) (-4184 . T) (-4179 . T) (-4190 . T) (-4191 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4183 . T) (-4187 . T) (-4182 . T) (-4193 . T) (-4194 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1024 S) +(-1025 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4192 . T) (-4193 . T) (-2181 . T)) +((-4195 . T) (-4196 . T) (-2169 . T)) NIL -(-1025 S |ndim| R |Row| |Col|) +(-1026 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-333))) (|HasAttribute| |#3| (QUOTE (-4194 "*"))) (|HasCategory| |#3| (QUOTE (-156)))) -(-1026 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-333))) (|HasAttribute| |#3| (QUOTE (-4197 "*"))) (|HasCategory| |#3| (QUOTE (-156)))) +(-1027 |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."))) -((-2181 . T) (-4192 . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-2169 . T) (-4195 . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1027 R |Row| |Col| M) +(-1028 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}."))) NIL NIL -(-1028 R |VarSet|) +(-1029 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -809) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -809) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4190)) (|HasCategory| |#1| (QUOTE (-421))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-832)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (-3747 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-1029 |Coef| |Var| SMP) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4193)) (|HasCategory| |#1| (QUOTE (-421))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-132))))) +(-1030 |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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) -(-1030 R E V P) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) +(-1031 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}"))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-1031 UP -1725) +(-1032 UP -4057) ((|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 -(-1032 R) +(-1033 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,{}lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,{}x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) NIL NIL -(-1033 R) +(-1034 R) ((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function func1 will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect,{} var,{} n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1,{} func2,{} newvar)} returns a function func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1034 R) +(-1035 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs,{} lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,{}x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,{}x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1035 S A) +(-1036 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,{}f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,{}f)} \\undocumented"))) NIL ((|HasCategory| |#1| (QUOTE (-779)))) -(-1036 R) +(-1037 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL NIL -(-1037 R) +(-1038 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); close2 set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if close2 is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and close2 indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument close2 equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} [props],{} prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{}[props],{}prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,{}p1,{}...,{}pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,{}[[r0],{}[r1],{}...,{}[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,{}[p0,{}p1,{}...,{}pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,{}R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,{}[[lr0],{}[lr1],{}...,{}[lrn],{}[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,{}[p0,{}p1,{}...,{}pn,{}p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,{}p1,{}p2,{}...,{}pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,{}[[p0],{}[p1],{}...,{}[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,{}[p0,{}p1,{}...,{}pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,{}i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,{}[x,{}y,{}z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,{}p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,{}i,{}p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,{}[p0,{}p1,{}...,{}pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,{}s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1038) +(-1039) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) NIL NIL -(-1039) +(-1040) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1040) +(-1041) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1041 V C) +(-1042 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1042 V C) +(-1043 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."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-1041 |#1| |#2|) (QUOTE (-1005))) (-12 (|HasCategory| (-1041 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1041) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1041 |#1| |#2|) (QUOTE (-1005)))) (|HasCategory| (-1041 |#1| |#2|) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-1041 |#1| |#2|) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-1041 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1041) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1041 |#1| |#2|) (QUOTE (-1005)))))) -(-1043 |ndim| R) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-1042 |#1| |#2|) (QUOTE (-1006))) (-12 (|HasCategory| (-1042 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1042) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1042 |#1| |#2|) (QUOTE (-1006)))) (|HasCategory| (-1042 |#1| |#2|) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-1042 |#1| |#2|) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-1042 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1042) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1042 |#1| |#2|) (QUOTE (-1006)))))) +(-1044 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}."))) -((-4189 . T) (-4181 |has| |#2| (-6 (-4194 "*"))) (-4192 . T) (-4186 . T) (-4187 . T)) -((|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-333))) (-3747 (|HasAttribute| |#2| (QUOTE (-4194 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3747 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -823) (QUOTE (-1076)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-156)))) -(-1044 S) +((-4192 . T) (-4184 |has| |#2| (-6 (-4197 "*"))) (-4195 . T) (-4189 . T) (-4190 . T)) +((|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4197 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-333))) (-3786 (|HasAttribute| |#2| (QUOTE (-4197 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3786 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-156)))) +(-1045 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1045) +(-1046) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-1046 R E V P TS) +(-1047 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.}"))) NIL NIL -(-1047 R E V P) +(-1048 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."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) -(-1048 S) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1006))) (-12 (|HasCategory| |#4| (QUOTE (-1006))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) +(-1049 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}."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-1049 A S) +((-4195 . T) (-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-1050 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1050 S) +(-1051 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})}."))) -((-2181 . T)) +((-2169 . T)) NIL -(-1051 |Key| |Ent| |dent|) +(-1052 |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."))) -((-4193 . T)) -((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-1052) +((-4196 . T)) +((|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|)))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-1053) ((|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 NIL -(-1053 |Coef|) +(-1054 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|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| (((|Stream| |#1|) (|Stream| |#1|)) "\\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| (((|Stream| |#1|) (|Stream| |#1|)) "\\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| (((|Stream| |#1|) (|Stream| |#1|)) "\\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 -(-1054 S) +(-1055 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}."))) NIL NIL -(-1055 A B) +(-1056 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL NIL -(-1056 A B C) +(-1057 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}."))) NIL NIL -(-1057 S) +(-1058 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4193 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-1058) +((-4196 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-1059) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-1059) +(-1060) NIL -((-4193 . T) (-4192 . T)) -((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1005))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3747 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1005))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787))))) -(-1060 |Entry|) +((-4196 . T) (-4195 . T)) +((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1006))) (-12 (|HasCategory| (-131) (QUOTE (-1006))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3786 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1006))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787))))) +(-1061 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (QUOTE (-1059))) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#1|)))))) (|HasCategory| (-1059) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-1005)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 (-1059)) (|:| -1859 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-1061 A) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (QUOTE (-1060))) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#1|)))))) (|HasCategory| (-1060) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (QUOTE (-1006))) (|HasCategory| |#1| (QUOTE (-1006)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 (-1060)) (|:| -1846 |#1|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-1062 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) -(-1062 |Coef|) +(-1063 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1063 |Coef|) +(-1064 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1064 R UP) +(-1065 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p,{} q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p,{} q)} returns \\spad{[p0,{}...,{}pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p,{} q)}."))) NIL ((|HasCategory| |#1| (QUOTE (-278)))) -(-1065 |n| R) +(-1066 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,{}\\spad{li})} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,{}\\spad{li},{}p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,{}\\spad{li},{}b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,{}ind,{}p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,{}\\spad{li},{}i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,{}\\spad{li},{}p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,{}s2,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,{}p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,{}\\spad{li},{}i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL -(-1069 R) +(-1070 R) ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) NIL NIL -(-1070 R S) +(-1071 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) 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T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2262) (LIST (|devaluate| |#1|) (QUOTE (-1077)))))) (-3786 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-882))) (|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1077))))) (|HasSignature| |#1| (LIST (QUOTE -2080) (LIST (LIST (QUOTE -583) (QUOTE (-1077))) (|devaluate| |#1|))))))) +(-1075 |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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1017))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) -(-1075) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1018))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2262) (LIST (|devaluate| |#1|) (QUOTE (-1077)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-882))) (|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1077))))) (|HasSignature| |#1| (LIST (QUOTE -2080) (LIST (LIST (QUOTE -583) (QUOTE (-1077))) (|devaluate| |#1|))))))) +(-1076) ((|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 NIL -(-1076) +(-1077) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,{}[a1,{}...,{}an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s,{} [a1,{}...,{}an])} returns \\spad{s} arg-scripted by \\spad{[a1,{}...,{}an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s,{} [a1,{}...,{}an])} returns \\spad{s} superscripted by \\spad{[a1,{}...,{}an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s,{} [a1,{}...,{}an])} returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s,{} [a,{}b,{}c])} is equivalent to \\spad{script(s,{}[a,{}b,{}c,{}[],{}[]])}.")) 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(|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r,{} n)} returns the vector of the elementary symmetric functions in \\spad{[r,{}r,{}...,{}r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,{}...,{}rn])} returns the vector of the elementary symmetric functions in the \\spad{\\spad{ri}'s}: \\spad{[r1 + ... + rn,{} r1 r2 + ... + r(n-1) rn,{} ...,{} r1 r2 ... rn]}."))) NIL NIL -(-1078 R) +(-1079 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-6 -4190)) (-4186 . T) (-4187 . T) (-4189 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| (-891) (QUOTE (-123))) (|HasCategory| |#1| (QUOTE (-509)))) (-3786 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4193))) +(-1080) ((|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 NIL -(-1080) +(-1081) ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,{}tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,{}tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,{}t,{}tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,{}t,{}tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) NIL NIL -(-1081) -((|constructor| (NIL "\\indented{1}{This domain provides a simple,{} general,{} and arguably} complete representation of Spad programs as objects of a term algebra built from ground terms of type boolean,{} integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity from a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} symbol,{} String,{} SExpression. See Also: SExpression.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} is \\spad{x} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} is \\spad{x} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} is \\spad{x} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} is \\spad{x} really is an Integer")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The return value is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (($ (|String|)) "\\spad{coerce(s)} injects the string value \\spad{`s'} into the syntax domain") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (($ (|Symbol|)) "\\spad{coerce(s)} injects the symbol \\spad{`s'} into the Syntax domain.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (($ (|DoubleFloat|)) "\\spad{coerce(f)} injects the float value \\spad{`f'} into the Syntax domain") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}") (($ (|Integer|)) "\\spad{coerce(i)} injects the integer value `i' into the Syntax domain")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cell ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) +(-1082) +((|constructor| (NIL "\\indented{1}{This domain provides a simple,{} general,{} and arguably} complete representation of Spad programs as objects of a term algebra built from ground terms of type boolean,{} integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity from a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} symbol,{} String,{} SExpression. See Also: SExpression.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} is \\spad{x} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} is \\spad{x} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} is \\spad{x} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} is \\spad{x} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The return value is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (($ (|String|)) "\\spad{coerce(s)} injects the string value \\spad{`s'} into the syntax domain") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (($ (|Symbol|)) "\\spad{coerce(s)} injects the symbol \\spad{`s'} into the Syntax domain.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (($ (|DoubleFloat|)) "\\spad{coerce(f)} injects the float value \\spad{`f'} into the Syntax domain") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}") (($ (|Integer|)) "\\spad{coerce(i)} injects the integer value `i' into the Syntax domain")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cell ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1082 R) +(-1083 R) ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,{}lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,{}v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,{}v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,{}lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-1083 S) +(-1084 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1084 S) +(-1085 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1085 |Key| |Entry|) +(-1086 |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}"))) -((-4192 . T) (-4193 . T)) -((|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (-12 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2585) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1859) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1005))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (QUOTE (-1005))) (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3747 (|HasCategory| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-1086 R) +((-4195 . T) (-4196 . T)) +((|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (-12 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2576) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1846) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1006))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| |#2| (QUOTE (-1006)))) (-12 (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (QUOTE (-1006))) (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (QUOTE (-1006))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-3786 (|HasCategory| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (LIST (QUOTE -557) (QUOTE (-787)))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-1087 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 NIL -(-1087 S |Key| |Entry|) +(-1088 S |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| |#3| |#3| |#3|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\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| ((|#3| $ |#2| |#3|) "\\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})}."))) NIL NIL -(-1088 |Key| |Entry|) +(-1089 |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})}."))) -((-4193 . T) (-2181 . T)) +((-4196 . T) (-2169 . T)) NIL -(-1089 |Key| |Entry|) +(-1090 |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."))) NIL NIL -(-1090) +(-1091) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1091 S) +(-1092 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1092) +(-1093) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) NIL NIL -(-1093) +(-1094) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,{}\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,{}s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1094 R) +(-1095 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1095) +(-1096) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1096 S) +(-1097 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1097) +(-1098) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1098 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}."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (QUOTE (-1005))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-1099 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (QUOTE (-1006))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-1100 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1100) +(-1101) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1101 R -1725) +(-1102 R -4057) ((|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 -(-1102 R |Row| |Col| M) +(-1103 R |Row| |Col| M) ((|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 -(-1103 R -1725) +(-1104 R -4057) ((|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 -558) (LIST (QUOTE -815) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -809) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -815) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -809) (|devaluate| |#1|))))) -(-1104 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -816) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -810) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -810) (|devaluate| |#1|))))) +(-1105 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-338)))) -(-1105 R E V P) +(-1106 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-1106 |Coef|) +(-1107 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) -(-1107 |Curve|) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) +(-1108 |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 NIL -(-1108) +(-1109) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,{}n,{}b,{}r,{}lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,{}sin(n - 1) a],{}...,{}[cos 2 a,{}sin 2 a],{}[cos a,{}sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,{}q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,{}x2,{}x3,{}c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1109 S) +(-1110 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) NIL -((|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) -(-1110 -1725) +((|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) +(-1111 -4057) ((|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 -(-1111) +(-1112) ((|constructor| (NIL "The fundamental Type."))) -((-2181 . T)) +((-2169 . T)) NIL -(-1112 S) +(-1113 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) NIL ((|HasCategory| |#1| (QUOTE (-779)))) -(-1113) +(-1114) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,{}...,{}an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1114 S) +(-1115 S) ((|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."))) NIL NIL -(-1115) +(-1116) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1116 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1117 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1117 |Coef|) +(-1118 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1118 S |Coef| UTS) +(-1119 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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-333)))) -(-1119 |Coef| UTS) +(-1120 |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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|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)}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-2181 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-2169 |has| |#1| (-333)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1120 |Coef| UTS) +(-1121 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . 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univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1123 R S) +(-1124 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-777)))) -(-1124 S) +(-1125 S) ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) NIL -((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1005)))) -(-1125 |x| R |y| S) +((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1006)))) +(-1126 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1126 R Q UP) +(-1127 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1127 R UP) +(-1128 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1128 R UP) +(-1129 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1129 R U) +(-1130 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) 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T)) +((|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3786 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-992) (LIST (QUOTE -810) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-349))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -810) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -810) (QUOTE (-517))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-349)))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -816) (QUOTE (-517)))))) (-12 (|HasCategory| (-992) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (-3786 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE -4193)) (|HasCategory| |#2| (QUOTE (-421))) (-3786 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-833)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-833)))) (-3786 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-833)))) (|HasCategory| |#2| (QUOTE (-132))))) +(-1132 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1132 S R) +(-1133 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-1052)))) -(-1133 R) +((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-1053)))) +(-1134 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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4188 |has| |#1| (-333)) (-4190 |has| |#1| (-6 -4190)) (-4187 . T) (-4186 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4191 |has| |#1| (-333)) (-4193 |has| |#1| (-6 -4193)) (-4190 . T) (-4189 . T) (-4192 . T)) NIL -(-1134 S |Coef| |Expon|) +(-1135 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 -823) (QUOTE (-1076)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1017))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2271) (LIST (|devaluate| |#2|) (QUOTE (-1076)))))) -(-1135 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1018))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2262) (LIST (|devaluate| |#2|) (QUOTE (-1077)))))) +(-1136 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1136 RC P) +(-1137 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1137 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1138 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1138 |Coef|) +(-1139 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1139 S |Coef| ULS) +(-1140 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1140 |Coef| ULS) +(-1141 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1141 |Coef| ULS) +(-1142 |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)}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) -(-1142 |Coef| |var| |cen|) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2262) (LIST (|devaluate| |#1|) (QUOTE (-1077)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3786 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-882))) (|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1077))))) (|HasSignature| |#1| (LIST (QUOTE -2080) (LIST (LIST (QUOTE -583) (QUOTE (-1077))) (|devaluate| |#1|))))))) +(-1143 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4190 |has| |#1| (-333)) (-4184 |has| |#1| (-333)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3747 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) -(-1143 R FE |var| |cen|) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4193 |has| |#1| (-333)) (-4187 |has| |#1| (-333)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3786 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2262) (LIST (|devaluate| |#1|) (QUOTE (-1077)))))) (-3786 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-882))) (|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1077))))) (|HasSignature| |#1| (LIST (QUOTE -2080) (LIST (LIST (QUOTE -583) (QUOTE (-1077))) (|devaluate| |#1|))))))) +(-1144 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))}."))) -(((-4194 "*") |has| (-1142 |#2| |#3| |#4|) (-156)) (-4185 |has| (-1142 |#2| |#3| |#4|) (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -954) (QUOTE (-517)))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-333))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-421))) (-3747 (|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1142 |#2| |#3| |#4|) (LIST (QUOTE -954) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| (-1142 |#2| |#3| |#4|) (QUOTE (-509)))) -(-1144 A S) +(((-4197 "*") |has| (-1143 |#2| |#3| |#4|) (-156)) (-4188 |has| (-1143 |#2| |#3| |#4|) (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| (-1143 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1143 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1143 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1143 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1143 |#2| |#3| |#4|) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1143 |#2| |#3| |#4|) (LIST (QUOTE -955) (QUOTE (-517)))) (|HasCategory| (-1143 |#2| |#3| |#4|) (QUOTE (-333))) (|HasCategory| (-1143 |#2| |#3| |#4|) (QUOTE (-421))) (-3786 (|HasCategory| (-1143 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1143 |#2| |#3| |#4|) (LIST (QUOTE -955) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| (-1143 |#2| |#3| |#4|) (QUOTE (-509)))) +(-1145 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4193))) -(-1145 S) +((|HasAttribute| |#1| (QUOTE -4196))) +(-1146 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2181 . T)) +((-2169 . T)) NIL -(-1146 |Coef1| |Coef2| UTS1 UTS2) +(-1147 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1147 S |Coef|) +(-1148 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-517)))) (|HasCategory| |#2| (QUOTE (-881))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasSignature| |#2| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2356) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1076))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) -(-1148 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-882))) (|HasCategory| |#2| (QUOTE (-1098))) (|HasSignature| |#2| (LIST (QUOTE -2080) (LIST (LIST (QUOTE -583) (QUOTE (-1077))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3296) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1077))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) +(-1149 |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."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1149 |Coef| |var| |cen|) +(-1150 |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}."))) -(((-4194 "*") |has| |#1| (-156)) (-4185 |has| |#1| (-509)) (-4186 . T) (-4187 . T) (-4189 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3747 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -823) (QUOTE (-1076)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1017))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2271) (LIST (|devaluate| |#1|) (QUOTE (-1076)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3747 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-881))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2356) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1076))))) (|HasSignature| |#1| (LIST (QUOTE -2097) (LIST (LIST (QUOTE -583) (QUOTE (-1076))) (|devaluate| |#1|))))))) -(-1150 |Coef| UTS) +(((-4197 "*") |has| |#1| (-156)) (-4188 |has| |#1| (-509)) (-4189 . T) (-4190 . T) (-4192 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3786 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -824) (QUOTE (-1077)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1018))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2262) (LIST (|devaluate| |#1|) (QUOTE (-1077)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3786 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-882))) (|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3296) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1077))))) (|HasSignature| |#1| (LIST (QUOTE -2080) (LIST (LIST (QUOTE -583) (QUOTE (-1077))) (|devaluate| |#1|))))))) +(-1151 |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 -(-1151 -1725 UP L UTS) +(-1152 -4057 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 (-509)))) -(-1152) +(-1153) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) -((-2181 . T)) +((-2169 . T)) NIL -(-1153 |sym|) +(-1154 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1154 S R) +(-1155 S 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| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "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| |#2|) $ $) "\\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| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|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."))) NIL -((|HasCategory| |#2| (QUOTE (-920))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1155 R) +((|HasCategory| |#2| (QUOTE (-921))) (|HasCategory| |#2| (QUOTE (-964))) (|HasCategory| |#2| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1156 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4193 . T) (-4192 . T) (-2181 . T)) +((-4196 . T) (-4195 . T) (-2169 . T)) NIL -(-1156 A B) +(-1157 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1157 R) +(-1158 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005))) (-3747 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3747 (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) -(-1158) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006))) (-3786 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1006)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-964))) (-12 (|HasCategory| |#1| (QUOTE (-921))) (|HasCategory| |#1| (QUOTE (-964)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3786 (-12 (|HasCategory| |#1| (QUOTE (-1006))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +(-1159) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1159) +(-1160) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1160) +(-1161) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1161) +(-1162) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1162) +(-1163) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1163 A S) +(-1164 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1164 S) +(-1165 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}."))) -((-4187 . T) (-4186 . T)) +((-4190 . T) (-4189 . T)) NIL -(-1165 R) +(-1166 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 -(-1166 K R UP -1725) +(-1167 K R UP -4057) ((|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 -(-1167 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1168 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights"))) -((-4187 |has| |#1| (-156)) (-4186 |has| |#1| (-156)) (-4189 . T)) +((-4190 |has| |#1| (-156)) (-4189 |has| |#1| (-156)) (-4192 . T)) ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) -(-1168 R E V P) +(-1169 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}}."))) -((-4193 . T) (-4192 . T)) -((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1005))) (-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) -(-1169 R) +((-4196 . T) (-4195 . T)) +((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1006))) (-12 (|HasCategory| |#4| (QUOTE (-1006))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#4| (LIST (QUOTE -557) (QUOTE (-787))))) +(-1170 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) -((-4186 . T) (-4187 . T) (-4189 . T)) +((-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1170 |vl| R) +(-1171 |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."))) -((-4189 . T) (-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4185))) -(-1171 R |VarSet| XPOLY) +((-4192 . T) (-4188 |has| |#2| (-6 -4188)) (-4190 . T) (-4189 . T)) +((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4188))) +(-1172 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 -(-1172 |vl| R) +(-1173 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) +((-4188 |has| |#2| (-6 -4188)) (-4190 . T) (-4189 . T) (-4192 . T)) NIL -(-1173 S -1725) +(-1174 S -4057) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134)))) -(-1174 -1725) +(-1175 -4057) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4184 . T) (-4190 . T) (-4185 . T) ((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +((-4187 . T) (-4193 . T) (-4188 . T) ((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL -(-1175 |VarSet| R) +(-1176 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -650) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasAttribute| |#2| (QUOTE -4185))) -(-1176 |vl| R) +((-4188 |has| |#2| (-6 -4188)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -650) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasAttribute| |#2| (QUOTE -4188))) +(-1177 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) +((-4188 |has| |#2| (-6 -4188)) (-4190 . T) (-4189 . T) (-4192 . T)) NIL -(-1177 R) +(-1178 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4185 |has| |#1| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasAttribute| |#1| (QUOTE -4185))) -(-1178 R E) +((-4188 |has| |#1| (-6 -4188)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#1| (QUOTE (-156))) (|HasAttribute| |#1| (QUOTE -4188))) +(-1179 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4189 . T) (-4190 |has| |#1| (-6 -4190)) (-4185 |has| |#1| (-6 -4185)) (-4187 . T) (-4186 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasAttribute| |#1| (QUOTE -4189)) (|HasAttribute| |#1| (QUOTE -4190)) (|HasAttribute| |#1| (QUOTE -4185))) -(-1179 |VarSet| R) +((-4192 . T) (-4193 |has| |#1| (-6 -4193)) (-4188 |has| |#1| (-6 -4188)) (-4190 . T) (-4189 . T)) +((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasAttribute| |#1| (QUOTE -4192)) (|HasAttribute| |#1| (QUOTE -4193)) (|HasAttribute| |#1| (QUOTE -4188))) +(-1180 |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."))) -((-4185 |has| |#2| (-6 -4185)) (-4187 . T) (-4186 . T) (-4189 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4185))) -(-1180 A) +((-4188 |has| |#2| (-6 -4188)) (-4190 . T) (-4189 . T) (-4192 . T)) +((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4188))) +(-1181 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 NIL -(-1181 R |ls| |ls2|) +(-1182 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} 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{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1182 R) +(-1183 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([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 the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1183 |p|) +(-1184 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4194 "*") . T) (-4186 . T) (-4187 . T) (-4189 . T)) +(((-4197 "*") . T) (-4189 . T) (-4190 . T) (-4192 . T)) NIL NIL NIL @@ -4684,4 +4688,4 @@ NIL NIL NIL NIL -((-1188 NIL 2225697 2225702 2225707 2225712) (-3 NIL 2225677 2225682 2225687 2225692) (-2 NIL 2225657 2225662 2225667 2225672) (-1 NIL 2225637 2225642 2225647 2225652) (0 NIL 2225617 2225622 2225627 2225632) (-1183 "ZMOD.spad" 2225426 2225439 2225555 2225612) (-1182 "ZLINDEP.spad" 2224470 2224481 2225416 2225421) (-1181 "ZDSOLVE.spad" 2214319 2214341 2224460 2224465) (-1180 "YSTREAM.spad" 2213812 2213823 2214309 2214314) (-1179 "XRPOLY.spad" 2213032 2213052 2213668 2213737) (-1178 "XPR.spad" 2210761 2210774 2212750 2212849) (-1177 "XPOLY.spad" 2210316 2210327 2210617 2210686) (-1176 "XPOLYC.spad" 2209633 2209649 2210242 2210311) (-1175 "XPBWPOLY.spad" 2208070 2208090 2209413 2209482) (-1174 "XF.spad" 2206531 2206546 2207972 2208065) (-1173 "XF.spad" 2204972 2204989 2206415 2206420) (-1172 "XFALG.spad" 2201996 2202012 2204898 2204967) (-1171 "XEXPPKG.spad" 2201247 2201273 2201986 2201991) (-1170 "XDPOLY.spad" 2200861 2200877 2201103 2201172) (-1169 "XALG.spad" 2200459 2200470 2200817 2200856) (-1168 "WUTSET.spad" 2196298 2196315 2200105 2200132) (-1167 "WP.spad" 2195312 2195356 2196156 2196223) (-1166 "WFFINTBS.spad" 2192875 2192897 2195302 2195307) (-1165 "WEIER.spad" 2191089 2191100 2192865 2192870) (-1164 "VSPACE.spad" 2190762 2190773 2191057 2191084) (-1163 "VSPACE.spad" 2190455 2190468 2190752 2190757) (-1162 "VOID.spad" 2190045 2190054 2190445 2190450) (-1161 "VIEW.spad" 2187667 2187676 2190035 2190040) (-1160 "VIEWDEF.spad" 2182864 2182873 2187657 2187662) (-1159 "VIEW3D.spad" 2166699 2166708 2182854 2182859) (-1158 "VIEW2D.spad" 2154436 2154445 2166689 2166694) (-1157 "VECTOR.spad" 2153113 2153124 2153364 2153391) (-1156 "VECTOR2.spad" 2151740 2151753 2153103 2153108) (-1155 "VECTCAT.spad" 2149628 2149639 2151696 2151735) (-1154 "VECTCAT.spad" 2147337 2147350 2149407 2149412) (-1153 "VARIABLE.spad" 2147117 2147132 2147327 2147332) (-1152 "UTYPE.spad" 2146751 2146760 2147097 2147112) (-1151 "UTSODETL.spad" 2146044 2146068 2146707 2146712) (-1150 "UTSODE.spad" 2144232 2144252 2146034 2146039) (-1149 "UTS.spad" 2139021 2139049 2142699 2142796) (-1148 "UTSCAT.spad" 2136472 2136488 2138919 2139016) (-1147 "UTSCAT.spad" 2133567 2133585 2136016 2136021) (-1146 "UTS2.spad" 2133160 2133195 2133557 2133562) (-1145 "URAGG.spad" 2127782 2127793 2133140 2133155) (-1144 "URAGG.spad" 2122378 2122391 2127738 2127743) (-1143 "UPXSSING.spad" 2120024 2120050 2121462 2121595) (-1142 "UPXS.spad" 2117051 2117079 2118156 2118305) (-1141 "UPXSCONS.spad" 2114808 2114828 2115183 2115332) (-1140 "UPXSCCA.spad" 2113266 2113286 2114654 2114803) (-1139 "UPXSCCA.spad" 2111866 2111888 2113256 2113261) (-1138 "UPXSCAT.spad" 2110447 2110463 2111712 2111861) (-1137 "UPXS2.spad" 2109988 2110041 2110437 2110442) (-1136 "UPSQFREE.spad" 2108400 2108414 2109978 2109983) (-1135 "UPSCAT.spad" 2105993 2106017 2108298 2108395) (-1134 "UPSCAT.spad" 2103292 2103318 2105599 2105604) (-1133 "UPOLYC.spad" 2098270 2098281 2103134 2103287) (-1132 "UPOLYC.spad" 2093140 2093153 2098006 2098011) (-1131 "UPOLYC2.spad" 2092609 2092628 2093130 2093135) (-1130 "UP.spad" 2089659 2089674 2090167 2090320) (-1129 "UPMP.spad" 2088549 2088562 2089649 2089654) (-1128 "UPDIVP.spad" 2088112 2088126 2088539 2088544) (-1127 "UPDECOMP.spad" 2086349 2086363 2088102 2088107) (-1126 "UPCDEN.spad" 2085556 2085572 2086339 2086344) (-1125 "UP2.spad" 2084918 2084939 2085546 2085551) (-1124 "UNISEG.spad" 2084271 2084282 2084837 2084842) (-1123 "UNISEG2.spad" 2083764 2083777 2084227 2084232) (-1122 "UNIFACT.spad" 2082865 2082877 2083754 2083759) (-1121 "ULS.spad" 2073424 2073452 2074517 2074946) (-1120 "ULSCONS.spad" 2067467 2067487 2067839 2067988) (-1119 "ULSCCAT.spad" 2065064 2065084 2067287 2067462) (-1118 "ULSCCAT.spad" 2062795 2062817 2065020 2065025) (-1117 "ULSCAT.spad" 2061011 2061027 2062641 2062790) (-1116 "ULS2.spad" 2060523 2060576 2061001 2061006) (-1115 "UFD.spad" 2059588 2059597 2060449 2060518) (-1114 "UFD.spad" 2058715 2058726 2059578 2059583) (-1113 "UDVO.spad" 2057562 2057571 2058705 2058710) (-1112 "UDPO.spad" 2054989 2055000 2057518 2057523) (-1111 "TYPE.spad" 2054911 2054920 2054969 2054984) (-1110 "TWOFACT.spad" 2053561 2053576 2054901 2054906) (-1109 "TUPLE.spad" 2052947 2052958 2053460 2053465) (-1108 "TUBETOOL.spad" 2049784 2049793 2052937 2052942) (-1107 "TUBE.spad" 2048425 2048442 2049774 2049779) (-1106 "TS.spad" 2047014 2047030 2047990 2048087) (-1105 "TSETCAT.spad" 2034129 2034146 2046970 2047009) (-1104 "TSETCAT.spad" 2021242 2021261 2034085 2034090) (-1103 "TRMANIP.spad" 2015608 2015625 2020948 2020953) (-1102 "TRIMAT.spad" 2014567 2014592 2015598 2015603) (-1101 "TRIGMNIP.spad" 2013084 2013101 2014557 2014562) (-1100 "TRIGCAT.spad" 2012596 2012605 2013074 2013079) (-1099 "TRIGCAT.spad" 2012106 2012117 2012586 2012591) (-1098 "TREE.spad" 2010677 2010688 2011713 2011740) (-1097 "TRANFUN.spad" 2010508 2010517 2010667 2010672) (-1096 "TRANFUN.spad" 2010337 2010348 2010498 2010503) (-1095 "TOPSP.spad" 2010011 2010020 2010327 2010332) (-1094 "TOOLSIGN.spad" 2009674 2009685 2010001 2010006) (-1093 "TEXTFILE.spad" 2008231 2008240 2009664 2009669) (-1092 "TEX.spad" 2005248 2005257 2008221 2008226) (-1091 "TEX1.spad" 2004804 2004815 2005238 2005243) (-1090 "TEMUTL.spad" 2004359 2004368 2004794 2004799) (-1089 "TBCMPPK.spad" 2002452 2002475 2004349 2004354) (-1088 "TBAGG.spad" 2001476 2001499 2002420 2002447) (-1087 "TBAGG.spad" 2000520 2000545 2001466 2001471) (-1086 "TANEXP.spad" 1999896 1999907 2000510 2000515) (-1085 "TABLE.spad" 1998307 1998330 1998577 1998604) (-1084 "TABLEAU.spad" 1997788 1997799 1998297 1998302) (-1083 "TABLBUMP.spad" 1994571 1994582 1997778 1997783) (-1082 "SYSSOLP.spad" 1992044 1992055 1994561 1994566) (-1081 "syntax.spad" 1988426 1988435 1992034 1992039) (-1080 "SYMTAB.spad" 1986482 1986491 1988416 1988421) (-1079 "SYMS.spad" 1982467 1982476 1986472 1986477) (-1078 "SYMPOLY.spad" 1981477 1981488 1981559 1981686) (-1077 "SYMFUNC.spad" 1980952 1980963 1981467 1981472) (-1076 "SYMBOL.spad" 1978288 1978297 1980942 1980947) (-1075 "SWITCH.spad" 1975045 1975054 1978278 1978283) (-1074 "SUTS.spad" 1971944 1971972 1973512 1973609) (-1073 "SUPXS.spad" 1968958 1968986 1970076 1970225) (-1072 "SUP.spad" 1965735 1965746 1966516 1966669) (-1071 "SUPFRACF.spad" 1964840 1964858 1965725 1965730) (-1070 "SUP2.spad" 1964230 1964243 1964830 1964835) (-1069 "SUMRF.spad" 1963196 1963207 1964220 1964225) (-1068 "SUMFS.spad" 1962829 1962846 1963186 1963191) (-1067 "SULS.spad" 1953375 1953403 1954481 1954910) (-1066 "SUCH.spad" 1953055 1953070 1953365 1953370) (-1065 "SUBSPACE.spad" 1945062 1945077 1953045 1953050) (-1064 "SUBRESP.spad" 1944222 1944236 1945018 1945023) (-1063 "STTF.spad" 1940321 1940337 1944212 1944217) (-1062 "STTFNC.spad" 1936789 1936805 1940311 1940316) (-1061 "STTAYLOR.spad" 1929187 1929198 1936670 1936675) (-1060 "STRTBL.spad" 1927692 1927709 1927841 1927868) (-1059 "STRING.spad" 1927101 1927110 1927115 1927142) (-1058 "STRICAT.spad" 1926877 1926886 1927057 1927096) (-1057 "STREAM.spad" 1923645 1923656 1926402 1926417) (-1056 "STREAM3.spad" 1923190 1923205 1923635 1923640) (-1055 "STREAM2.spad" 1922258 1922271 1923180 1923185) (-1054 "STREAM1.spad" 1921962 1921973 1922248 1922253) (-1053 "STINPROD.spad" 1920868 1920884 1921952 1921957) (-1052 "STEP.spad" 1920069 1920078 1920858 1920863) (-1051 "STBL.spad" 1918595 1918623 1918762 1918777) (-1050 "STAGG.spad" 1917660 1917671 1918575 1918590) (-1049 "STAGG.spad" 1916733 1916746 1917650 1917655) (-1048 "STACK.spad" 1916084 1916095 1916340 1916367) (-1047 "SREGSET.spad" 1913788 1913805 1915730 1915757) (-1046 "SRDCMPK.spad" 1912333 1912353 1913778 1913783) (-1045 "SRAGG.spad" 1907418 1907427 1912289 1912328) (-1044 "SRAGG.spad" 1902535 1902546 1907408 1907413) (-1043 "SQMATRIX.spad" 1900161 1900179 1901069 1901156) (-1042 "SPLTREE.spad" 1894713 1894726 1899597 1899624) (-1041 "SPLNODE.spad" 1891301 1891314 1894703 1894708) (-1040 "SPFCAT.spad" 1890078 1890087 1891291 1891296) (-1039 "SPECOUT.spad" 1888628 1888637 1890068 1890073) (-1038 "spad-parser.spad" 1888093 1888102 1888618 1888623) (-1037 "SPACEC.spad" 1872106 1872117 1888083 1888088) (-1036 "SPACE3.spad" 1871882 1871893 1872096 1872101) (-1035 "SORTPAK.spad" 1871427 1871440 1871838 1871843) (-1034 "SOLVETRA.spad" 1869184 1869195 1871417 1871422) (-1033 "SOLVESER.spad" 1867704 1867715 1869174 1869179) (-1032 "SOLVERAD.spad" 1863714 1863725 1867694 1867699) (-1031 "SOLVEFOR.spad" 1862134 1862152 1863704 1863709) (-1030 "SNTSCAT.spad" 1861722 1861739 1862090 1862129) (-1029 "SMTS.spad" 1859982 1860008 1861287 1861384) (-1028 "SMP.spad" 1857424 1857444 1857814 1857941) (-1027 "SMITH.spad" 1856267 1856292 1857414 1857419) (-1026 "SMATCAT.spad" 1854365 1854395 1856199 1856262) (-1025 "SMATCAT.spad" 1852407 1852439 1854243 1854248) (-1024 "SKAGG.spad" 1851356 1851367 1852363 1852402) (-1023 "SINT.spad" 1849664 1849673 1851222 1851351) (-1022 "SIMPAN.spad" 1849392 1849401 1849654 1849659) (-1021 "SIGNRF.spad" 1848500 1848511 1849382 1849387) (-1020 "SIGNEF.spad" 1847769 1847786 1848490 1848495) (-1019 "SHP.spad" 1845687 1845702 1847725 1847730) (-1018 "SHDP.spad" 1837077 1837104 1837586 1837715) (-1017 "SGROUP.spad" 1836543 1836552 1837067 1837072) (-1016 "SGROUP.spad" 1836007 1836018 1836533 1836538) (-1015 "SGCF.spad" 1828888 1828897 1835997 1836002) (-1014 "SFRTCAT.spad" 1827804 1827821 1828844 1828883) (-1013 "SFRGCD.spad" 1826867 1826887 1827794 1827799) (-1012 "SFQCMPK.spad" 1821504 1821524 1826857 1826862) (-1011 "SFORT.spad" 1820939 1820953 1821494 1821499) (-1010 "SEXOF.spad" 1820782 1820822 1820929 1820934) (-1009 "SEX.spad" 1820674 1820683 1820772 1820777) (-1008 "SEXCAT.spad" 1817778 1817818 1820664 1820669) (-1007 "SET.spad" 1816078 1816089 1817199 1817238) (-1006 "SETMN.spad" 1814512 1814529 1816068 1816073) (-1005 "SETCAT.spad" 1813997 1814006 1814502 1814507) (-1004 "SETCAT.spad" 1813480 1813491 1813987 1813992) (-1003 "SETAGG.spad" 1810003 1810014 1813448 1813475) (-1002 "SETAGG.spad" 1806546 1806559 1809993 1809998) (-1001 "SEGXCAT.spad" 1805658 1805671 1806526 1806541) (-1000 "SEG.spad" 1805471 1805482 1805577 1805582) (-999 "SEGCAT.spad" 1804291 1804301 1805451 1805466) (-998 "SEGBIND.spad" 1803364 1803374 1804246 1804251) (-997 "SEGBIND2.spad" 1803061 1803073 1803354 1803359) (-996 "SEG2.spad" 1802487 1802499 1803017 1803022) (-995 "SDVAR.spad" 1801764 1801774 1802477 1802482) (-994 "SDPOL.spad" 1799163 1799173 1799453 1799580) (-993 "SCPKG.spad" 1797243 1797253 1799153 1799158) (-992 "SCACHE.spad" 1795926 1795936 1797233 1797238) (-991 "SAOS.spad" 1795799 1795807 1795916 1795921) (-990 "SAERFFC.spad" 1795513 1795532 1795789 1795794) (-989 "SAE.spad" 1793692 1793707 1794302 1794437) (-988 "SAEFACT.spad" 1793394 1793413 1793682 1793687) (-987 "RURPK.spad" 1791036 1791051 1793384 1793389) (-986 "RULESET.spad" 1790478 1790501 1791026 1791031) (-985 "RULE.spad" 1788683 1788706 1790468 1790473) (-984 "RULECOLD.spad" 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"RMATCAT.spad" 1698633 1698665 1703057 1703062) (-964 "RINTERP.spad" 1698522 1698541 1698623 1698628) (-963 "RING.spad" 1697880 1697888 1698502 1698517) (-962 "RING.spad" 1697246 1697256 1697870 1697875) (-961 "RIDIST.spad" 1696631 1696639 1697236 1697241) (-960 "RGCHAIN.spad" 1695211 1695226 1696116 1696143) (-959 "RF.spad" 1692826 1692836 1695201 1695206) (-958 "RFFACTOR.spad" 1692289 1692299 1692816 1692821) (-957 "RFFACT.spad" 1692025 1692036 1692279 1692284) (-956 "RFDIST.spad" 1691014 1691022 1692015 1692020) (-955 "RETSOL.spad" 1690432 1690444 1691004 1691009) (-954 "RETRACT.spad" 1689782 1689792 1690422 1690427) (-953 "RETRACT.spad" 1689130 1689142 1689772 1689777) (-952 "RESULT.spad" 1687191 1687199 1687777 1687804) (-951 "RESRING.spad" 1686539 1686585 1687129 1687186) (-950 "RESLATC.spad" 1685864 1685874 1686529 1686534) (-949 "REPSQ.spad" 1685594 1685604 1685854 1685859) (-948 "REP.spad" 1683147 1683155 1685584 1685589) (-947 "REPDB.spad" 1682853 1682863 1683137 1683142) 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(-364 "FORMULA.spad" 627992 628000 630644 630649) (-363 "FORMULA1.spad" 627471 627481 627982 627987) (-362 "FORDER.spad" 627162 627186 627461 627466) (-361 "FOP.spad" 626363 626371 627152 627157) (-360 "FNLA.spad" 625787 625809 626331 626358) (-359 "FNCAT.spad" 624115 624123 625777 625782) (-358 "FNAME.spad" 624007 624015 624105 624110) (-357 "FMTC.spad" 623805 623813 623933 624002) (-356 "FMONOID.spad" 620860 620870 623761 623766) (-355 "FM.spad" 620555 620567 620794 620821) (-354 "FMFUN.spad" 617575 617583 620535 620550) (-353 "FMC.spad" 616617 616625 617555 617570) (-352 "FMCAT.spad" 614271 614289 616585 616612) (-351 "FM1.spad" 613628 613640 614205 614232) (-350 "FLOATRP.spad" 611349 611363 613618 613623) (-349 "FLOAT.spad" 604513 604521 611215 611344) (-348 "FLOATCP.spad" 601930 601944 604503 604508) (-347 "FLINEXP.spad" 601642 601652 601910 601925) (-346 "FLINEXP.spad" 601308 601320 601578 601583) (-345 "FLASORT.spad" 600628 600640 601298 601303) (-344 "FLALG.spad" 598274 598293 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"FFNBX.spad" 544918 544938 546122 546215) (-322 "FFNBP.spad" 543431 543448 544634 544727) (-321 "FFNB.spad" 541896 541917 543112 543205) (-320 "FFINTBAS.spad" 539310 539329 541886 541891) (-319 "FFIELDC.spad" 536885 536893 539212 539305) (-318 "FFIELDC.spad" 534546 534556 536875 536880) (-317 "FFHOM.spad" 533294 533311 534536 534541) (-316 "FFF.spad" 530729 530740 533284 533289) (-315 "FFCGX.spad" 529576 529596 530445 530538) (-314 "FFCGP.spad" 528465 528485 529292 529385) (-313 "FFCG.spad" 527257 527278 528146 528239) (-312 "FFCAT.spad" 520158 520180 527096 527252) (-311 "FFCAT.spad" 513138 513162 520078 520083) (-310 "FFCAT2.spad" 512883 512923 513128 513133) (-309 "FEXPR.spad" 504596 504642 512643 512682) (-308 "FEVALAB.spad" 504302 504312 504586 504591) (-307 "FEVALAB.spad" 503793 503805 504079 504084) (-306 "FDIV.spad" 503235 503259 503783 503788) (-305 "FDIVCAT.spad" 501277 501301 503225 503230) (-304 "FDIVCAT.spad" 499317 499343 501267 501272) (-303 "FDIV2.spad" 498971 499011 499307 499312) (-302 "FCPAK1.spad" 497524 497532 498961 498966) (-301 "FCOMP.spad" 496903 496913 497514 497519) (-300 "FC.spad" 486728 486736 496893 496898) (-299 "FAXF.spad" 479663 479677 486630 486723) (-298 "FAXF.spad" 472650 472666 479619 479624) (-297 "FARRAY.spad" 470796 470806 471833 471860) (-296 "FAMR.spad" 468916 468928 470694 470791) (-295 "FAMR.spad" 467020 467034 468800 468805) (-294 "FAMONOID.spad" 466670 466680 466974 466979) (-293 "FAMONC.spad" 464892 464904 466660 466665) (-292 "FAGROUP.spad" 464498 464508 464788 464815) (-291 "FACUTIL.spad" 462694 462711 464488 464493) (-290 "FACTFUNC.spad" 461870 461880 462684 462689) (-289 "EXPUPXS.spad" 458703 458726 460002 460151) (-288 "EXPRTUBE.spad" 455931 455939 458693 458698) (-287 "EXPRODE.spad" 452803 452819 455921 455926) (-286 "EXPR.spad" 448105 448115 448819 449222) (-285 "EXPR2UPS.spad" 444197 444210 448095 448100) (-284 "EXPR2.spad" 443900 443912 444187 444192) (-283 "EXPEXPAN.spad" 440841 440866 441475 441568) (-282 "EXIT.spad" 440512 440520 440831 440836) (-281 "EVALCYC.spad" 439970 439984 440502 440507) (-280 "EVALAB.spad" 439534 439544 439960 439965) (-279 "EVALAB.spad" 439096 439108 439524 439529) (-278 "EUCDOM.spad" 436638 436646 439022 439091) (-277 "EUCDOM.spad" 434242 434252 436628 436633) (-276 "ESTOOLS.spad" 426082 426090 434232 434237) (-275 "ESTOOLS2.spad" 425683 425697 426072 426077) (-274 "ESTOOLS1.spad" 425368 425379 425673 425678) (-273 "ES.spad" 417915 417923 425358 425363) (-272 "ES.spad" 410370 410380 417815 417820) (-271 "ESCONT.spad" 407143 407151 410360 410365) (-270 "ESCONT1.spad" 406892 406904 407133 407138) (-269 "ES2.spad" 406387 406403 406882 406887) (-268 "ES1.spad" 405953 405969 406377 406382) (-267 "ERROR.spad" 403274 403282 405943 405948) (-266 "EQTBL.spad" 401746 401768 401955 401982) (-265 "EQ.spad" 396630 396640 399429 399538) (-264 "EQ2.spad" 396346 396358 396620 396625) (-263 "EP.spad" 392660 392670 396336 396341) (-262 "ENTIRER.spad" 392328 392336 392604 392655) (-261 "EMR.spad" 391529 391570 392254 392323) (-260 "ELTAGG.spad" 389769 389788 391519 391524) (-259 "ELTAGG.spad" 387973 387994 389725 389730) (-258 "ELTAB.spad" 387420 387438 387963 387968) (-257 "ELFUTS.spad" 386799 386818 387410 387415) (-256 "ELEMFUN.spad" 386488 386496 386789 386794) (-255 "ELEMFUN.spad" 386175 386185 386478 386483) (-254 "ELAGG.spad" 384106 384116 386143 386170) (-253 "ELAGG.spad" 381986 381998 384025 384030) (-252 "EFUPXS.spad" 378762 378792 381942 381947) (-251 "EFULS.spad" 375598 375621 378718 378723) (-250 "EFSTRUC.spad" 373553 373569 375588 375593) (-249 "EF.spad" 368319 368335 373543 373548) (-248 "EAB.spad" 366595 366603 368309 368314) (-247 "E04UCFA.spad" 366131 366139 366585 366590) (-246 "E04NAFA.spad" 365708 365716 366121 366126) (-245 "E04MBFA.spad" 365288 365296 365698 365703) (-244 "E04JAFA.spad" 364824 364832 365278 365283) (-243 "E04GCFA.spad" 364360 364368 364814 364819) (-242 "E04FDFA.spad" 363896 363904 364350 364355) (-241 "E04DGFA.spad" 363432 363440 363886 363891) (-240 "E04AGNT.spad" 359274 359282 363422 363427) (-239 "DVARCAT.spad" 355959 355969 359264 359269) (-238 "DVARCAT.spad" 352642 352654 355949 355954) (-237 "DSMP.spad" 350076 350090 350381 350508) (-236 "DROPT.spad" 344021 344029 350066 350071) (-235 "DROPT1.spad" 343684 343694 344011 344016) (-234 "DROPT0.spad" 338511 338519 343674 343679) (-233 "DRAWPT.spad" 336666 336674 338501 338506) (-232 "DRAW.spad" 329266 329279 336656 336661) (-231 "DRAWHACK.spad" 328574 328584 329256 329261) (-230 "DRAWCX.spad" 326016 326024 328564 328569) (-229 "DRAWCURV.spad" 325553 325568 326006 326011) (-228 "DRAWCFUN.spad" 314725 314733 325543 325548) (-227 "DQAGG.spad" 312881 312891 314681 314720) (-226 "DPOLCAT.spad" 308222 308238 312749 312876) (-225 "DPOLCAT.spad" 303649 303667 308178 308183) (-224 "DPMO.spad" 297636 297652 297774 298070) (-223 "DPMM.spad" 291636 291654 291761 292057) (-222 "domain.spad" 291152 291160 291626 291631) (-221 "DMP.spad" 288377 288392 288949 289076) (-220 "DLP.spad" 287725 287735 288367 288372) (-219 "DLIST.spad" 286137 286147 286908 286935) (-218 "DLAGG.spad" 284538 284548 286117 286132) (-217 "DIVRING.spad" 283985 283993 284482 284533) (-216 "DIVRING.spad" 283476 283486 283975 283980) (-215 "DISPLAY.spad" 281656 281664 283466 283471) (-214 "DIRPROD.spad" 272915 272931 273555 273684) (-213 "DIRPROD2.spad" 271723 271741 272905 272910) (-212 "DIRPCAT.spad" 270655 270671 271577 271718) (-211 "DIRPCAT.spad" 269327 269345 270251 270256) (-210 "DIOSP.spad" 268152 268160 269317 269322) (-209 "DIOPS.spad" 267124 267134 268120 268147) (-208 "DIOPS.spad" 266082 266094 267080 267085) (-207 "DIFRING.spad" 265374 265382 266062 266077) (-206 "DIFRING.spad" 264674 264684 265364 265369) (-205 "DIFEXT.spad" 263833 263843 264654 264669) (-204 "DIFEXT.spad" 262909 262921 263732 263737) (-203 "DIAGG.spad" 262527 262537 262877 262904) (-202 "DIAGG.spad" 262165 262177 262517 262522) (-201 "DHMATRIX.spad" 260469 260479 261622 261649) (-200 "DFSFUN.spad" 253877 253885 260459 260464) (-199 "DFLOAT.spad" 250400 250408 253767 253872) (-198 "DFINTTLS.spad" 248609 248625 250390 250395) (-197 "DERHAM.spad" 246519 246551 248589 248604) (-196 "DEQUEUE.spad" 245837 245847 246126 246153) (-195 "DEGRED.spad" 245452 245466 245827 245832) (-194 "DEFINTRF.spad" 242977 242987 245442 245447) (-193 "DEFINTEF.spad" 241473 241489 242967 242972) (-192 "DECIMAL.spad" 239357 239365 239943 240036) (-191 "DDFACT.spad" 237156 237173 239347 239352) (-190 "DBLRESP.spad" 236754 236778 237146 237151) (-189 "DBASE.spad" 235326 235336 236744 236749) (-188 "D03FAFA.spad" 235154 235162 235316 235321) (-187 "D03EEFA.spad" 234974 234982 235144 235149) (-186 "D03AGNT.spad" 234054 234062 234964 234969) (-185 "D02EJFA.spad" 233516 233524 234044 234049) (-184 "D02CJFA.spad" 232994 233002 233506 233511) (-183 "D02BHFA.spad" 232484 232492 232984 232989) (-182 "D02BBFA.spad" 231974 231982 232474 232479) (-181 "D02AGNT.spad" 226778 226786 231964 231969) (-180 "D01WGTS.spad" 225097 225105 226768 226773) (-179 "D01TRNS.spad" 225074 225082 225087 225092) (-178 "D01GBFA.spad" 224596 224604 225064 225069) (-177 "D01FCFA.spad" 224118 224126 224586 224591) (-176 "D01ASFA.spad" 223586 223594 224108 224113) (-175 "D01AQFA.spad" 223032 223040 223576 223581) (-174 "D01APFA.spad" 222456 222464 223022 223027) (-173 "D01ANFA.spad" 221950 221958 222446 222451) (-172 "D01AMFA.spad" 221460 221468 221940 221945) (-171 "D01ALFA.spad" 221000 221008 221450 221455) (-170 "D01AKFA.spad" 220526 220534 220990 220995) (-169 "D01AJFA.spad" 220049 220057 220516 220521) (-168 "D01AGNT.spad" 216108 216116 220039 220044) (-167 "CYCLOTOM.spad" 215614 215622 216098 216103) (-166 "CYCLES.spad" 212446 212454 215604 215609) (-165 "CVMP.spad" 211863 211873 212436 212441) (-164 "CTRIGMNP.spad" 210353 210369 211853 211858) (-163 "CSTTOOLS.spad" 209596 209609 210343 210348) (-162 "CRFP.spad" 203300 203313 209586 209591) (-161 "CRAPACK.spad" 202343 202353 203290 203295) (-160 "CPMATCH.spad" 201843 201858 202268 202273) (-159 "CPIMA.spad" 201548 201567 201833 201838) (-158 "COORDSYS.spad" 196441 196451 201538 201543) (-157 "CONTFRAC.spad" 192053 192063 196343 196436) (-156 "COMRING.spad" 191727 191735 191991 192048) (-155 "COMPPROP.spad" 191241 191249 191717 191722) (-154 "COMPLPAT.spad" 191008 191023 191231 191236) (-153 "COMPLEX.spad" 185041 185051 185285 185546) (-152 "COMPLEX2.spad" 184754 184766 185031 185036) (-151 "COMPFACT.spad" 184356 184370 184744 184749) (-150 "COMPCAT.spad" 182412 182422 184078 184351) (-149 "COMPCAT.spad" 180175 180187 181843 181848) (-148 "COMMUPC.spad" 179921 179939 180165 180170) (-147 "COMMONOP.spad" 179454 179462 179911 179916) (-146 "COMM.spad" 179263 179271 179444 179449) (-145 "COMBOPC.spad" 178168 178176 179253 179258) (-144 "COMBINAT.spad" 176913 176923 178158 178163) (-143 "COMBF.spad" 174281 174297 176903 176908) (-142 "COLOR.spad" 173118 173126 174271 174276) (-141 "CMPLXRT.spad" 172827 172844 173108 173113) (-140 "CLIP.spad" 168919 168927 172817 172822) (-139 "CLIF.spad" 167558 167574 168875 168914) (-138 "CLAGG.spad" 164033 164043 167538 167553) (-137 "CLAGG.spad" 160389 160401 163896 163901) (-136 "CINTSLPE.spad" 159714 159727 160379 160384) (-135 "CHVAR.spad" 157792 157814 159704 159709) (-134 "CHARZ.spad" 157707 157715 157772 157787) (-133 "CHARPOL.spad" 157215 157225 157697 157702) (-132 "CHARNZ.spad" 156968 156976 157195 157210) (-131 "CHAR.spad" 154858 154866 156958 156963) (-130 "CFCAT.spad" 154174 154182 154848 154853) (-129 "CDEN.spad" 153332 153346 154164 154169) (-128 "CCLASS.spad" 151481 151489 152743 152782) (-127 "CARTEN.spad" 146584 146608 151471 151476) (-126 "CARTEN2.spad" 145970 145997 146574 146579) (-125 "CARD.spad" 143259 143267 145944 145965) (-124 "CACHSET.spad" 142881 142889 143249 143254) (-123 "CABMON.spad" 142434 142442 142871 142876) (-122 "BTREE.spad" 141503 141513 142041 142068) (-121 "BTOURN.spad" 140506 140516 141110 141137) (-120 "BTCAT.spad" 139882 139892 140462 140501) (-119 "BTCAT.spad" 139290 139302 139872 139877) (-118 "BTAGG.spad" 138306 138314 139246 139285) (-117 "BTAGG.spad" 137354 137364 138296 138301) (-116 "BSTREE.spad" 136089 136099 136961 136988) (-115 "BRILL.spad" 134284 134295 136079 136084) (-114 "BRAGG.spad" 133198 133208 134264 134279) (-113 "BRAGG.spad" 132086 132098 133154 133159) (-112 "BPADICRT.spad" 130070 130082 130325 130418) (-111 "BPADIC.spad" 129734 129746 129996 130065) (-110 "BOUNDZRO.spad" 129390 129407 129724 129729) (-109 "BOP.spad" 124854 124862 129380 129385) (-108 "BOP1.spad" 122240 122250 124810 124815) (-107 "BOOLEAN.spad" 121098 121106 122230 122235) (-106 "BMODULE.spad" 120810 120822 121066 121093) (-105 "BITS.spad" 120229 120237 120446 120473) (-104 "BINFILE.spad" 119572 119580 120219 120224) (-103 "BINARY.spad" 117465 117473 118042 118135) (-102 "BGAGG.spad" 116650 116660 117433 117460) (-101 "BGAGG.spad" 115855 115867 116640 116645) (-100 "BFUNCT.spad" 115419 115427 115835 115850) (-99 "BEZOUT.spad" 114554 114580 115369 115374) (-98 "BBTREE.spad" 111374 111383 114161 114188) (-97 "BASTYPE.spad" 111047 111054 111364 111369) (-96 "BASTYPE.spad" 110718 110727 111037 111042) (-95 "BALFACT.spad" 110158 110170 110708 110713) (-94 "AUTOMOR.spad" 109605 109614 110138 110153) (-93 "ATTREG.spad" 106324 106331 109357 109600) (-92 "ATTRBUT.spad" 102347 102354 106304 106319) (-91 "ATRIG.spad" 101817 101824 102337 102342) (-90 "ATRIG.spad" 101285 101294 101807 101812) (-89 "ASTACK.spad" 100618 100627 100892 100919) (-88 "ASSOCEQ.spad" 99418 99429 100574 100579) (-87 "ASP9.spad" 98499 98512 99408 99413) (-86 "ASP8.spad" 97542 97555 98489 98494) (-85 "ASP80.spad" 96864 96877 97532 97537) (-84 "ASP7.spad" 96024 96037 96854 96859) (-83 "ASP78.spad" 95475 95488 96014 96019) (-82 "ASP77.spad" 94844 94857 95465 95470) (-81 "ASP74.spad" 93936 93949 94834 94839) (-80 "ASP73.spad" 93207 93220 93926 93931) (-79 "ASP6.spad" 91839 91852 93197 93202) (-78 "ASP55.spad" 90348 90361 91829 91834) (-77 "ASP50.spad" 88165 88178 90338 90343) (-76 "ASP4.spad" 87460 87473 88155 88160) (-75 "ASP49.spad" 86459 86472 87450 87455) (-74 "ASP42.spad" 84866 84905 86449 86454) (-73 "ASP41.spad" 83445 83484 84856 84861) (-72 "ASP35.spad" 82433 82446 83435 83440) (-71 "ASP34.spad" 81734 81747 82423 82428) (-70 "ASP33.spad" 81294 81307 81724 81729) (-69 "ASP31.spad" 80434 80447 81284 81289) (-68 "ASP30.spad" 79326 79339 80424 80429) (-67 "ASP29.spad" 78792 78805 79316 79321) (-66 "ASP28.spad" 70065 70078 78782 78787) (-65 "ASP27.spad" 68962 68975 70055 70060) (-64 "ASP24.spad" 68049 68062 68952 68957) (-63 "ASP20.spad" 67265 67278 68039 68044) (-62 "ASP1.spad" 66646 66659 67255 67260) (-61 "ASP19.spad" 61332 61345 66636 66641) (-60 "ASP12.spad" 60746 60759 61322 61327) (-59 "ASP10.spad" 60017 60030 60736 60741) (-58 "ARRAY2.spad" 59377 59386 59624 59651) (-57 "ARRAY1.spad" 58212 58221 58560 58587) (-56 "ARRAY12.spad" 56881 56892 58202 58207) (-55 "ARR2CAT.spad" 52531 52552 56837 56876) (-54 "ARR2CAT.spad" 48213 48236 52521 52526) (-53 "APPRULE.spad" 47457 47479 48203 48208) (-52 "APPLYORE.spad" 47072 47085 47447 47452) (-51 "ANY.spad" 45414 45421 47062 47067) (-50 "ANY1.spad" 44485 44494 45404 45409) (-49 "ANTISYM.spad" 42924 42940 44465 44480) (-48 "ANON.spad" 42837 42844 42914 42919) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-1189 NIL 2226417 2226422 2226427 2226432) (-3 NIL 2226397 2226402 2226407 2226412) (-2 NIL 2226377 2226382 2226387 2226392) (-1 NIL 2226357 2226362 2226367 2226372) (0 NIL 2226337 2226342 2226347 2226352) (-1184 "ZMOD.spad" 2226146 2226159 2226275 2226332) (-1183 "ZLINDEP.spad" 2225190 2225201 2226136 2226141) (-1182 "ZDSOLVE.spad" 2215039 2215061 2225180 2225185) (-1181 "YSTREAM.spad" 2214532 2214543 2215029 2215034) (-1180 "XRPOLY.spad" 2213752 2213772 2214388 2214457) (-1179 "XPR.spad" 2211481 2211494 2213470 2213569) (-1178 "XPOLY.spad" 2211036 2211047 2211337 2211406) (-1177 "XPOLYC.spad" 2210353 2210369 2210962 2211031) (-1176 "XPBWPOLY.spad" 2208790 2208810 2210133 2210202) (-1175 "XF.spad" 2207251 2207266 2208692 2208785) (-1174 "XF.spad" 2205692 2205709 2207135 2207140) (-1173 "XFALG.spad" 2202716 2202732 2205618 2205687) (-1172 "XEXPPKG.spad" 2201967 2201993 2202706 2202711) (-1171 "XDPOLY.spad" 2201581 2201597 2201823 2201892) (-1170 "XALG.spad" 2201179 2201190 2201537 2201576) (-1169 "WUTSET.spad" 2197018 2197035 2200825 2200852) (-1168 "WP.spad" 2196032 2196076 2196876 2196943) (-1167 "WFFINTBS.spad" 2193595 2193617 2196022 2196027) (-1166 "WEIER.spad" 2191809 2191820 2193585 2193590) (-1165 "VSPACE.spad" 2191482 2191493 2191777 2191804) (-1164 "VSPACE.spad" 2191175 2191188 2191472 2191477) (-1163 "VOID.spad" 2190765 2190774 2191165 2191170) (-1162 "VIEW.spad" 2188387 2188396 2190755 2190760) (-1161 "VIEWDEF.spad" 2183584 2183593 2188377 2188382) (-1160 "VIEW3D.spad" 2167419 2167428 2183574 2183579) (-1159 "VIEW2D.spad" 2155156 2155165 2167409 2167414) (-1158 "VECTOR.spad" 2153833 2153844 2154084 2154111) (-1157 "VECTOR2.spad" 2152460 2152473 2153823 2153828) (-1156 "VECTCAT.spad" 2150348 2150359 2152416 2152455) (-1155 "VECTCAT.spad" 2148057 2148070 2150127 2150132) (-1154 "VARIABLE.spad" 2147837 2147852 2148047 2148052) (-1153 "UTYPE.spad" 2147471 2147480 2147817 2147832) (-1152 "UTSODETL.spad" 2146764 2146788 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(-487 "INBFF.spad" 843220 843231 847440 847445) (-486 "IMATRIX.spad" 842165 842191 842677 842704) (-485 "IMATQF.spad" 841259 841303 842121 842126) (-484 "IMATLIN.spad" 839864 839888 841215 841220) (-483 "ILIST.spad" 838520 838535 839047 839074) (-482 "IIARRAY2.spad" 837908 837946 838127 838154) (-481 "IFF.spad" 837318 837334 837589 837682) (-480 "IFARRAY.spad" 834805 834820 836501 836528) (-479 "IFAMON.spad" 834667 834684 834761 834766) (-478 "IEVALAB.spad" 834056 834068 834657 834662) (-477 "IEVALAB.spad" 833443 833457 834046 834051) (-476 "IDPO.spad" 833241 833253 833433 833438) (-475 "IDPOAMS.spad" 832997 833009 833231 833236) (-474 "IDPOAM.spad" 832717 832729 832987 832992) (-473 "IDPC.spad" 831651 831663 832707 832712) (-472 "IDPAM.spad" 831396 831408 831641 831646) (-471 "IDPAG.spad" 831143 831155 831386 831391) (-470 "IDECOMP.spad" 828380 828398 831133 831138) (-469 "IDEAL.spad" 823303 823342 828315 828320) (-468 "ICDEN.spad" 822454 822470 823293 823298) (-467 "ICARD.spad" 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"FRNAAF2.spad" 656145 656163 656681 656686) (-384 "FRMOD.spad" 655540 655570 656077 656082) (-383 "FRIDEAL.spad" 654735 654756 655520 655535) (-382 "FRIDEAL2.spad" 654337 654369 654725 654730) (-381 "FRETRCT.spad" 653848 653858 654327 654332) (-380 "FRETRCT.spad" 653227 653239 653708 653713) (-379 "FRAMALG.spad" 651555 651568 653183 653222) (-378 "FRAMALG.spad" 649915 649930 651545 651550) (-377 "FRAC.spad" 647018 647028 647421 647594) (-376 "FRAC2.spad" 646621 646633 647008 647013) (-375 "FR2.spad" 645955 645967 646611 646616) (-374 "FPS.spad" 642764 642772 645845 645950) (-373 "FPS.spad" 639601 639611 642684 642689) (-372 "FPC.spad" 638643 638651 639503 639596) (-371 "FPC.spad" 637771 637781 638633 638638) (-370 "FPATMAB.spad" 637523 637533 637751 637766) (-369 "FPARFRAC.spad" 635996 636013 637513 637518) (-368 "FORTRAN.spad" 634496 634545 635986 635991) (-367 "FORT.spad" 633425 633433 634486 634491) (-366 "FORTFN.spad" 630585 630593 633405 633420) (-365 "FORTCAT.spad" 630259 630267 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T)) @@ -1184,11 +1186,11 @@ (|has| |#1| (-37 (-377 (-517)))) ((((-787)) . T)) ((((-493)) |has| |#1| (-558 (-493)))) -((((-787)) -3747 (|has| |#1| (-557 (-787))) (|has| |#1| (-1005)))) -(((|#2|) -3747 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-963))) (($) |has| |#2| (-156))) +((((-787)) -3786 (|has| |#1| (-557 (-787))) (|has| |#1| (-1006)))) +(((|#2|) -3786 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-964))) (($) |has| |#2| (-156))) (|has| $ (-134)) ((((-377 |#2|)) . T)) -((((-377 (-517))) |has| #0=(-377 |#2|) (-954 (-377 (-517)))) (((-517)) |has| #0# (-954 (-517))) ((#0#) . T)) +((((-377 (-517))) |has| #0=(-377 |#2|) (-955 (-377 (-517)))) (((-517)) |has| #0# (-955 (-517))) ((#0#) . T)) (((|#2| |#2|) . T)) (((|#4|) |has| |#4| (-156))) (|has| |#2| (-132)) @@ -1196,19 +1198,19 @@ (((|#3|) |has| |#3| (-156))) (|has| |#1| (-134)) (|has| |#1| (-132)) -(-3747 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3786 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) -(-3747 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3786 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) -(-3747 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3786 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-207)) -((((-1076) (-51)) . T)) +((((-1077) (-51)) . T)) ((((-787)) . T)) (((|#1| |#1|) . T)) -((((-1076)) |has| |#2| (-823 (-1076)))) +((((-1077)) |has| |#2| (-824 (-1077)))) ((((-517) (-107)) . T)) (|has| |#1| (-509)) (((|#2|) . T)) @@ -1224,44 +1226,44 @@ (|has| |#1| (-37 (-377 (-517)))) (((|#1|) . T)) ((((-787)) . T)) -((((-493)) . T) (((-815 (-517))) . T) (((-349)) . T) (((-199)) . T)) +((((-493)) . T) (((-816 (-517))) . T) (((-349)) . 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T) (((-517)) . T) (((-556 $)) . T)) @@ -1735,15 +1737,15 @@ (|has| |#1| (-779)) ((((-787)) . T)) (((|#1| (-489 |#2|) |#2|) . T)) -(((|#1| (-517) (-991)) . T)) -((((-833 |#1|)) . T)) +(((|#1| (-517) (-992)) . T)) +((((-834 |#1|)) . T)) ((((-787)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((|#1| (-377 (-517)) (-991)) . T)) -(((|#1| (-703) (-991)) . T)) +(((|#1| (-377 (-517)) (-992)) . T)) +(((|#1| (-703) (-992)) . T)) (((#0=(-377 |#2|) #0#) . T) ((#1=(-377 (-517)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-517)) -3747 (|has| (-377 (-517)) (-954 (-517))) (|has| |#1| (-954 (-517)))) (((-377 (-517))) . T)) +(((|#1|) . T) (((-517)) -3786 (|has| (-377 (-517)) (-955 (-517))) (|has| |#1| (-955 (-517)))) (((-377 (-517))) . T)) (((|#1| (-548 |#1| |#3|) (-548 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-156))) (((|#1|) . T)) @@ -1762,41 +1764,41 @@ ((((-632)) . 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T)) @@ -1817,17 +1819,17 @@ (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-779)) -((((-2 (|:| -2585 (-1059)) (|:| -1859 |#1|))) . T)) +((((-2 (|:| -2576 (-1060)) (|:| -1846 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-134)) (|has| |#1| (-132)) -((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) |has| (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)) (-280 (-2 (|:| -2585 |#1|) (|:| -1859 |#2|)))) ((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1005)))) +((((-2 (|:| -2576 |#1|) (|:| -1846 |#2|))) |has| (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)) (-280 (-2 (|:| -2576 |#1|) (|:| -1846 |#2|)))) ((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1006)))) (((|#2|) . T)) (((|#3|) . T)) ((((-111 |#1|)) . T)) (|has| |#1| (-338)) (|has| |#1| (-779)) -(((|#2|) . T) (((-377 (-517))) |has| |#1| (-954 (-377 (-517)))) (((-517)) |has| |#1| (-954 (-517))) ((|#1|) . T)) +(((|#2|) . T) (((-377 (-517))) |has| |#1| (-955 (-377 (-517)))) (((-517)) |has| |#1| (-955 (-517))) ((|#1|) . T)) ((((-111 |#1|)) . T)) (((|#2|) |has| |#2| (-156))) (((|#1|) . T)) @@ -1836,44 +1838,44 @@ (|has| |#1| (-333)) ((((-787)) . T)) ((((-787)) . T)) -((((-493)) |has| |#1| (-558 (-493))) (((-815 (-517))) |has| |#1| (-558 (-815 (-517)))) (((-815 (-349))) |has| |#1| (-558 (-815 (-349)))) (((-349)) . #0=(|has| |#1| (-939))) (((-199)) . #0#)) +((((-493)) |has| |#1| (-558 (-493))) (((-816 (-517))) |has| |#1| (-558 (-816 (-517)))) (((-816 (-349))) |has| |#1| (-558 (-816 (-349)))) (((-349)) . #0=(|has| |#1| (-940))) (((-199)) . #0#)) (((|#1|) |has| |#1| (-333))) ((((-787)) . T)) -((((-2 (|:| -2585 |#1|) (|:| -1859 |#2|))) . T)) +((((-2 (|:| -2576 |#1|) (|:| -1846 |#2|))) . T)) ((($ $) . T) (((-556 $) $) . T)) -(-3747 (|has| |#1| (-333)) (|has| |#1| (-509))) -((($) . T) (((-1143 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517))) . 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T) (((-377 (-517))) |has| #0# (-37 (-377 (-517)))) (($) . T)) ((((-517)) . T)) (|has| |#1| (-333)) -(-3747 (-12 (|has| (-1149 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) -(-3747 (-12 (|has| (-1149 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) +(-3786 (-12 (|has| (-1150 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) +(-3786 (-12 (|has| (-1150 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) (|has| |#1| (-333)) (|has| |#1| (-132)) (|has| |#1| (-134)) @@ -1886,39 +1888,39 @@ ((((-787)) . T)) ((((-517)) |has| |#2| (-579 (-517))) ((|#2|) . T)) (((|#2|) . T)) -(|has| |#1| (-1005)) +(|has| |#1| (-1006)) (((|#1| |#2|) . T)) (((|#1|) . 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. -97) T) ((-283 . -97) T) ((-261 . -23) T) ((-139 . -123) T) ((-356 . -659) T) ((-796 . -969) 130901) ((-833 . -557) 130883) ((-833 . -558) 130865) ((-796 . -106) 130803) ((-127 . -97) T) ((-109 . -97) T) ((-645 . -1133) 130787) ((-647 . -963) T) ((-627 . -319) NIL) ((-482 . -557) 130719) ((-349 . -727) T) ((-197 . -1005) T) ((-349 . -724) T) ((-199 . -726) T) ((-199 . -723) T) ((-57 . -558) 130680) ((-57 . -557) 130592) ((-199 . -659) T) ((-480 . -558) 130553) ((-480 . -557) 130465) ((-462 . -557) 130397) ((-461 . -558) 130358) ((-461 . -557) 130270) ((-989 . -333) 130221) ((-39 . -381) 130198) ((-75 . -1111) T) ((-795 . -832) NIL) ((-329 . -299) 130182) ((-329 . -333) T) ((-323 . -299) 130166) ((-323 . -333) T) ((-315 . -299) 130150) ((-315 . -333) T) ((-286 . -256) 130129) ((-103 . -333) T) ((-68 . -1111) T) ((-1121 . -308) 130081) ((-795 . -585) 130026) ((-1121 . -347) 129978) ((-886 . -123) 129833) ((-747 . -123) 129704) ((-880 . -588) 129688) ((-994 . -156) 129599) ((-880 . 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116455) ((-875 . -823) 116436) ((-1130 . -46) 116413) ((-833 . -338) T) ((-57 . -588) 116397) ((-480 . -588) 116381) ((-449 . -823) 116358) ((-69 . -410) T) ((-69 . -365) T) ((-461 . -588) 116342) ((-57 . -343) 116326) ((-564 . -156) T) ((-480 . -343) 116310) ((-461 . -343) 116294) ((-759 . -642) 116278) ((-1072 . -278) 116257) ((-1078 . -123) T) ((-112 . -156) T) ((-1047 . -280) 116195) ((-153 . -1111) T) ((-575 . -677) 116179) ((-551 . -677) 116163) ((-1167 . -123) T) ((-1142 . -843) 116142) ((-1121 . -843) 116121) ((-1121 . -752) NIL) ((-627 . -650) 116071) ((-1120 . -832) 116024) ((-941 . -1005) T) ((-795 . -347) 116001) ((-795 . -308) 115978) ((-828 . -1017) T) ((-153 . -807) 115962) ((-153 . -809) 115887) ((-454 . -1017) T) ((-324 . -1005) T) ((-192 . -1017) T) ((-74 . -410) T) ((-74 . -365) T) ((-153 . -954) 115785) ((-289 . -779) T) ((-1157 . -478) 115718) ((-1141 . -585) 115615) ((-1120 . -585) 115485) ((-796 . -726) 115464) ((-796 . -723) 115443) ((-796 . -659) T) ((-454 . 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. -954) 92150) ((-712 . -954) 92009) ((-112 . -585) 91954) ((-423 . -954) 91832) ((-586 . -954) 91816) ((-567 . -97) T) ((-196 . -456) 91800) ((-1157 . -33) T) ((-575 . -650) 91784) ((-551 . -650) 91768) ((-607 . -37) 91728) ((-289 . -97) T) ((-83 . -557) 91710) ((-49 . -954) 91694) ((-1023 . -969) 91681) ((-994 . -347) 91665) ((-58 . -55) 91627) ((-632 . -726) T) ((-632 . -723) T) ((-530 . -954) 91614) ((-481 . -954) 91591) ((-632 . -659) T) ((-286 . -963) 91482) ((-294 . -123) T) ((-283 . -963) T) ((-153 . -1017) T) ((-714 . -347) 91466) ((-712 . -347) 91450) ((-44 . -138) 91400) ((-922 . -911) 91382) ((-423 . -347) 91366) ((-377 . -156) T) ((-286 . -217) 91345) ((-283 . -217) T) ((-283 . -207) NIL) ((-265 . -1005) 91128) ((-199 . -123) T) ((-1023 . -106) 91113) ((-153 . -23) T) ((-731 . -134) 91092) ((-731 . -132) 91071) ((-224 . -579) 90979) ((-223 . -579) 90887) ((-289 . -256) 90853) ((-1057 . -478) 90786) ((-1036 . -1005) T) ((-199 . -972) T) ((-747 . -280) 90724) ((-994 . -823) 90660) ((-714 . -823) 90604) ((-712 . -823) 90588) ((-1177 . -37) 90558) ((-1175 . -37) 90528) ((-1130 . -1017) T) ((-784 . -1017) T) ((-423 . -823) 90505) ((-786 . -1005) T) ((-1130 . -23) T) ((-524 . -1017) T) ((-784 . -23) T) ((-564 . -659) T) ((-325 . -843) T) ((-322 . -843) T) ((-261 . -97) T) ((-314 . -843) T) ((-974 . -123) T) ((-875 . -123) T) ((-112 . -726) NIL) ((-112 . -723) NIL) ((-112 . -659) T) ((-627 . -832) NIL) ((-960 . -478) 90406) ((-449 . -123) T) ((-524 . -23) T) ((-611 . -280) 90344) ((-575 . -694) T) ((-551 . -694) T) ((-1121 . -779) NIL) ((-921 . -262) T) ((-224 . -21) T) ((-627 . -585) 90294) ((-321 . -1005) T) ((-224 . -25) T) ((-223 . -21) T) ((-223 . -25) T) ((-139 . -37) 90278) ((-2 . -97) T) ((-833 . -843) T) ((-450 . -1164) 90248) ((-197 . -954) 90225) ((-1023 . -963) T) ((-644 . -278) T) ((-265 . -650) 90167) ((-634 . -970) T) ((-454 . -421) T) ((-377 . -478) 90079) ((-192 . -421) T) ((-1023 . -207) T) ((-266 . -138) 90029) ((-917 . -558) 89990) ((-917 . 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. -91) 87101) ((-524 . -458) T) ((-1073 . -34) 87067) ((-1067 . -1097) 87033) ((-1067 . -1100) 86999) ((-1067 . -91) 86965) ((-331 . -1017) T) ((-329 . -1052) 86944) ((-323 . -1052) 86923) ((-315 . -1052) 86902) ((-1067 . -34) 86868) ((-1029 . -34) 86834) ((-1029 . -91) 86800) ((-103 . -1052) T) ((-1029 . -1100) 86766) ((-765 . -970) 86745) ((-584 . -280) 86683) ((-572 . -280) 86534) ((-1029 . -1097) 86500) ((-645 . -963) T) ((-974 . -579) 86482) ((-989 . -37) 86350) ((-875 . -579) 86298) ((-922 . -134) T) ((-922 . -132) NIL) ((-349 . -1017) T) ((-294 . -25) T) ((-292 . -23) T) ((-866 . -779) 86277) ((-645 . -296) 86254) ((-449 . -579) 86202) ((-39 . -954) 86092) ((-634 . -650) 86079) ((-645 . -207) T) ((-309 . -1005) T) ((-157 . -1005) T) ((-301 . -779) T) ((-388 . -421) 86029) ((-349 . -23) T) ((-329 . -37) 85994) ((-323 . -37) 85959) ((-315 . -37) 85924) ((-78 . -410) T) ((-78 . -365) T) ((-199 . -25) T) ((-199 . -21) T) ((-766 . -1017) T) ((-103 . -37) 85874) ((-759 . -1017) T) 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84650) ((-82 . -354) T) ((-82 . -365) T) ((-634 . -156) T) ((-94 . -659) T) ((-450 . -97) 84461) ((-94 . -442) T) ((-111 . -156) T) ((-1018 . -37) 84431) ((-153 . -579) 84379) ((-967 . -97) T) ((-795 . -25) T) ((-747 . -212) 84358) ((-795 . -21) T) ((-750 . -97) T) ((-384 . -97) T) ((-355 . -97) T) ((-105 . -280) NIL) ((-201 . -97) 84336) ((-122 . -1111) T) ((-116 . -1111) T) ((-951 . -123) T) ((-607 . -337) 84320) ((-917 . -963) T) ((-1130 . -579) 84268) ((-1009 . -557) 84250) ((-921 . -557) 84232) ((-479 . -23) T) ((-474 . -23) T) ((-313 . -278) T) ((-472 . -23) T) ((-292 . -123) T) ((-3 . -1005) T) ((-921 . -558) 84216) ((-917 . -217) 84195) ((-917 . -207) 84174) ((-1183 . -659) T) ((-1149 . -132) 84153) ((-765 . -1005) T) ((-1149 . -134) 84132) ((-1142 . -134) 84111) ((-1142 . -132) 84090) ((-1141 . -1115) 84069) ((-1121 . -132) 83976) ((-1121 . -134) 83883) ((-1120 . -1115) 83862) ((-349 . -123) T) ((-517 . -809) 83844) ((0 . -1005) T) ((-157 . -156) T) ((-153 . -21) T) ((-153 . -25) T) ((-48 . -1005) T) ((-1143 . -585) 83749) ((-1141 . -509) 83700) ((-647 . -1017) T) ((-1120 . -509) 83651) ((-517 . -954) 83633) ((-542 . -134) 83612) ((-542 . -132) 83591) ((-460 . -954) 83534) ((-85 . -354) T) ((-85 . -365) T) ((-796 . -333) T) ((-766 . -123) T) ((-759 . -123) T) ((-647 . -23) T) ((-467 . -557) 83516) ((-1179 . -970) T) ((-349 . -972) T) ((-943 . -1005) 83494) ((-824 . -33) T) ((-450 . -280) 83432) ((-1057 . -558) 83393) ((-1057 . -557) 83325) ((-1072 . -779) 83304) ((-44 . -97) T) ((-1028 . -779) 83283) ((-749 . -97) T) ((-1130 . -25) T) ((-1130 . -21) T) ((-784 . -25) T) ((-43 . -337) 83267) ((-784 . -21) T) ((-664 . -421) 83218) ((-1178 . -557) 83200) ((-524 . -25) T) ((-524 . -21) T) ((-360 . -1005) T) ((-967 . -280) 83138) ((-562 . -1005) T) ((-632 . -809) 83120) ((-1157 . -1111) T) ((-201 . -280) 83058) ((-131 . -338) T) ((-960 . -558) 83000) ((-960 . -557) 82943) ((-283 . -832) NIL) ((-632 . -954) 82888) ((-644 . -843) T) ((-443 . -1115) 82867) ((-1073 . -421) 82846) ((-1067 . -421) 82825) ((-300 . -97) T) ((-796 . -1017) T) ((-286 . -585) 82647) ((-283 . -585) 82576) ((-443 . -509) 82527) ((-309 . -478) 82493) ((-503 . -138) 82443) ((-39 . -278) T) ((-772 . -557) 82425) ((-634 . -262) T) ((-796 . -23) T) ((-349 . -458) T) ((-989 . -205) 82395) ((-476 . -97) T) ((-377 . -558) 82203) ((-377 . -557) 82185) ((-236 . -557) 82167) ((-111 . -262) T) ((-1143 . -659) T) ((-1141 . -333) 82146) ((-1120 . -333) 82125) ((-1168 . -33) T) ((-112 . -1111) T) ((-103 . -205) 82107) ((-1078 . -97) T) ((-446 . -1005) T) ((-486 . -456) 82091) ((-670 . -33) T) ((-450 . -37) 82061) ((-128 . -33) T) ((-112 . -807) 82038) ((-112 . -809) NIL) ((-564 . -954) 81923) ((-583 . -779) 81902) ((-1167 . -97) T) ((-266 . -97) T) ((-645 . -338) 81881) ((-112 . -954) 81858) ((-360 . -650) 81842) ((-562 . -650) 81826) ((-44 . -280) 81630) ((-748 . -132) 81609) ((-748 . -134) 81588) ((-1178 . -352) 81567) ((-751 . -779) T) ((-1159 . -1005) T) ((-1060 . -203) 81514) 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. -1005) T) ((-922 . -97) T) ((-890 . -97) T) ((-837 . -97) T) ((-816 . -954) 68865) ((-1043 . -659) T) ((-921 . -585) 68810) ((-445 . -1005) T) ((-432 . -1005) T) ((-534 . -23) T) ((-524 . -34) T) ((-524 . -91) T) ((-397 . -97) T) ((-975 . -203) 68756) ((-1074 . -37) 68653) ((-790 . -659) T) ((-627 . -843) T) ((-475 . -25) T) ((-471 . -21) T) ((-471 . -25) T) ((-1073 . -37) 68494) ((-309 . -963) T) ((-1067 . -37) 68290) ((-989 . -156) T) ((-157 . -963) T) ((-1029 . -37) 68187) ((-645 . -46) 68164) ((-329 . -156) T) ((-323 . -156) T) ((-482 . -55) 68138) ((-462 . -55) 68088) ((-321 . -1174) 68065) ((-199 . -421) T) ((-289 . -262) 68016) ((-315 . -156) T) ((-157 . -217) T) ((-1120 . -779) 67915) ((-103 . -156) T) ((-796 . -911) 67899) ((-595 . -1017) T) ((-530 . -333) T) ((-530 . -299) 67886) ((-481 . -299) 67863) ((-481 . -333) T) ((-286 . -278) 67842) ((-283 . -278) T) ((-548 . -779) 67821) ((-1018 . -650) 67763) ((-483 . -254) 67747) ((-595 . -23) T) ((-388 . -205) 67731) ((-283 . 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. -779) 16397) ((-644 . -37) 16362) ((-542 . -207) 16321) ((-39 . -657) 16293) ((-321 . -299) 16270) ((-321 . -333) T) ((-989 . -278) 16221) ((-265 . -1017) 16103) ((-1011 . -1111) T) ((-155 . -97) T) ((-1124 . -557) 16070) ((-772 . -123) 16022) ((-583 . -1145) 16006) ((-766 . -650) 15976) ((-759 . -650) 15946) ((-450 . -1111) T) ((-329 . -278) T) ((-323 . -278) T) ((-315 . -278) T) ((-583 . -550) 15923) ((-377 . -123) T) ((-483 . -603) 15907) ((-103 . -278) T) ((-265 . -23) 15791) ((-483 . -588) 15775) ((-627 . -372) NIL) ((-483 . -343) 15759) ((-89 . -1005) 15737) ((-103 . -939) T) ((-517 . -130) T) ((-1157 . -138) 15721) ((-450 . -954) 15550) ((-1143 . -132) 15511) ((-1143 . -134) 15472) ((-967 . -1111) T) ((-912 . -557) 15454) ((-787 . -557) 15436) ((-748 . -969) 15279) ((-994 . -280) 15266) ((-201 . -1111) T) ((-714 . -280) 15253) ((-712 . -280) 15240) ((-748 . -106) 15069) ((-423 . -280) 15056) ((-1072 . -558) NIL) ((-1072 . -557) 15038) ((-1028 . -557) 15020) ((-1028 . -558) 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. -97) T) ((-286 . -881) 10327) ((-125 . -1017) T) ((-111 . -1017) T) ((-548 . -1155) 10311) ((-634 . -23) T) ((-548 . -1005) 10261) ((-89 . -478) 10194) ((-157 . -333) T) ((-286 . -91) 10173) ((-286 . -34) 10152) ((-552 . -456) 10086) ((-125 . -23) T) ((-111 . -23) T) ((-651 . -1005) T) ((-444 . -456) 10023) ((-377 . -579) 9971) ((-590 . -954) 9869) ((-880 . -456) 9853) ((-325 . -970) T) ((-322 . -970) T) ((-314 . -970) T) ((-237 . -970) T) ((-221 . -970) T) ((-795 . -558) NIL) ((-795 . -557) 9835) ((-1178 . -21) T) ((-524 . -920) T) ((-664 . -659) T) ((-1178 . -25) T) ((-224 . -963) 9766) ((-223 . -963) 9697) ((-70 . -1111) T) ((-224 . -207) 9650) ((-223 . -207) 9603) ((-39 . -97) T) ((-833 . -970) T) ((-1074 . -659) T) ((-1073 . -659) T) ((-1067 . -659) T) ((-1067 . -723) NIL) ((-1067 . -726) NIL) ((-844 . -97) T) ((-1029 . -659) T) ((-703 . -97) T) ((-608 . -97) T) ((-443 . -1005) T) ((-309 . -1017) T) ((-157 . -1017) T) ((-289 . -843) 9582) ((-1141 . -650) 9423) ((-796 . -156) T) 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. -21) T) ((-575 . -25) T) ((-551 . -21) T) ((-313 . -37) 7416) ((-627 . -657) 7383) ((-454 . -807) 7365) ((-454 . -809) 7347) ((-443 . -650) 7188) ((-192 . -807) 7170) ((-62 . -1111) T) ((-192 . -809) 7152) ((-551 . -25) T) ((-397 . -585) 7126) ((-454 . -954) 7086) ((-796 . -478) 6998) ((-192 . -954) 6958) ((-214 . -33) T) ((-918 . -1005) 6936) ((-1141 . -156) 6867) ((-1120 . -156) 6798) ((-645 . -132) 6777) ((-645 . -134) 6756) ((-634 . -123) T) ((-127 . -434) 6733) ((-595 . -593) 6717) ((-1048 . -557) 6649) ((-111 . -123) T) ((-446 . -1115) T) ((-552 . -550) 6625) ((-444 . -550) 6604) ((-306 . -305) 6573) ((-493 . -1005) T) ((-446 . -509) T) ((-1072 . -963) T) ((-1028 . -963) T) ((-783 . -963) T) ((-214 . -723) 6552) ((-214 . -726) 6503) ((-214 . -725) 6482) ((-1072 . -296) 6459) ((-214 . -659) 6390) ((-880 . -19) 6374) ((-454 . -347) 6356) ((-454 . -308) 6338) ((-1028 . -296) 6310) ((-324 . -1164) 6287) ((-192 . -347) 6269) ((-192 . -308) 6251) ((-880 . -550) 6228) ((-1072 . -207) 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. -659) T) ((-1024 . -777) T) ((-816 . -955) 113456) ((-103 . -779) T) ((-595 . -970) 113440) ((-454 . -123) T) ((-1144 . -971) T) ((-192 . -123) T) ((-1058 . -97) 113418) ((-94 . -1006) T) ((-219 . -603) 113402) ((-219 . -588) 113386) ((-595 . -106) 113365) ((-286 . -381) 113349) ((-219 . -343) 113333) ((-1061 . -209) 113280) ((-918 . -205) 113264) ((-72 . -1112) T) ((-47 . -156) T) ((-634 . -357) T) ((-634 . -130) T) ((-1179 . -97) T) ((-995 . -970) 113107) ((-237 . -833) 113086) ((-221 . -833) 113065) ((-714 . -970) 112888) ((-712 . -970) 112731) ((-552 . -1112) T) ((-1066 . -557) 112713) ((-995 . -106) 112542) ((-961 . -97) T) ((-444 . -1112) T) ((-430 . -970) 112513) ((-423 . -970) 112356) ((-601 . -585) 112340) ((-795 . -278) T) ((-714 . -106) 112149) ((-712 . -106) 111978) ((-325 . -585) 111930) ((-322 . -585) 111882) ((-314 . -585) 111834) ((-237 . -585) 111759) ((-221 . -585) 111684) ((-1060 . -779) T) ((-430 . -106) 111645) ((-423 . -106) 111474) ((-996 . -955) 111458) ((-986 . -955) 111435) ((-919 . -33) T) ((-881 . -1112) T) ((-121 . -929) 111419) ((-886 . -1018) T) ((-795 . -940) NIL) ((-668 . -1018) T) ((-648 . -1018) T) ((-1158 . -456) 111403) ((-1044 . -37) 111363) ((-886 . -23) T) ((-772 . -97) T) ((-749 . -21) T) ((-749 . -25) T) ((-668 . -23) T) ((-648 . -23) T) ((-105 . -598) T) ((-834 . -585) 111328) ((-530 . -970) 111293) ((-481 . -970) 111238) ((-201 . -55) 111196) ((-422 . -23) T) ((-377 . -97) T) ((-236 . -97) T) ((-627 . -262) T) ((-790 . -37) 111166) ((-530 . -106) 111122) ((-481 . -106) 111051) ((-388 . -1018) T) ((-286 . -971) 110942) ((-283 . -971) T) ((-595 . -964) T) ((-1184 . -1006) T) ((-153 . -278) 110873) ((-388 . -23) T) ((-39 . -557) 110855) ((-39 . -558) 110839) ((-103 . -912) 110821) ((-111 . -793) 110805) ((-47 . -478) 110771) ((-1099 . -929) 110755) ((-1082 . -557) 110737) ((-1086 . -33) T) ((-845 . -557) 110719) ((-1019 . -779) 110670) ((-703 . -557) 110652) ((-608 . -557) 110634) ((-1058 . -280) 110572) ((-447 . -33) T) 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. -550) 109469) ((-1169 . -1006) T) ((-987 . -1006) T) ((-907 . -1006) T) ((-886 . -123) T) ((-670 . -1006) T) ((-668 . -123) T) ((-648 . -123) T) ((-475 . -725) T) ((-377 . -1053) 109447) ((-422 . -123) T) ((-475 . -726) T) ((-197 . -964) T) ((-265 . -97) 109230) ((-128 . -1006) T) ((-632 . -921) T) ((-89 . -1112) T) ((-122 . -557) 109162) ((-116 . -557) 109094) ((-1184 . -156) T) ((-1074 . -333) 109073) ((-1068 . -333) 109052) ((-286 . -1006) T) ((-388 . -123) T) ((-283 . -1006) T) ((-377 . -37) 109004) ((-1037 . -97) T) ((-1144 . -650) 108896) ((-591 . -971) T) ((-289 . -132) 108875) ((-289 . -134) 108854) ((-127 . -1006) T) ((-109 . -1006) T) ((-786 . -97) T) ((-529 . -557) 108836) ((-517 . -558) 108735) ((-517 . -557) 108717) ((-460 . -557) 108699) ((-460 . -558) 108644) ((-452 . -23) T) ((-450 . -779) 108595) ((-454 . -579) 108577) ((-192 . -579) 108559) ((-199 . -374) T) ((-599 . -585) 108543) ((-1073 . -844) 108522) ((-664 . -1018) T) ((-321 . -97) T) ((-750 . -779) T) ((-664 . -23) T) ((-313 . -970) 108467) ((-1060 . -1059) T) ((-1049 . -102) 108451) ((-1075 . -1018) T) ((-1074 . -1018) T) ((-479 . -955) 108435) ((-1068 . -1018) T) ((-1030 . -1018) T) ((-313 . -106) 108364) ((-923 . -1116) T) ((-121 . -1112) T) ((-838 . -1116) T) ((-627 . -258) NIL) ((-1159 . -557) 108346) ((-1075 . -23) T) ((-1074 . -23) T) ((-923 . -509) T) ((-1068 . -23) T) ((-838 . -509) T) ((-1044 . -205) 108330) ((-222 . -557) 108312) ((-1030 . -23) T) ((-985 . -1006) T) ((-731 . -123) T) ((-286 . -650) 108222) ((-283 . -650) 108151) ((-632 . -557) 108133) ((-632 . -558) 108078) ((-377 . -370) 108062) ((-408 . -1006) T) ((-454 . -25) T) ((-454 . -21) T) ((-1024 . -1006) T) ((-192 . -25) T) ((-192 . -21) T) ((-645 . -381) 108046) ((-647 . -955) 108015) ((-1158 . -557) 107927) ((-1158 . -558) 107888) ((-1144 . -156) T) ((-219 . -33) T) ((-850 . -894) T) ((-1099 . -1112) T) ((-599 . -723) 107867) ((-599 . -726) 107846) ((-368 . -365) T) ((-486 . -97) 107824) ((-953 . -1006) T) ((-196 . 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. -209) 102554) ((-995 . -833) 102533) ((-111 . -37) 102520) ((-185 . -732) T) ((-184 . -732) T) ((-183 . -732) T) ((-182 . -732) T) ((-796 . -940) 102499) ((-1169 . -456) 102483) ((-714 . -833) 102462) ((-712 . -833) 102441) ((-1086 . -1112) T) ((-423 . -833) 102420) ((-670 . -456) 102404) ((-995 . -585) 102329) ((-714 . -585) 102254) ((-564 . -970) 102241) ((-447 . -1112) T) ((-313 . -338) T) ((-128 . -456) 102223) ((-712 . -585) 102148) ((-1043 . -1112) T) ((-430 . -585) 102119) ((-237 . -810) 101978) ((-221 . -810) NIL) ((-112 . -970) 101923) ((-423 . -585) 101848) ((-601 . -955) 101825) ((-564 . -106) 101810) ((-325 . -955) 101794) ((-322 . -955) 101778) ((-314 . -955) 101762) ((-237 . -955) 101608) ((-221 . -955) 101486) ((-112 . -106) 101415) ((-57 . -1112) T) ((-482 . -1112) T) ((-480 . -1112) T) ((-462 . -1112) T) ((-461 . -1112) T) ((-407 . -557) 101397) ((-404 . -557) 101379) ((-3 . -97) T) ((-945 . -1106) 101348) ((-765 . -97) T) ((-623 . -55) 101306) ((-632 . -964) T) 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90884) ((-1037 . -1006) T) ((-199 . -973) T) ((-747 . -280) 90822) ((-995 . -824) 90758) ((-714 . -824) 90702) ((-712 . -824) 90686) ((-1178 . -37) 90656) ((-1176 . -37) 90626) ((-1131 . -1018) T) ((-784 . -1018) T) ((-423 . -824) 90603) ((-786 . -1006) T) ((-1131 . -23) T) ((-524 . -1018) T) ((-784 . -23) T) ((-564 . -659) T) ((-325 . -844) T) ((-322 . -844) T) ((-261 . -97) T) ((-314 . -844) T) ((-975 . -123) T) ((-876 . -123) T) ((-112 . -726) NIL) ((-112 . -723) NIL) ((-112 . -659) T) ((-627 . -833) NIL) ((-961 . -478) 90504) ((-449 . -123) T) ((-524 . -23) T) ((-611 . -280) 90442) ((-575 . -694) T) ((-551 . -694) T) ((-1122 . -779) NIL) ((-922 . -262) T) ((-224 . -21) T) ((-627 . -585) 90392) ((-321 . -1006) T) ((-224 . -25) T) ((-223 . -21) T) ((-223 . -25) T) ((-139 . -37) 90376) ((-2 . -97) T) ((-834 . -844) T) ((-450 . -1165) 90346) ((-197 . -955) 90323) ((-1024 . -964) T) ((-644 . -278) T) ((-265 . -650) 90265) ((-634 . -971) T) ((-454 . -421) T) ((-377 . -478) 90177) ((-192 . -421) T) ((-1024 . -207) T) ((-266 . -138) 90127) ((-918 . -558) 90088) ((-918 . -557) 90070) ((-909 . -557) 90052) ((-111 . -971) T) ((-591 . -970) 90036) ((-199 . -458) T) ((-369 . -557) 90018) ((-369 . -558) 89995) ((-968 . -1165) 89965) ((-591 . -106) 89944) ((-1044 . -456) 89928) ((-747 . -37) 89898) ((-61 . -410) T) ((-61 . -365) T) ((-1061 . -97) T) ((-795 . -123) T) ((-451 . -97) 89876) ((-1184 . -338) T) ((-990 . -97) T) ((-974 . -97) T) ((-321 . -650) 89821) ((-664 . -134) 89800) ((-664 . -132) 89779) ((-942 . -585) 89716) ((-486 . -1006) 89694) ((-329 . -97) T) ((-323 . -97) T) ((-315 . -97) T) ((-103 . -97) T) ((-469 . -1006) T) ((-324 . -585) 89639) ((-1073 . -579) 89587) ((-1029 . -579) 89535) ((-355 . -473) 89514) ((-765 . -777) 89493) ((-349 . -1116) T) ((-627 . -659) T) ((-309 . -971) T) ((-1122 . -912) 89445) ((-157 . -971) T) ((-98 . -557) 89377) ((-1075 . -132) 89356) ((-1075 . -134) 89335) ((-349 . -509) T) ((-1074 . -134) 89314) ((-1074 . -132) 89293) ((-1068 . -132) 89200) ((-377 . -262) T) ((-1068 . -134) 89107) ((-1030 . -134) 89086) ((-1030 . -132) 89065) ((-289 . -37) 88906) ((-153 . -123) T) ((-283 . -727) NIL) ((-283 . -724) NIL) ((-591 . -964) T) ((-47 . -585) 88871) ((-913 . -21) T) ((-122 . -929) 88855) ((-116 . -929) 88839) ((-913 . -25) T) ((-825 . -114) 88823) ((-1060 . -97) T) ((-748 . -779) 88802) ((-1131 . -123) T) ((-1073 . -25) T) ((-1073 . -21) T) ((-784 . -123) T) ((-1029 . -25) T) ((-1029 . -21) T) ((-783 . -25) T) ((-783 . -21) T) ((-714 . -278) 88781) ((-584 . -97) 88759) ((-572 . -97) T) ((-1061 . -280) 88554) ((-524 . -123) T) ((-562 . -777) 88533) ((-1058 . -456) 88517) ((-1052 . -138) 88467) ((-1048 . -557) 88429) ((-1048 . -558) 88390) ((-942 . -723) T) ((-942 . -726) T) ((-942 . -659) T) ((-451 . -280) 88328) ((-422 . -387) 88298) ((-321 . -156) T) ((-261 . -37) 88285) ((-247 . -97) T) ((-246 . -97) T) ((-245 . -97) T) ((-244 . -97) T) ((-243 . -97) T) ((-242 . -97) T) ((-241 . -97) T) ((-313 . -955) 88262) ((-188 . -97) T) ((-187 . -97) T) ((-185 . -97) T) ((-184 . -97) T) ((-183 . -97) T) ((-182 . -97) T) ((-179 . -97) T) ((-178 . -97) T) ((-645 . -970) 88085) ((-177 . -97) T) ((-176 . -97) T) ((-175 . -97) T) ((-174 . -97) T) ((-173 . -97) T) ((-172 . -97) T) ((-171 . -97) T) ((-170 . -97) T) ((-169 . -97) T) ((-324 . -659) T) ((-645 . -106) 87894) ((-607 . -205) 87878) ((-530 . -278) T) ((-481 . -278) T) ((-265 . -478) 87827) ((-103 . -280) NIL) ((-70 . -365) T) ((-1019 . -97) 87638) ((-765 . -381) 87622) ((-1024 . -727) T) ((-1024 . -724) T) ((-634 . -1006) T) ((-349 . -333) T) ((-153 . -458) 87600) ((-196 . -557) 87532) ((-125 . -1006) T) ((-111 . -1006) T) ((-47 . -659) T) ((-961 . -456) 87497) ((-128 . -395) 87479) ((-128 . -338) T) ((-945 . -97) T) ((-476 . -473) 87458) ((-445 . -97) T) ((-432 . -97) T) ((-952 . -1018) T) ((-1075 . -34) 87424) ((-1075 . -91) 87390) ((-1075 . -1101) 87356) ((-1075 . -1098) 87322) ((-1060 . -280) NIL) ((-87 . -366) T) ((-87 . -365) T) ((-990 . -1053) 87301) ((-1074 . -1098) 87267) ((-1074 . -1101) 87233) ((-952 . -23) T) ((-1074 . -91) 87199) ((-524 . -458) T) ((-1074 . -34) 87165) ((-1068 . -1098) 87131) ((-1068 . -1101) 87097) ((-1068 . -91) 87063) ((-331 . -1018) T) ((-329 . -1053) 87042) ((-323 . -1053) 87021) ((-315 . -1053) 87000) ((-1068 . -34) 86966) ((-1030 . -34) 86932) ((-1030 . -91) 86898) ((-103 . -1053) T) ((-1030 . -1101) 86864) ((-765 . -971) 86843) ((-584 . -280) 86781) ((-572 . -280) 86632) ((-1030 . -1098) 86598) ((-645 . -964) T) ((-975 . -579) 86580) ((-990 . -37) 86448) ((-876 . -579) 86396) ((-923 . -134) T) ((-923 . -132) NIL) ((-349 . -1018) T) ((-294 . -25) T) ((-292 . -23) T) ((-867 . -779) 86375) ((-645 . -296) 86352) ((-449 . -579) 86300) ((-39 . -955) 86190) ((-634 . -650) 86177) ((-645 . -207) T) ((-309 . -1006) T) ((-157 . -1006) T) ((-301 . -779) T) ((-388 . -421) 86127) ((-349 . -23) T) ((-329 . -37) 86092) ((-323 . -37) 86057) ((-315 . -37) 86022) ((-78 . -410) T) ((-78 . -365) T) ((-199 . -25) T) 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. -810) 83942) ((0 . -1006) T) ((-157 . -156) T) ((-153 . -21) T) ((-153 . -25) T) ((-48 . -1006) T) ((-1144 . -585) 83847) ((-1142 . -509) 83798) ((-647 . -1018) T) ((-1121 . -509) 83749) ((-517 . -955) 83731) ((-542 . -134) 83710) ((-542 . -132) 83689) ((-460 . -955) 83632) ((-85 . -354) T) ((-85 . -365) T) ((-796 . -333) T) ((-766 . -123) T) ((-759 . -123) T) ((-647 . -23) T) ((-467 . -557) 83614) ((-1180 . -971) T) ((-349 . -973) T) ((-944 . -1006) 83592) ((-825 . -33) T) ((-450 . -280) 83530) ((-1058 . -558) 83491) ((-1058 . -557) 83423) ((-1073 . -779) 83402) ((-44 . -97) T) ((-1029 . -779) 83381) ((-749 . -97) T) ((-1131 . -25) T) ((-1131 . -21) T) ((-784 . -25) T) ((-43 . -337) 83365) ((-784 . -21) T) ((-664 . -421) 83316) ((-1179 . -557) 83298) ((-524 . -25) T) ((-524 . -21) T) ((-360 . -1006) T) ((-968 . -280) 83236) ((-562 . -1006) T) ((-632 . -810) 83218) ((-1158 . -1112) T) ((-201 . -280) 83156) ((-131 . -338) T) ((-961 . -558) 83098) ((-961 . -557) 83041) ((-283 . -833) NIL) ((-632 . -955) 82986) ((-644 . -844) T) ((-443 . -1116) 82965) ((-1074 . -421) 82944) ((-1068 . -421) 82923) ((-300 . -97) T) ((-796 . -1018) T) ((-286 . -585) 82745) ((-283 . -585) 82674) ((-443 . -509) 82625) ((-309 . -478) 82591) ((-503 . -138) 82541) ((-39 . -278) T) ((-772 . -557) 82523) ((-634 . -262) T) ((-796 . -23) T) ((-349 . -458) T) ((-990 . -205) 82493) ((-476 . -97) T) ((-377 . -558) 82301) ((-377 . -557) 82283) ((-236 . -557) 82265) ((-111 . -262) T) ((-1144 . -659) T) ((-1142 . -333) 82244) ((-1121 . -333) 82223) ((-1169 . -33) T) ((-112 . -1112) T) ((-103 . -205) 82205) ((-1079 . -97) T) ((-446 . -1006) T) ((-486 . -456) 82189) ((-670 . -33) T) ((-450 . -37) 82159) ((-128 . -33) T) ((-112 . -808) 82136) ((-112 . -810) NIL) ((-564 . -955) 82021) ((-583 . -779) 82000) ((-1168 . -97) T) ((-266 . -97) T) ((-645 . -338) 81979) ((-112 . -955) 81956) ((-360 . -650) 81940) ((-562 . -650) 81924) ((-44 . -280) 81728) ((-748 . -132) 81707) ((-748 . -134) 81686) ((-1179 . -352) 81665) ((-751 . -779) T) ((-1160 . -1006) T) ((-1061 . -203) 81612) ((-356 . -779) 81591) ((-1150 . -1101) 81557) ((-1150 . -1098) 81523) ((-1143 . -1098) 81489) ((-479 . -123) T) ((-1143 . -1101) 81455) ((-1122 . -1098) 81421) ((-1122 . -1101) 81387) ((-1150 . -34) 81353) ((-1150 . -91) 81319) ((-575 . -557) 81288) ((-551 . -557) 81257) ((-199 . -779) T) ((-1143 . -91) 81223) ((-1143 . -34) 81189) ((-1142 . -1018) T) ((-1024 . -585) 81176) ((-1122 . -91) 81142) ((-1121 . -1018) T) ((-540 . -138) 81124) ((-990 . -319) 81103) ((-112 . -347) 81080) ((-112 . -308) 81057) ((-157 . -262) T) ((-1122 . -34) 81023) ((-794 . -278) T) ((-283 . -726) NIL) ((-283 . -723) NIL) ((-286 . -659) 80873) ((-283 . -659) T) ((-443 . -333) 80852) ((-329 . -319) 80831) ((-323 . -319) 80810) ((-315 . -319) 80789) ((-286 . -442) 80768) ((-1142 . -23) T) ((-1121 . -23) T) ((-651 . -1018) T) ((-647 . -123) T) ((-590 . -97) T) ((-446 . -650) 80733) ((-44 . -254) 80683) ((-100 . -1006) T) ((-66 . -557) 80665) ((-789 . -97) T) ((-564 . -824) 80624) ((-1180 . -1006) T) ((-351 . -1006) T) ((-80 . -1112) T) ((-975 . -779) T) ((-876 . -779) 80603) ((-112 . -824) NIL) ((-714 . -844) 80582) ((-646 . -779) T) ((-489 . -1006) T) ((-465 . -1006) T) ((-325 . -1116) T) ((-322 . -1116) T) ((-314 . -1116) T) ((-237 . -1116) 80561) ((-221 . -1116) 80540) ((-1019 . -205) 80510) ((-449 . -779) 80489) ((-1044 . -970) 80473) ((-360 . -694) T) ((-1060 . -760) T) ((-627 . -1112) T) ((-325 . -509) T) ((-322 . -509) T) ((-314 . -509) T) ((-237 . -509) 80404) ((-221 . -509) 80335) ((-1044 . -106) 80314) ((-422 . -677) 80284) ((-790 . -970) 80254) ((-749 . -37) 80196) ((-627 . -808) 80178) ((-627 . -810) 80160) ((-266 . -280) 79964) ((-834 . -1116) T) ((-607 . -381) 79948) ((-790 . -106) 79913) ((-627 . -955) 79858) ((-923 . -421) T) ((-834 . -509) T) ((-530 . -844) T) ((-443 . -1018) T) ((-481 . -844) T) ((-1058 . -260) 79835) ((-838 . -421) T) ((-63 . -557) 79817) ((-572 . -203) 79763) ((-443 . -23) T) 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77979) ((-601 . -23) T) ((-450 . -205) 77949) ((-139 . -971) T) ((-325 . -23) T) ((-322 . -23) T) ((-314 . -23) T) ((-112 . -278) T) ((-237 . -23) T) ((-221 . -23) T) ((-922 . -964) T) ((-645 . -833) 77928) ((-922 . -207) 77900) ((-922 . -217) T) ((-112 . -940) NIL) ((-834 . -1018) T) ((-1143 . -421) 77879) ((-1122 . -421) 77858) ((-486 . -557) 77790) ((-645 . -585) 77715) ((-377 . -970) 77667) ((-469 . -557) 77649) ((-834 . -23) T) ((-454 . -280) NIL) ((-443 . -123) T) ((-192 . -280) NIL) ((-377 . -106) 77587) ((-747 . -971) 77518) ((-670 . -1004) 77502) ((-1142 . -458) 77468) ((-1121 . -458) 77434) ((-128 . -1004) 77416) ((-446 . -262) T) ((-1179 . -964) T) ((-976 . -97) T) ((-465 . -478) NIL) ((-636 . -97) T) ((-450 . -212) 77395) ((-1073 . -132) 77374) ((-1073 . -134) 77353) ((-1029 . -134) 77332) ((-1029 . -132) 77311) ((-575 . -970) 77295) ((-551 . -970) 77279) ((-607 . -1006) T) ((-607 . -967) 77219) ((-1075 . -1149) 77203) ((-1075 . -1136) 77180) ((-454 . -1053) T) ((-1074 . -1141) 77141) ((-1074 . -1136) 77111) ((-1074 . -1139) 77095) ((-192 . -1053) T) ((-313 . -844) T) ((-750 . -239) 77079) ((-575 . -106) 77058) ((-551 . -106) 77037) ((-1068 . -1120) 76998) ((-772 . -964) 76977) ((-1068 . -1136) 76954) ((-479 . -25) T) ((-460 . -273) T) ((-475 . -23) T) ((-474 . -25) T) ((-472 . -25) T) ((-471 . -23) T) ((-1068 . -1118) 76938) ((-377 . -964) T) ((-289 . -971) T) ((-627 . -278) T) ((-103 . -777) T) ((-377 . -217) T) ((-377 . -207) 76917) ((-645 . -659) T) ((-454 . -37) 76867) ((-192 . -37) 76817) ((-443 . -458) 76783) ((-1060 . -1046) T) ((-1007 . -97) T) ((-634 . -557) 76765) ((-634 . -558) 76680) ((-647 . -21) T) ((-647 . -25) T) ((-125 . -557) 76662) ((-111 . -557) 76644) ((-142 . -25) T) ((-1178 . -1006) T) ((-796 . -579) 76592) ((-1176 . -1006) T) ((-886 . -97) T) ((-668 . -97) T) ((-648 . -97) T) ((-422 . -97) T) ((-748 . -421) 76543) ((-43 . -1006) T) ((-996 . -779) T) ((-601 . -123) T) ((-976 . -280) 76394) ((-607 . -650) 76378) ((-261 . -971) T) 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. -102) 63908) ((-446 . -964) T) ((-447 . -209) 63858) ((-1061 . -456) 63792) ((-1180 . -970) 63776) ((-351 . -970) 63760) ((-446 . -217) T) ((-748 . -97) T) ((-647 . -134) 63739) ((-647 . -132) 63718) ((-451 . -456) 63702) ((-452 . -305) 63671) ((-1180 . -106) 63650) ((-476 . -1006) T) ((-450 . -156) 63629) ((-918 . -347) 63613) ((-383 . -97) T) ((-351 . -106) 63592) ((-918 . -308) 63576) ((-252 . -903) 63560) ((-251 . -903) 63544) ((-1178 . -557) 63526) ((-1176 . -557) 63508) ((-105 . -478) NIL) ((-1073 . -1134) 63492) ((-783 . -781) 63476) ((-1079 . -1006) T) ((-98 . -1112) T) ((-876 . -873) 63437) ((-749 . -650) 63379) ((-1122 . -1053) NIL) ((-449 . -873) 63324) ((-975 . -130) T) ((-58 . -97) 63302) ((-43 . -557) 63284) ((-76 . -557) 63266) ((-321 . -585) 63211) ((-1168 . -1006) T) ((-475 . -779) T) ((-313 . -1018) T) ((-266 . -1006) T) ((-918 . -824) 63170) ((-266 . -554) 63149) ((-1150 . -37) 63046) ((-1143 . -37) 62887) ((-454 . -971) T) ((-1122 . -37) 62683) ((-192 . -971) T) 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. -971) T) ((-876 . -971) T) ((-286 . -579) 32500) ((-283 . -579) 32461) ((-449 . -971) T) ((-447 . -97) T) ((-406 . -557) 32443) ((-1073 . -1006) T) ((-1029 . -1006) T) ((-783 . -1006) T) ((-1043 . -97) T) ((-748 . -262) 32374) ((-886 . -970) 32257) ((-446 . -940) T) ((-668 . -970) 32227) ((-422 . -970) 32197) ((-1049 . -1025) 32181) ((-1008 . -478) 32114) ((-886 . -106) 31983) ((-834 . -97) T) ((-668 . -106) 31948) ((-57 . -97) 31898) ((-483 . -558) 31859) ((-483 . -557) 31771) ((-482 . -97) 31749) ((-480 . -97) 31699) ((-462 . -97) 31677) ((-461 . -97) 31627) ((-422 . -106) 31590) ((-224 . -156) 31569) ((-223 . -156) 31548) ((-388 . -970) 31522) ((-1107 . -893) 31484) ((-918 . -1018) T) ((-867 . -478) 31417) ((-454 . -727) T) ((-443 . -37) 31258) ((-388 . -106) 31225) ((-454 . -724) T) ((-919 . -280) 31163) ((-192 . -727) T) ((-192 . -724) T) ((-918 . -23) T) ((-645 . -123) T) ((-1121 . -370) 31133) ((-286 . -25) 30986) ((-153 . -381) 30970) ((-286 . -21) 30842) ((-283 . -25) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 9c88271d..b6ba6655 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3409435989) -(4195 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3409486830) +(4198 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -301,7 +301,7 @@ |OrdSetInts| |OutputForm| |OutputPackage| |OrderedVariableList| |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger| - |PAdicRational| |PAdicRationalConstructor| |Palette| + |PAdicRational| |PAdicRationalConstructor| |Pair| |Palette| |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |Parser| |ParametricSurfaceFunctions2| @@ -458,639 +458,638 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |Category| |setvalue!| |hermiteH| |generalLambert| - |digits| |divideExponents| |operators| |infieldIntegrate| - |radicalOfLeftTraceForm| |prinshINFO| |pointColorPalette| |binaryTree| - |perfectSquare?| |diagonals| |prem| |mathieu22| - |genericLeftMinimalPolynomial| |c06gqf| |getZechTable| |maxRowIndex| - |leadingIndex| |romberg| |f01brf| |changeName| |position| |iisec| - |listOfMonoms| |neglist| |difference| |rischNormalize| |s17ahf| - |monicDecomposeIfCan| |discriminant| |hdmpToP| |cTan| |square?| - |squareFreePart| |iExquo| |log| |genericPosition| |linGenPos| - |cyclicEntries| |uniform01| |clikeUniv| |pointColor| |iiasech| - |continuedFraction| |besselJ| |fglmIfCan| |tree| |makeGraphImage| - |expintfldpoly| |removeConstantTerm| |magnitude| |nil?| - |GospersMethod| |upDateBranches| |generalTwoFactor| |cyclicCopy| - |pack!| |complexNormalize| |pushdterm| |f01rdf| |hexDigit| - |countRealRoots| |normalized?| |LiePolyIfCan| |rationalApproximation| - |leftExactQuotient| |stoseIntegralLastSubResultant| |dequeue!| - |prime?| |approxNthRoot| |d01gbf| |checkForZero| |var2Steps| - |generateIrredPoly| |showSummary| |commutative?| |dfRange| - |constantRight| |infinite?| |definingEquations| |critpOrder| |moduloP| - |brillhartIrreducible?| |fortranDouble| |FormatArabic| |poisson| - |tanQ| RF2UTS |sech2cosh| |rk4f| |iiGamma| |currentSubProgram| |cCsch| - |rightCharacteristicPolynomial| |showAttributes| |linearPolynomials| - |cschIfCan| |ef2edf| |closedCurve?| |setClipValue| |splitSquarefree| - |rightRegularRepresentation| |transpose| - |generalizedContinuumHypothesisAssumed?| |const| |rectangularMatrix| - |e04naf| |besselK| |ellipticCylindrical| |redPo| |rootRadius| - |totalDegree| |ffactor| |primitiveElement| |transcendenceDegree| - |usingTable?| |removeSuperfluousCases| |OMputAttr| |acosIfCan| - |LazardQuotient| |semiIndiceSubResultantEuclidean| |asinIfCan| |mdeg| - |dimensionOfIrreducibleRepresentation| |singularAtInfinity?| - |completeHensel| |realEigenvectors| |generator| |subNodeOf?| |less?| - |jacobiIdentity?| |light| |modularGcdPrimitive| |presub| |directory| - |interpolate| BY |changeNameToObjf| |traverse| |graphStates| |c06ecf| - |removeSquaresIfCan| |alphabetic?| |OMputVariable| |monomRDE| - |removeZeroes| |s18aff| |lexGroebner| |pattern| |separate| |subSet| - |uniform| |stripCommentsAndBlanks| |leftTraceMatrix| - |stoseInternalLastSubResultant| |cSec| |extractClosed| |mr| - |rootSplit| |startPolynomial| |child| |comparison| |s17adf| - |characteristicSet| |wordInStrongGenerators| |eisensteinIrreducible?| - |lyndonIfCan| |extension| |s18dcf| |combineFeatureCompatibility| - |sumOfSquares| |systemCommand| |wholePart| |debug| |yellow| - |homogeneous?| |formula| |torsion?| |semiLastSubResultantEuclidean| - |updatD| |curve?| |constantCoefficientRicDE| |companionBlocks| - |reducedForm| |groebner| |one?| |pToDmp| |split| - |removeSuperfluousQuasiComponents| |showRegion| |e02aef| |rowEchelon| - |stiffnessAndStabilityOfODEIF| |d01gaf| |constant| |hMonic| |normal| - |d01amf| |areEquivalent?| |generalPosition| |mainPrimitivePart| |root| - |sample| |extractIndex| |order| |iiatanh| |rightTraceMatrix| |kernel| - |removeDuplicates!| |f01qef| |purelyAlgebraic?| |constantKernel| - |complexNumeric| |s21bcf| |adjoint| |stoseInvertible?| |op| - |linearlyDependent?| |collectUnder| |pleskenSplit| |sortConstraints| - |leftTrace| |palgintegrate| |imagI| |stopTableGcd!| |copies| |iiasin| - |integralRepresents| |OMParseError?| |sort!| |nrows| |erf| |remove| - |kernels| |linearAssociatedLog| |createNormalElement| - |factorByRecursion| |bsolve| |setCondition!| |cup| |leftUnits| |cAcos| - |SturmHabicht| |triangulate| |ncols| |deleteProperty!| |tanNa| - |linearlyDependentOverZ?| |birth| |univariate| |outlineRender| - |d01alf| |hdmpToDmp| |rightUnits| |addMatch| |last| |true| |vark| - |laplacian| |match?| |csch2sinh| |ListOfTerms| |mainMonomials| - |selectIntegrationRoutines| |lambert| |crest| |distribute| |mapSolve| - |assoc| |dilog| |superHeight| |scanOneDimSubspaces| |closeComponent| - |trim| |triangularSystems| |cyclotomicDecomposition| - |leftRankPolynomial| |OMreadStr| |ptFunc| |d01apf| |sin| |iitan| - |stop| |quadraticNorm| |separateFactors| |character?| |prologue| - |trigs2explogs| |leftRemainder| |isPower| |f01ref| |aQuadratic| |cos| - |reduceBasisAtInfinity| |unit| |cAsec| |constantToUnaryFunction| - |lyndon| |nary?| |primaryDecomp| |badValues| |basis| |internalAugment| - |tan| |functionIsContinuousAtEndPoints| |binary| |OMputApp| |imagE| - |draw| |fortranLinkerArgs| |cRationalPower| |exptMod| - |partialFraction| |sh| |mathieu12| |mesh| |cot| |fortranLiteralLine| - |lift| |factors| |seed| |groebner?| |elRow1!| |primlimintfrac| - |string| |solve| |leftDivide| |removeSinSq| |argumentListOf| |sec| - |computeCycleLength| |reduce| |mainCoefficients| |OMopenString| - |backOldPos| |symbolIfCan| |duplicates| |find| |cAcoth| |ParCondList| - |shade| |scan| |csc| |parts| |compiledFunction| |palgint| |dimension| - |aQuartic| |vspace| |readIfCan!| |tail| |fortranTypeOf| - |validExponential| |musserTrials| |showAllElements| |quotientByP| - |quatern| |asin| |zeroSquareMatrix| |makeObject| |ldf2vmf| - |sqfrFactor| |rename| |integralMatrixAtInfinity| |polyred| - |cyclotomic| |processTemplate| |Si| |OMcloseConn| |s17akf| - |laurentRep| |acos| |charpol| |irreducibleFactor| |power!| |e01bhf| - |indiceSubResultantEuclidean| |head| |status| |open?| - |constantOpIfCan| |binarySearchTree| |lieAdmissible?| |f04maf| - |s01eaf| |atan| |genericRightNorm| |e02zaf| |f01mcf| - |axesColorDefault| |lyndon?| |coef| |complexSolve| = - |groebnerFactorize| |hasTopPredicate?| |indicialEquations| |realSolve| - |acot| |leftRecip| |mirror| |schema| |tanhIfCan| |radix| - |tryFunctionalDecomposition?| |sizePascalTriangle| - |addMatchRestricted| |hessian| |orbits| |asec| |modularGcd| |f02abf| - |inGroundField?| |subresultantVector| |roughSubIdeal?| SEGMENT - |reciprocalPolynomial| < |partitions| |subCase?| |f04atf| - |viewDeltaXDefault| |acsc| |withPredicates| |pushup| |sparsityIF| - |OMUnknownSymbol?| > |buildSyntax| |coth2tanh| |toScale| - |beauzamyBound| |deepExpand| |sinh| |showTypeInOutput| |bfKeys| - |ocf2ocdf| |generalizedInverse| |cyclotomicFactorization| <= |heap| - |f01rcf| |pastel| |radicalEigenvalues| |cosh| |rightFactorCandidate| - |rootBound| |OMgetError| |maximumExponent| |certainlySubVariety?| - |recolor| >= |OMgetVariable| |surface| |semiResultantReduitEuclidean| - |factorFraction| |freeOf?| |tanh| |reset| |newLine| |curve| - |factorSquareFreeByRecursion| |isPlus| |dihedral| |d02gaf| |deepCopy| - |scaleRoots| |divideIfCan| |LyndonCoordinates| |coth| |routines| - |latex| |lazyIrreducibleFactors| |taylorRep| |createZechTable| - |safeFloor| |genericRightTraceForm| |infinityNorm| |divergence| |sech| - |OMgetEndAttr| |write| |modulus| |lquo| |LyndonWordsList| |conjug| - |critBonD| + |rightRankPolynomial| |monomialIntPoly| |harmonic| |csch| - |minRowIndex| |sincos| |save| |measure2Result| |internalIntegrate0| - |lazyPseudoDivide| |coefficient| |predicate| |factorial| - - |identitySquareMatrix| |pol| |complement| |cAsinh| |asinh| - |bivariatePolynomials| |characteristicPolynomial| - |coercePreimagesImages| |lexico| |setrest!| |constantOperator| / - |f07fdf| |quoByVar| |createMultiplicationMatrix| |presuper| |acosh| - |monomRDEsys| |singular?| |simpson| |t| |coleman| |points| - |bezoutMatrix| |representationType| |log2| - |removeRedundantFactorsInPols| |btwFact| |algint| |atanh| - |selectPDERoutines| |close| F |digit| |enterInCache| |block| |maxint| - |d03faf| |composites| |initiallyReduced?| |hypergeometric0F1| - |prefixRagits| |acoth| |lazyPquo| |leftUnit| |tanAn| |nilFactor| - |imagk| |frst| |overset?| |characteristicSerie| |makeFR| |choosemon| - |showFortranOutputStack| |insert| |symbolTableOf| |spherical| - |OMgetBind| |qinterval| |htrigs| |concat!| |makeViewport3D| |generic?| - |isQuotient| |display| |createPrimitiveElement| |fixedPoint| |cfirst| - |conjugates| |principalIdeal| |rightExactQuotient| |polyRDE| - |superscript| |even?| |findCycle| |tableForDiscreteLogarithm| - |reduction| |toseSquareFreePart| |mainContent| |quasiMonic?| - |tryFunctionalDecomposition| |midpoint| |showAll?| |f01bsf| - |graphCurves| |deepestTail| |KrullNumber| |leftFactorIfCan| - |stopTable!| |setClosed| |d02bhf| |OMputAtp| |showTheSymbolTable| - |cSin| |csc2sin| |aCubic| |nthFactor| |pointSizeDefault| |mapmult| - |modifyPointData| |setPoly| |probablyZeroDim?| |algebraicOf| - |quickSort| |bumptab1| |iitanh| |genericLeftNorm| |RemainderList| - |mainDefiningPolynomial| |karatsubaOnce| |inspect| |rootPoly| - |exprHasAlgebraicWeight| |removeRoughlyRedundantFactorsInPols| - |besselI| |f04jgf| |height| |input| |numerators| |coerceP| - |diagonalProduct| |makeMulti| |internalZeroSetSplit| - |functionIsOscillatory| |e02daf| |conditionP| |mightHaveRoots| - |getOperator| |colorDef| |library| |nthFlag| |drawToScale| |pointPlot| - |getDatabase| |hspace| |octon| |reverseLex| |geometric| |monic?| - |diagonal?| |medialSet| |generalizedContinuumHypothesisAssumed| - |insertTop!| |froot| |expenseOfEvaluation| |generalSqFr| |getlo| - |setFormula!| |redpps| |conjugate| |rational| |distance| |symbolTable| - |iiacsc| |genericLeftTraceForm| |f02ajf| |log10| |OMUnknownCD?| - |size?| |polCase| |e02ddf| |f02xef| |leadingCoefficientRicDE| - |augment| |delta| |linearMatrix| |entry| |OMbindTCP| - |SturmHabichtMultiple| |numerator| |subTriSet?| |powerAssociative?| - |SturmHabichtCoefficients| |viewWriteAvailable| |f04mcf| |opeval| - |pushFortranOutputStack| |integerBound| |increasePrecision| - |rightRemainder| |reorder| |baseRDEsys| |basisOfMiddleNucleus| - |symmetricRemainder| |identification| |arg1| |nthExpon| |pole?| - |mainSquareFreePart| |keys| |popFortranOutputStack| |set| - |balancedBinaryTree| |cond| |dAndcExp| |collectQuasiMonic| |d02raf| - |firstUncouplingMatrix| |unitNormalize| |rightRank| |tracePowMod| - |palgint0| |arg2| |vectorise| |pointColorDefault| |outputAsFortran| - |imaginary| |say| |copyInto!| |fortranCharacter| |members| - |countRealRootsMultiple| |acschIfCan| |groebSolve| |divideIfCan!| - |reverse| |factorset| |changeVar| |fractRadix| |declare| - |genericLeftDiscriminant| |infieldint| |fixedDivisor| |tablePow| - |binomial| |clearTheSymbolTable| |isobaric?| |iilog| |s17ajf| - |secIfCan| |particularSolution| |conditions| |rubiksGroup| - |integerIfCan| |untab| |terms| |explicitEntries?| |trigs| |tubePlot| - |rootSimp| |zeroDimPrime?| |operator| |tubeRadiusDefault| - |monicRightDivide| |match| |times!| |leaves| |elliptic?| |frobenius| - |point?| |gcdPolynomial| |headReduced?| |d01aqf| |palgLODE| - |monomialIntegrate| |changeBase| |corrPoly| |OMgetInteger| |lambda| - |negative?| |useSingleFactorBound?| |padicallyExpand| - |interpretString| |internalIntegrate| |bivariate?| - |resultantEuclidean| |numberOfIrreduciblePoly| |Is| |subset?| |iroot| - |setEpilogue!| |iicot| |computePowers| |ratDenom| |lexTriangular| - |bipolar| |getGraph| |setref| |deepestInitial| |extractProperty| - |iicsc| |logIfCan| |numberOfComposites| |oddintegers| |cycleElt| - |deleteRoutine!| |algintegrate| |vertConcat| |linkToFortran| |mkPrim| - |redmat| |fortranInteger| |printInfo!| |show| |iflist2Result| - |outputForm| |maxIndex| |B1solve| |factorsOfDegree| |pow| - |intcompBasis| |minset| |power| |powers| |compose| |coefficients| - |algebraic?| |sylvesterMatrix| |OMgetFloat| |balancedFactorisation| - |badNum| |cycleRagits| |setlast!| |edf2efi| |cAcsc| - |removeRedundantFactors| |trace| |subMatrix| Y - |createLowComplexityNormalBasis| |pointLists| |alternative?| - |commonDenominator| |anfactor| |pmComplexintegrate| |realZeros| - |solveLinearPolynomialEquation| |rotatex| |airyAi| |zeroMatrix| - |printTypes| |qPot| |intChoose| |sin?| |leftMult| |clipParametric| - |copy!| |startTableInvSet!| |jordanAdmissible?| |expintegrate| - |makeCos| |swap!| |numberOfOperations| |rdregime| |node| |in?| |rule| - |discriminantEuclidean| |fractionPart| |s21bbf| |splitLinear| |void| - |read!| |cycle| |f02axf| |vector| |setColumn!| |e02agf| |increment| - |chebyshevU| |setleft!| |computeBasis| |bernoulliB| |testDim| |cCot| - |f02agf| |commutator| |differentiate| |reducedDiscriminant| - |printingInfo?| |genericLeftTrace| |denomLODE| |stirling2| |is?| - |OMconnOutDevice| |OMgetEndError| |RittWuCompare| |univariate?| - |inconsistent?| |prepareSubResAlgo| |realRoots| |associates?| - |selectFiniteRoutines| |region| |swapRows!| |monomial| |extractTop!| - |BasicMethod| |f01maf| LODO2FUN |s17aff| |localReal?| |unaryFunction| - |multivariate| |getExplanations| |createNormalPoly| |monicModulo| - |pushucoef| |rewriteSetByReducingWithParticularGenerators| |nthRoot| - |rightRecip| |univariateSolve| |tubePoints| |rightGcd| |variables| - |denom| |jacobi| |invertIfCan| |moebiusMu| |getStream| |viewpoint| - |f02akf| |setOfMinN| |oddInfiniteProduct| |sumOfKthPowerDivisors| - |rk4| |overlabel| |e04mbf| |genus| |reify| |quartic| |rowEchLocal| - |Nul| |pi| |f07aef| |multisect| ~= |closed?| |exponent| |consnewpol| - |fixedPoints| |leadingTerm| |infinity| |imagK| |purelyTranscendental?| - |cCosh| |messagePrint| |socf2socdf| |safetyMargin| |cSech| - |traceMatrix| |drawStyle| |OMputFloat| |pair?| |moebius| |quadratic| - |rootProduct| |credPol| |physicalLength!| |shift| |nullary| - |permutation| |taylor| |algDsolve| |minrank| |option?| |gbasis| - |setVariableOrder| |Lazard| |setPredicates| |expandPower| |laurent| - |normalDenom| |indicialEquation| |resultant| |lo| |listYoungTableaus| - |sn| |screenResolution| |chiSquare1| |sort| |prindINFO| |puiseux| - |sorted?| |makeEq| |incr| |check| |taylorQuoByVar| |plot| - |univariatePolynomial| |fTable| |hi| |tanh2coth| |dictionary| - |setEmpty!| |trailingCoefficient| |countable?| |li| |nil| - |makeFloatFunction| |symmetricProduct| |equiv| |lieAlgebra?| - |UnVectorise| |position!| |infLex?| |c05nbf| |unit?| |univcase| - |discreteLog| |plenaryPower| |minPoints| |listBranches| F2FG - |bandedJacobian| |fracPart| |children| |e01bff| |c06fuf| |random| - |ran| |approximate| |dimensionsOf| |tan2cot| |reducedSystem| - |rightMinimalPolynomial| |dflist| |stFunc2| |segment| |ratpart| - |df2mf| |outputAsScript| |cAtan| |phiCoord| |makeSketch| |normDeriv2| - |selectNonFiniteRoutines| |mapUp!| |f04adf| |getBadValues| |legendreP| - |numberOfHues| |write!| |showTheFTable| |function| - |wordsForStrongGenerators| |getMeasure| |rewriteSetWithReduction| - |cycleEntry| |makeSeries| |partialNumerators| |horizConcat| - |univariatePolynomialsGcds| |aspFilename| |OMgetEndBind| |limit| - |coth2trigh| |firstNumer| |mainVariables| |po| |nextItem| |rightUnit| - |laurentIfCan| |setStatus| |qfactor| |cartesian| |assign| |datalist| - |symbol| |weighted| |integral?| |blue| |setfirst!| |squareTop| - |initializeGroupForWordProblem| |morphism| |intersect| |tanintegrate| - |red| |irreducibleRepresentation| |graphImage| |output| |zeroSetSplit| - |generate| |e01saf| |integer| |delay| |mapBivariate| |coerce| |ord| - |innerEigenvectors| |OMconnectTCP| |case| |factorSquareFreePolynomial| - |s18adf| |algebraicDecompose| |addPoint2| |implies| |stopTableInvSet!| - |smith| |incrementBy| |cscIfCan| |parametric?| |f02wef| |d01fcf| - |construct| |clearCache| |changeWeightLevel| |alphanumeric?| - |leftMinimalPolynomial| |permanent| |xor| |c06ekf| |expand| - |mainVariable| |cylindrical| |ScanArabic| |inv| |permutationGroup| - |OMreadFile| |coordinate| |generalInfiniteProduct| |invertibleSet| - |filterWhile| |close!| |sncndn| |getCode| |ground?| |changeMeasure| - |d02kef| |prevPrime| |moreAlgebraic?| |squareMatrix| |filterUntil| - |f01qcf| |lazyVariations| |mathieu11| |insertBottom!| |ground| - |binaryFunction| |internalSubQuasiComponent?| |list| |select| |cross| - |shellSort| |f02fjf| |exquo| |squareFreePrim| |getOrder| |lcm| |plus| - |zag| |leadingMonomial| |setDifference| |numericalIntegration| - |quotedOperators| |readLine!| |OMputEndBind| |div| |ODESolve| - |viewSizeDefault| |wrregime| |selectMultiDimensionalRoutines| |pdf2df| - |leadingCoefficient| |interpret| |setIntersection| |lastSubResultant| - |scalarMatrix| |decompose| |iisech| |quo| |eulerE| |integrate| |prime| - |cAsin| |primitiveMonomials| |sign| |derivative| |setUnion| - |OMencodingBinary| |var2StepsDefault| |linears| |HenselLift| - |completeEchelonBasis| |curveColor| |basisOfRightAnnihilator| |gcd| - |matrix| |rischDE| |reductum| |s20acf| |apply| |abs| |nullary?| - |s19abf| |rem| |monicCompleteDecompose| |noKaratsuba| |completeEval| - |upperCase?| |union| |gethi| |times| |definingPolynomial| |aLinear| - |elColumn2!| |unrankImproperPartitions1| |condition| |mkcomm| - |leftQuotient| |empty?| |leftGcd| |false| |randomLC| |exprToXXP| - |size| |makeRecord| |multiplyExponents| |extensionDegree| |setnext!| - |exprToGenUPS| |karatsuba| |listRepresentation| |cyclePartition| - |ptree| |maxrank| |sinhIfCan| |alternatingGroup| |prolateSpheroidal| - |iisin| |palgextint0| |e01bgf| |shanksDiscLogAlgorithm| - |clipWithRanges| |curryRight| |quasiRegular?| |OMencodingSGML| - |linearAssociatedExp| |doubleComplex?| |removeSinhSq| - |useNagFunctions| |monom| |singRicDE| |oneDimensionalArray| - |compactFraction| |first| |accuracyIF| |separant| |repeating?| - |twoFactor| |digit?| |OMread| |antiCommutative?| - |semiResultantEuclidean1| |setTex!| |rest| |limitedint| |node?| - |subscript| |identityMatrix| |asinhIfCan| |setelt| |cosIfCan| - |property| |substitute| |evaluate| |limitPlus| |iiabs| |empty| - |cycleLength| |expandTrigProducts| |removeDuplicates| |OMserve| - |remove!| |f04axf| |OMsupportsSymbol?| |e01sef| |OMputBind| |copy| - |setAttributeButtonStep| |zeroDimensional?| |lifting1| |paraboloidal| - |critT| |numberOfCycles| |bringDown| |OMunhandledSymbol| |logGamma| - |result| |units| |d01asf| |hclf| |squareFreeLexTriangular| |f07fef| - |setButtonValue| |not| |oddlambert| |totalLex| ^= |integral| - |denominator| |elements| |mathieu24| |expt| |ravel| |iiasinh| - |maxPoints| |autoCoerce| |saturate| |simpsono| |meshPar2Var| - |rationalPower| |lastSubResultantElseSplit| |more?| |reshape| - |palgRDE| |radicalSolve| |roughBase?| |exponents| |fractionFreeGauss!| - |SturmHabichtSequence| |back| |cyclicParents| - |degreeSubResultantEuclidean| |lhs| |rdHack1| |normalizedAssociate| - |createGenericMatrix| |bezoutResultant| |extractIfCan| - |realElementary| |rhs| |code| |forLoop| |rationalIfCan| |compile| - |structuralConstants| |cardinality| |OMsetEncoding| |cPower| - |trueEqual| |rationalPoints| |repeatUntilLoop| |subNode?| - |diagonalMatrix| |returnType!| |OMlistSymbols| |slex| |elliptic| - |dmpToHdmp| |getCurve| |update| |solid?| |hue| |separateDegrees| - |leastMonomial| |zoom| |leftAlternative?| |karatsubaDivide| - |figureUnits| |subHeight| |insertionSort!| |lfinfieldint| |e04ycf| - |normal?| |reverse!| |ScanFloatIgnoreSpaces| |suffix?| |e04jaf| |top| - |rightNorm| |exteriorDifferential| |supRittWu?| |nonSingularModel| - |OMputError| |unitNormal| |recip| |continue| |rightDivide| - |create3Space| |divisors| |setMaxPoints3D| |qelt| - |rewriteIdealWithRemainder| |convergents| - |stiffnessAndStabilityFactor| |subResultantGcdEuclidean| |prefix?| - |reducedQPowers| |call| |testModulus| |viewWriteDefault| |second| - |mapCoef| |newSubProgram| |revert| |boundOfCauchy| - |integralCoordinates| |polygon?| |laplace| |pushdown| |key| |third| - |init| |solveLinear| |basisOfCommutingElements| |quadratic?| - |knownInfBasis| |numberOfChildren| |semiSubResultantGcdEuclidean1| - |upperCase| |lex| |options| |roughBasicSet| |computeInt| |exQuo| - |goodPoint| |setLabelValue| |acoshIfCan| |primintegrate| |An| - |atanhIfCan| |schwerpunkt| |setLegalFortranSourceExtensions| - |subPolSet?| |elt| |filename| |tanSum| |coord| |s17aef| |flatten| - 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|mainMonomials| + |KrullNumber| |pow| |inGroundField?| |weakBiRank| |vectorise| |mr| + |nthExponent| |tablePow| |pointSizeDefault| |nextNormalPrimitivePoly| + |viewDeltaYDefault| |unitsColorDefault| |cosSinInfo| |raisePolynomial| + |selectIntegrationRoutines| |leftRemainder| |normal01| |outputGeneral| + |lfextendedint| |systemCommand| |e02dff| |debug| |nand| |complexSolve| + |generalSqFr| |getlo| |initializeGroupForWordProblem| |formula| + |f02aef| |makeEq| |subPolSet?| |functionIsFracPolynomial?| + |rightMinimalPolynomial| |atoms| |iisqrt2| |topFortranOutputStack| + |stopTableGcd!| |adjoint| |singular?| |outputArgs| |pdf2df| + |coordinates| |constant| |sizePascalTriangle| |normal| |f07aef| + |numberOfFractionalTerms| |removeRoughlyRedundantFactorsInPols| UTS2UP + |d01ajf| |compound?| |palgint| |numericIfCan| |binaryTournament| + |kernel| |OMputEndError| |oddintegers| |complexNumeric| |roman| + |nextLatticePermutation| |LiePolyIfCan| |iExquo| |swapRows!| + 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|complementaryBasis| |acosh| + |uncouplingMatrices| |node?| |t| |externalList| |commonDenominator| + |copyInto!| |symmetricProduct| |atanh| |perspective| |getMeasure| + |stoseLastSubResultant| |presub| |graphStates| |close| |cAcsch| + |viewport3D| |expPot| |f02bjf| |Ci| |maxColIndex| |moreAlgebraic?| + |red| |stripCommentsAndBlanks| |acoth| |permanent| |isobaric?| + |exponent| |d01alf| |quasiMonic?| |makeGraphImage| |infinite?| + |pureLex| |multiEuclidean| |lazyResidueClass| |perfectNthRoot| + |insert| |setAdaptive3D| |basisOfRightNucleus| |patternMatchTimes| + |d02gaf| |imagk| |buildSyntax| |hitherPlane| |isQuotient| |isTimes| + |display| |rightUnit| |meshFun2Var| |f04maf| |geometric| |remove!| + |oneDimensionalArray| |leadingIdeal| |midpoints| |decreasePrecision| + |empty?| |factorAndSplit| |setelt!| |insertMatch| |fillPascalTriangle| + |getOperator| |pomopo!| |leftMult| |power| |aQuadratic| + |univariatePolynomial| |sizeLess?| |simplifyLog| |cot2tan| + |plenaryPower| |resultantEuclidean| |eq?| |kmax| |movedPoints| + |padicFraction| |readIfCan!| |rootPower| |mkIntegral| |poisson| + |stoseIntegralLastSubResultant| |minordet| |basisOfNucleus| |ranges| + |points| |subtractIfCan| |decompose| |dequeue| |recolor| |vconcat| + |supDimElseRittWu?| |complexNormalize| |cyclic| + |expenseOfEvaluationIF| |integralRepresents| + |rightRegularRepresentation| |symbolIfCan| |height| |euler| |input| + |setPosition| |invertIfCan| |sub| |tryFunctionalDecomposition| |heap| + |alphanumeric| |exprHasWeightCosWXorSinWX| |irreducibleRepresentation| + |f01maf| |normalizedDivide| |mainVariable?| |library| |anfactor| + |palginfieldint| |prefixRagits| |numberOfComputedEntries| |setOrder| + |numerators| |distribute| |gethi| |characteristic| |root?| |cosh2sech| + |elRow2!| |pToDmp| |nodes| |userOrdered?| |setlast!| + |doubleFloatFormat| |fortranCharacter| |linearDependence| |rdHack1| + |leftTraceMatrix| |leftScalarTimes!| |symbolTable| |virtualDegree| + |consnewpol| |subscript| |calcRanges| |monic?| |mapExpon| |frst| + |equiv| |stFuncN| |c06ecf| |leftGcd| |delta| |iilog| |entry| |cAcot| + |hdmpToDmp| |semiResultantEuclideannaif| + |halfExtendedSubResultantGcd1| |iidsum| |reduceBasisAtInfinity| + |conjugate| |c06ekf| |trunc| |pushFortranOutputStack| |modTree| + |mainKernel| |varselect| |rangeIsFinite| |shiftLeft| |innerint| + |basisOfLeftAnnihilator| |finiteBasis| |nextPrimitivePoly| |fTable| + |arg1| |pseudoDivide| |keys| |popFortranOutputStack| |set| + |alternating| |cond| |pr2dmp| |laurentIfCan| |packageCall| |cAcos| + |leftAlternative?| |bezoutMatrix| |iisech| |pmintegrate| + |squareMatrix| |arg2| |numberOfChildren| |outputAsFortran| |say| + |interval| |clearTheFTable| |toseInvertible?| |f04axf| |s01eaf| + |simpsono| |rotatez| |reverse| |legendre| |definingEquations| + |fortranTypeOf| |monicRightFactorIfCan| |declare| + |numberOfIrreduciblePoly| |antiAssociative?| |makeop| |dequeue!| + |colorDef| |totalGroebner| |mapDown!| |duplicates| |algebraicSort| + |deepCopy| |conditions| |transpose| |symmetric?| |tanQ| + |minimalPolynomial| |transform| |e02bdf| |OMgetVariable| + |fortranInteger| |decrease| |clipParametric| |delete!| |decomposeFunc| + |f02awf| |match| |leaves| |csubst| |arrayStack| |iicosh| |approxSqrt| + |pmComplexintegrate| |minPoints| |toseInvertibleSet| |relerror| + |OMgetAttr| LODO2FUN |graphImage| |imagi| |lambda| |coefficient| + |moebiusMu| |pushdterm| |normFactors| |tValues| + |removeRedundantFactorsInContents| |fortranDoubleComplex| |ipow| + |removeSquaresIfCan| |stoseInternalLastSubResultant| |member?| + |prepareDecompose| |identityMatrix| |fixedPoints| |critT| + |quasiComponent| |splitDenominator| |randomLC| |overset?| + |mainVariable| |rootKerSimp| |clikeUniv| |crushedSet| |lazyPquo| + |rightUnits| |acothIfCan| |e04ucf| |unit| |closedCurve| |constant?| + |maxIndex| |commutator| |show| |OMputEndObject| |nextColeman| + |diagonal?| |split| |karatsubaDivide| |explimitedint| |eulerE| + |semiSubResultantGcdEuclidean1| |minimize| |f04atf| |midpoint| + |product| |infinityNorm| |find| |tensorProduct| |tanh2coth| |complex?| + |hasPredicate?| |baseRDEsys| |trace| |zero?| |solve| |readable?| + |returnTypeOf| |extendedint| |reseed| |validExponential| + |getGoodPrime| |dmpToP| |OMputEndBind| |leftTrace| |mathieu22| + |lazyPseudoRemainder| |finite?| |addmod| |complexLimit| |meshPar2Var| + |c05pbf| |generalizedContinuumHypothesisAssumed?| |mix| |sqfree| + |nthCoef| |pushdown| |inspect| |FormatRoman| |screenResolution3D| + |divide| |increase| |node| |rule| |prime?| |writable?| |usingTable?| + |unit?| |void| |seriesToOutputForm| |completeEchelonBasis| |scale| + |vector| |solid| |jacobiIdentity?| |genericRightNorm| |surface| + |complexZeros| |LyndonWordsList1| |exprToXXP| |factorial| + |computeCycleLength| |generalTwoFactor| |sinhcosh| |differentiate| + |numericalIntegration| |gderiv| |asimpson| |realZeros| |printInfo!| + |OMconnectTCP| |external?| |ocf2ocdf| |integralLastSubResultant| + |pushuconst| |constantIfCan| |OMopenFile| |cAtanh| |f01rcf| |Is| + |enumerate| |monomial| |subResultantGcdEuclidean| |nsqfree| + |mathieu12| |balancedFactorisation| |setScreenResolution3D| + |firstDenom| |subscriptedVariables| |integralCoordinates| |sncndn| + |multivariate| |split!| |indicialEquation| |OMgetBVar| |f02bbf| + |cycleTail| |exists?| |bits| |coord| |viewThetaDefault| |figureUnits| + |variables| |fortranLinkerArgs| |denom| |rCoord| |diophantineSystem| + FG2F |interpolate| |reducedDiscriminant| |nodeOf?| |var2StepsDefault| + |transcendent?| |cyclicSubmodule| |acscIfCan| |ldf2lst| |asinIfCan| + |solveLinearPolynomialEquationByFractions| |basisOfMiddleNucleus| + |leftDivide| |push!| |oblateSpheroidal| |directSum| |cyclicEqual?| + |pi| |idealiserMatrix| |refine| ~= |genericLeftMinimalPolynomial| + |gcdcofact| |OMgetType| |torsion?| |divergence| |infinity| |smith| + |multiplyExponents| |morphism| |nthFactor| |exponential1| |iFTable| + |nlde| |polyRDE| |rationalPower| |errorKind| |mesh| |iitanh| |entry?| + |differentialVariables| |createLowComplexityTable| |shift| |light| + |aspFilename| |simplify| |taylor| |cCos| |resultant| + |tryFunctionalDecomposition?| |stoseInvertible?| |positiveSolve| + |inverse| |jacobian| |iflist2Result| |laurent| |normDeriv2| |f04mbf| + |subResultantsChain| |lo| |lprop| |basisOfRightNucloid| |truncate| + |power!| |sort| |printStatement| |puiseux| |kovacic| |rowEch| |incr| + |numberOfComposites| |identitySquareMatrix| |trapezoidal| |corrPoly| + |algSplitSimple| |inverseIntegralMatrix| |genericPosition| + |OMgetEndAtp| |hi| |cothIfCan| |Lazard2| |c06gbf| |s19adf| |li| |nil| + |degreeSubResultant| |roughSubIdeal?| |transcendentalDecompose| + |recoverAfterFail| |scripted?| |palgLODE0| |linearPart| + |extensionDegree| |elliptic| |invertible?| |d01fcf| |printingInfo?| + |associator| |lllp| |subHeight| |listYoungTableaus| |iiatanh| + |intersect| |f02fjf| |optAttributes| |radicalEigenvectors| + |setMinPoints3D| |random| |s13aaf| |approximate| |removeZero| + |linearlyDependent?| |s17acf| |mapCoef| |symmetricRemainder| + |rightExtendedGcd| |semiLastSubResultantEuclidean| |segment| + |OMgetEndAttr| |lifting| |rotate!| |genericLeftNorm| |groebner?| + |c06gqf| |totolex| |superscript| |lastSubResultantElseSplit| GF2FG + |mdeg| |ReduceOrder| |fortranLiteral| |makeViewport2D| |lazy?| + |function| |logical?| |setnext!| |cExp| |coefChoose| |normalForm| + |genus| |checkRur| |setvalue!| |divisor| |cscIfCan| |bfEntry| |middle| + |e01bhf| |alphabetic| |sn| |fortranLiteralLine| |genericLeftTrace| + |headRemainder| |OMgetInteger| |prinpolINFO| |df2ef| |retractable?| + |datalist| |pol| |symbol| |triangSolve| |semicolonSeparate| |typeList| + |modularFactor| |mapdiv| |logpart| |OMconnInDevice| |primes| |df2fi| + |insertionSort!| |dimensionOfIrreducibleRepresentation| + |relativeApprox| |output| |generate| |integer| |sturmVariationsOf| + |unexpand| |basisOfLeftNucloid| |coerce| |modulus| |e02baf| + |OMputVariable| |more?| |reify| |updatD| |integers| |exprToGenUPS| + |parametric?| |implies| |incrementBy| |linGenPos| |iiasec| |case| + |cAcosh| |even?| |construct| |clearCache| |numberOfImproperPartitions| + |leadingSupport| |factors| |xor| |revert| |reciprocalPolynomial| + |expand| |getZechTable| |insertBottom!| |mesh?| |inv| |OMbindTCP| + |primeFactor| |primlimintfrac| |column| |plus!| |filterWhile| + |identification| |OMgetEndBind| |applyRules| |ground?| |monicDivide| + |integralDerivationMatrix| |e02adf| |screenResolution| |tanintegrate| + |filterUntil| |binomThmExpt| |removeRoughlyRedundantFactorsInPol| + |indiceSubResultantEuclidean| |ground| |hermiteH| |cap| |rst| |list| + |collectUnder| |select| |quotedOperators| |maxrow| |wronskianMatrix| + |negative?| |unravel| |lcm| |plus| |leadingMonomial| |setDifference| + |enterPointData| |less?| |internalDecompose| |pointColor| |polygon?| + |complement| |exquo| |totalfract| |cos2sec| |leadingCoefficient| + |parametersOf| |interpret| |setIntersection| |zag| |monomRDE| + |RemainderList| |palgRDE| |linears| |div| |viewDeltaXDefault| + |stirling1| |shallowExpand| |lfinfieldint| |primitiveMonomials| + |exponentialOrder| |setUnion| |exactQuotient!| |perfectSqrt| |s17aef| + |quo| |denomLODE| |B1solve| |quartic| |addPoint| |gcd| |matrix| + |commaSeparate| |reductum| |apply| |boundOfCauchy| |karatsuba| + |cyclicEntries| |removeSinSq| |high| |largest| |cot2trig| + |OMputEndApp| |union| |c06frf| |times| |rk4a| |OMencodingBinary| + |setImagSteps| |partitions| |palgintegrate| |condition| |rem| + |complete| |binaryFunction| |curve?| |false| |lquo| |chiSquare1| + |size| |pleskenSplit| |makeRecord| |selectSumOfSquaresRoutines| + |rootPoly| |nthExpon| |outputFixed| |findCycle| + |removeIrreducibleRedundantFactors| |ptree| |localUnquote| + |singularAtInfinity?| |d03edf| |modularGcdPrimitive| |shrinkable| + |solveLinearlyOverQ| |limit| |minimumExponent| + |exprHasLogarithmicWeights| |key?| |showArrayValues| + |mainDefiningPolynomial| |iiasech| |maxRowIndex| |drawComplex| |head| + |monom| |SturmHabichtMultiple| |f02wef| |removeZeroes| |first| + |e04dgf| |aromberg| |withPredicates| |chineseRemainder| |digit?| + |useSingleFactorBound?| |generalLambert| |listRepresentation| |rest| + |viewWriteDefault| |doubleRank| |factorsOfDegree| |generators| + |moduleSum| |pToHdmp| |setelt| |f2st| |property| |substitute| |regime| + |seed| |uniform01| |solveid| |rowEchLocal| |factorsOfCyclicGroupSize| + |removeDuplicates| |prindINFO| |completeHermite| |outputForm| + |stirling2| |internalSubQuasiComponent?| |meatAxe| |copy| |zerosOf| + |jordanAlgebra?| |slash| |subCase?| |algebraicDecompose| |cAsinh| + |coth2trigh| |tableForDiscreteLogarithm| |result| |elements| |units| + |createNormalPrimitivePoly| |completeHensel| |sortConstraints| + |partialFraction| |null?| |factorSquareFree| ^= |direction| + |modifyPointData| |integralBasisAtInfinity| |fortranCarriageReturn| + |denominators| |Vectorise| |ravel| |not| |coshIfCan| + |constantCoefficientRicDE| |autoCoerce| |cCsc| |s18aff| |sinIfCan| + |karatsubaOnce| |cCoth| |sechIfCan| |reshape| |iiacoth| + |unitCanonical| |hessian| |iiacos| |LazardQuotient| |escape| + |rightTrace| |fintegrate| |standardBasisOfCyclicSubmodule| |lhs| + |cyclePartition| |extendedEuclidean| |accuracyIF| |llprop| |open?| + |deleteRoutine!| |rhs| |code| |sorted?| |addPoint2| |prinshINFO| + |compile| |Nul| |padicallyExpand| |OMwrite| |univariate?| + |numberOfMonomials| |sh| |f04mcf| |showClipRegion| |completeSmith| + |failed?| |back| |compiledFunction| |bipolarCylindrical| + |algebraicCoefficients?| |update| |goodnessOfFit| |thetaCoord| + |solid?| |basisOfCenter| |e01sff| |loopPoints| |determinant| + |symmetricTensors| |setPoly| |listOfMonoms| |nextIrreduciblePoly| + |semiIndiceSubResultantEuclidean| |exteriorDifferential| |cPower| + |selectPDERoutines| |suffix?| |OMencodingUnknown| |top| |mathieu24| + |d02raf| |lexGroebner| |setprevious!| |s17agf| + |generalizedEigenvector| |rombergo| |continue| |companionBlocks| + |removeCoshSq| |fmecg| |maxrank| |qelt| |stopTableInvSet!| |f02xef| + |minRowIndex| |monicModulo| |prefix?| |reduction| |call| |pdct| + |squareFreeFactors| |second| |iisinh| |leadingExponent| |minus!| + |controlPanel| |constantOperator| |orbits| |quadraticNorm| + |selectAndPolynomials| |key| |third| |init| |computeBasis| |changeVar| + |digamma| |select!| |lepol| |simpleBounds?| |primintegrate| + |rationalFunction| |options| |separant| |resultantReduit| + |fractionPart| |constantOpIfCan| |algintegrate| |f02adf| + |prolateSpheroidal| |sdf2lst| |pointColorPalette| |repeating| |addiag| + |contractSolve| |filename| |inconsistent?| |untab| + |multiplyCoefficients| |flatten| |e02ajf| |printInfo| |symFunc| + |clearTable!| |generic| |divisors| |explicitlyFinite?| |elt| + |cyclicParents| |hexDigit?| |d02cjf| |digit| |initial| |opeval| + |shiftRoots| |infix?| |possiblyNewVariety?| |rewriteSetWithReduction| + |hue| |gcdcofactprim| |bitLength| |minrank| |primeFrobenius| |mask| + |pushucoef| |leadingCoefficientRicDE| |d02gbf| |permutations| + |stopMusserTrials| |primitive?| |firstUncouplingMatrix| |cCsch| + |parse| |setchildren!| |HermiteIntegrate| |f01qdf| |Si| + |internalAugment| |expt| |expIfCan| |hyperelliptic| |f04adf| + |OMputAtp| |countable?| |bernoulliB| |selectfirst| |inverseColeman| + |dn| |limitedIntegrate| |probablyZeroDim?| |mainMonomial| |iisin| + |sumOfKthPowerDivisors| |infiniteProduct| |gcdprim| |supRittWu?| + |startStats!| |expandLog| |s15aef| |gcdPolynomial| |equality| |f07fdf| + |chvar| |OMgetString| |c06gsf| |s21bbf| |positive?| |besselJ| + |repeating?| |nextSubsetGray| |totalDegree| |problemPoints| + |expressIdealMember| |option?| |empty| |leftRecip| |outerProduct| + |sparsityIF| |sincos| |factorOfDegree| |critB| |se2rfi| |tan2trig| + |vertConcat| |signAround| |separateFactors| |maxPoints3D| |isList| + |fortran| |mergeFactors| |OMputEndAtp| |f04arf| |roughUnitIdeal?| + |combineFeatureCompatibility| |setMaxPoints3D| |xRange| + |solveLinearPolynomialEquationByRecursion| |prepareSubResAlgo| |An| + |stFunc2| |dimensionsOf| |integerBound| |intcompBasis| |fractRadix| + |augment| |functionIsContinuousAtEndPoints| |fixedPoint| |yRange| + |floor| |s20acf| |critMonD1| |inRadical?| |setref| |binaryTree| + |copies| |inf| |selectODEIVPRoutines| |recur| |OMlistCDs| |zRange| + |separateDegrees| |rootsOf| |e02bef| |definingInequation| |bag| + |dioSolve| |explogs2trigs| |dominantTerm| |extractPoint| + |integralBasis| |genericRightDiscriminant| |cycleEntry| |map!| + |iiasinh| |unitNormalize| |rightCharacteristicPolynomial| + |palgextint0| |antiCommutator| |setCondition!| |localAbs| |anticoord| + |e02bcf| |besselI| |ffactor| |duplicates?| |qsetelt!| |psolve| + |iicsch| |getBadValues| |torsionIfCan| |summation| + |squareFreeLexTriangular| |splitLinear| |lazyPseudoQuotient| |s13adf| + |hconcat| |OMcloseConn| |rightQuotient| |algebraicOf| + |LowTriBddDenomInv| |inverseIntegralMatrixAtInfinity| |gbasis| + |conditionP| |mainPrimitivePart| |alphabetic?| |measure2Result| + |LagrangeInterpolation| |mvar| |quotient| |rewriteIdealWithRemainder| + |lp| |pseudoRemainder| |droot| |d01akf| |rk4| |factorList| + |showTheSymbolTable| |optimize| |cylindrical| |nonSingularModel| + |merge!| |enterInCache| |generalInfiniteProduct| |headReduced?| + |linkToFortran| |leastPower| |ratpart| |cycleLength| |univcase| + |removeCosSq| |linearMatrix| |testDim| + |rewriteSetByReducingWithParticularGenerators| |symbol?| |binary| + |submod| |character?| |rroot| |index| |quoByVar| |d02ejf| ^ + |factorSFBRlcUnit| |cyclicCopy| + |removeRoughlyRedundantFactorsInContents| |bumptab| |upperCase| + |twoFactor| |restorePrecision| |selectOptimizationRoutines| |acsch| + |generalizedEigenvectors| |realRoots| |brillhartTrials| + |definingPolynomial| |generalizedInverse| |tan2cot| |iibinom| + |rightPower| |sayLength| |cAcoth| |sumOfSquares| F2FG |dmp2rfi| |abs| + |e01bgf| |atanhIfCan| |partialDenominators| |mirror| |script| |polar| + |genericLeftDiscriminant| |fill!| |stoseInvertible?reg| |makeSeries| + |eigenMatrix| |leastMonomial| |argument| |quasiRegular?| |pair| + |bivariateSLPEBR| |showScalarValues| |objectOf| |increasePrecision| + |xn| |connect| |hexDigit| |initTable!| |quickSort| |rightRank| + |chebyshevT| |viewSizeDefault| |stack| |deepestInitial| |iiacsch| + |perfectSquare?| |yCoordinates| |entries| |eulerPhi| |cfirst| + |numberOfFactors| |gramschmidt| |associatedEquations| + |setVariableOrder| |eigenvectors| |tex| |OMgetAtp| |read!| + |stosePrepareSubResAlgo| |resultantReduitEuclidean| + |radicalEigenvalues| |maxPoints| |polarCoordinates| |df2mf| |cLog| + |viewport2D| |block| |leftLcm| |linear| |addPointLast| |d01aqf| + |removeRedundantFactors| |viewZoomDefault| |pointData| + |rightAlternative?| |linearPolynomials| |solve1| |internalIntegrate0| + |createIrreduciblePoly| |OMread| |s17akf| |s17dlf| + |ramifiedAtInfinity?| |nullary?| |rightTrim| |flexibleArray| + |legendreP| |root| |diff| |showIntensityFunctions| |polynomial| + |viewDefaults| |antisymmetricTensors| |chiSquare| |dec| |mkPrim| + |createMultiplicationMatrix| |leftTrim| |shanksDiscLogAlgorithm| + |complexRoots| |cSin| |cCot| |lowerCase?| |graphState| + |deleteProperty!| |s13acf| |outputSpacing| |polygamma| |overlabel| + |infix| |f07fef| |leftExtendedGcd| |cycle| + |rewriteIdealWithQuasiMonicGenerators| |lowerPolynomial| + |initiallyReduce| |hex| |iidprod| |message| |Lazard| + |expandTrigProducts| |dom| |bat| |rotatey| |patternMatch| |nthRoot| + |partialNumerators| |OMputBind| |Hausdorff| |associates?| |xCoord| + |aLinear| |reducedSystem| |rightRemainder| |arity| |computeCycleEntry| + |conjugates| |pointPlot| |iipow| |zoom| |OMencodingSGML| |schwerpunkt| + |outputAsScript| |schema| |diagonals| |equation| |infieldint| + |plotPolar| |bandedJacobian| |wholePart| |float?| |saturate| + |tracePowMod| |commutativeEquality| |prologue| |minColIndex| |iisqrt3| + |iiperm| |viewPosDefault| |showTheIFTable| |subresultantSequence| + |realEigenvectors| |palglimint0| |e02def| |simplifyExp| |wrregime| + |name| |extractProperty| |functionIsOscillatory| |complexIntegrate| + |sts2stst| |e04fdf| |cons| |stoseInvertible?sqfreg| |countRealRoots| + |squareFreePrim| |bumptab1| |createMultiplicationTable| + |clipWithRanges| |linearDependenceOverZ| |factorials| + |factorByRecursion| |SFunction| |rightTraceMatrix| |exp1| + |roughEqualIdeals?| |rightFactorCandidate| |laurentRep| + |resultantnaif| |f04faf| |e01daf| |LyndonBasis| |antisymmetric?| + |leviCivitaSymbol| |getMultiplicationMatrix| |reopen!| |pade| + |fullDisplay| |cotIfCan| |antiCommutative?| |e02gaf| |cAcsc| |label| + |changeWeightLevel| |redmat| |reindex| |setPredicates| |monomial?| + |setButtonValue| |e| |palgLODE| |basicSet| |mapGen| |lazyPseudoDivide| + |maxint| |f02axf| |subMatrix| |d02bbf| |newSubProgram| |cubic| + |listConjugateBases| |numberOfHues| |indiceSubResultant| |sample| + |ratPoly| |c05nbf| |highCommonTerms| |monicDecomposeIfCan| |double?| + |isExpt| |vedf2vef| |s21bdf| |elRow1!| |iomode| |presuper| |cAtan| + |cschIfCan| |shufflein| |approximants| |exponential| |flagFactor| + |f02agf| |drawToScale| |createRandomElement| |s17dcf| |color| |imagJ| + |tube| |linearAssociatedExp| |e04mbf| |OMputObject| |brace| |csc2sin| + |upDateBranches| |reorder| |weighted| |rightRecip| |s20adf| + |setAttributeButtonStep| |yellow| |selectFiniteRoutines| |OMserve| + |irreducibleFactors| |makeResult| |bfKeys| |rightZero| + |removeDuplicates!| |dihedralGroup| |npcoef| |exactQuotient| |tanNa| + |title| |s19abf| |curryRight| |ode2| |tanhIfCan| |trace2PowMod| |prem| + |integralAtInfinity?| |iprint| |horizConcat| |getDatabase| |palgint0| + |exprToUPS| |ParCond| |iicsc| |setColumn!| |isMult| + |toseLastSubResultant| |numeric| |solveInField| |principalIdeal| + |mainForm| |idealSimplify| |matrixGcd| |elColumn2!| |overbar| |value| + |error| |radical| |discriminant| |fixedDivisor| |selectOrPolynomials| + |finiteBound| |fracPart| |leftFactor| + |setLegalFortranSourceExtensions| |expandPower| |fortranLogical| |dim| + |assert| |ceiling| |collect| |numberOfComponents| |charpol| |s15adf| + |trigs2explogs| |bernoulli| |substring?| |phiCoord| |plusInfinity| + |setScreenResolution| |depth| |integral?| |makeprod| |evenlambert| + |monomialIntegrate| |normalized?| |doubleComplex?| + |selectMultiDimensionalRoutines| |sec2cos| |OMlistSymbols| + |minusInfinity| |properties| |setright!| |f01qef| |option| |e04gcf| + |rootBound| |create| |getMultiplicationTable| |pquo| |oddlambert| + |insertRoot!| |makingStats?| |central?| + |createLowComplexityNormalBasis| |lists| |normalDenom| |round| + |extractIndex| |useEisensteinCriterion?| |d03faf| |number?| + |upperCase!| |beauzamyBound| |rename!| |createThreeSpace| |aCubic| + |noLinearFactor?| |extend| |homogeneous?| |range| |extractBottom!| + |id| |ef2edf| |showTheRoutinesTable| |extractSplittingLeaf| + |translate| |rightExactQuotient| |henselFact| |coefficients| + |makeSketch| |write!| |deriv| |realElementary| |polyPart| |coHeight| + ** |stoseInvertibleSetsqfreg| |table| |parabolic| |mapUnivariateIfCan| + |radix| |trim| |univariatePolynomialsGcds| |linearlyDependentOverZ?| + |float| |pdf2ef| |new| |unparse| |unrankImproperPartitions1| + |logIfCan| |f02ajf| |fi2df| |zeroDimensional?| |linearAssociatedLog| + |failed| EQ |outputList| |radicalRoots| |atanIfCan| + |irreducibleFactor| |hspace| |palgRDE0| |retractIfCan| + |leftRankPolynomial| |OMputEndAttr| |kroneckerDelta| |child?| + |replace| |nextPrimitiveNormalPoly| |s17def| |makeMulti| + |outputFloating| |OMclose| |collectUpper| |latex| |changeBase| + |children| |position!| |matrixConcat3D| |ode1| |slex| |makeCos| + |stronglyReduced?| |s17ajf| |drawStyle| |nor| |bubbleSort!| |s17adf| + |zeroSetSplit| |nil?| |derivationCoordinates| + |halfExtendedSubResultantGcd2| |order| |stFunc1| |OMgetBind| + |clearDenominator| |lighting| |deepExpand| |OMputAttr| |over| + |nextPrime| |totalLex| |forLoop| |zeroDimPrimary?| |modifyPoint| + |subNodeOf?| GE |s18adf| |lagrange| |tubeRadius| RF2UTS + |triangularSystems| |setErrorBound| |cAsec| |alphanumeric?| GT + |rightFactorIfCan| |algebraic?| |iiacosh| |leftUnit| |computePowers| + |badNum| |level| |log10| |iiatan| |sqfrFactor| |testModulus| + |primextendedint| LE |left| |nextPartition| |getStream| |OMputFloat| + |rspace| |remainder| |leader| |resetNew| |complexForm| |integrate| + |createNormalElement| |exptMod| LT |getOrder| |car| |right| |c05adf| + |sinh2csch| |getVariableOrder| |squareFree| |quote| |s17dgf| + |tubeRadiusDefault| |c02agf| |cdr| |map| |laguerreL| |paren| |low| + |has?| |cup| |cycles| |const| |OMreceive| |sPol| |changeThreshhold| + |intensity| |scalarTypeOf| |asinhIfCan| |swap| |rur| |irreducible?| + |lazyIrreducibleFactors| |e01saf| |subQuasiComponent?| |e02daf| + |acosIfCan| |internalZeroSetSplit| |lSpaceBasis| |OMreadStr| |d01gaf| + |mightHaveRoots| |OMgetFloat| |inverseLaplace| |leftRank| + |strongGenerators| |bsolve| |module| |primPartElseUnitCanonical!| + |infLex?| |pair?| D |printHeader| |tab1| |swap!| + |constantToUnaryFunction| |characteristicSet| |resultantEuclideannaif| + |common| |graphs| |eigenvalues| |blankSeparate| |bottom!| + |nonLinearPart| |elementary| |errorInfo| |qinterval| |evaluateInverse| + |unvectorise| |GospersMethod| |convert| |numberOfPrimitivePoly| + |secIfCan| |leftFactorIfCan| |cyclotomicDecomposition| |endOfFile?| + |OMputString| |prime| |varList| |showTypeInOutput| |flexible?| + |postfix| |chainSubResultants| |space| |hdmpToP| |setsubMatrix!| + |rename| |moebius| |charthRoot| |ratDenom| |operation| |euclideanSize| + |rationalIfCan| |monicRightDivide| |rectangularMatrix| |normalise| + |sech2cosh| |groebnerFactorize| |blue| |OMUnknownCD?| |fibonacci| + |invertibleElseSplit?| |powerSum| |atrapezoidal| |pascalTriangle| + |retract| |purelyAlgebraic?| |startTableGcd!| |ratDsolve| |delay| + |identity| |OMgetSymbol| |pop!| |lowerCase!| |OMputError| + |shallowCopy| |index?| |tanAn| |repSq| |taylorRep| + |wordInStrongGenerators| |move| |minPoly| |cosIfCan| |print| |d03eef| + |numberOfOperations| |lyndon| |pile| |quadratic| |viewpoint| |hMonic| + |distFact| |cAsin| |htrigs| |point| |getRef| |ptFunc| + |OMunhandledSymbol| |width| |ksec| |unprotectedRemoveRedundantFactors| + |insert!| |att2Result| |lflimitedint| |radicalEigenvector| |size?| + |integralMatrixAtInfinity| |indicialEquationAtInfinity| |f02aaf| + |interReduce| |odd?| |structuralConstants| |associative?| |e04naf| + |series| |rootProduct| |particularSolution| |stopTable!| |precision| + |iiexp| |mapBivariate| |times!| |linear?| |enqueue!| |int| + |clipPointsDefault| |complexEigenvectors| |ScanFloatIgnoreSpacesIfCan| + |Beta| |resize| |listOfLists| |optional| |makeUnit| + |branchPointAtInfinity?| |solveRetract| |rk4f| |OMgetEndBVar| + |hasTopPredicate?| |sum| |createZechTable| |eisensteinIrreducible?| + |unitNormal| |min| |c06gcf| |f02akf| |lexTriangular| |sumOfDivisors| + |nary?| |getOperands| |next| |box| |credPol| |evaluate| + |quasiAlgebraicSet| |extendedIntegrate| |rdregime| |deref| |concat!| + |ddFact| |iteratedInitials| |primintfldpoly| + |basisOfCommutingElements| |explicitlyEmpty?| |clip| |sign| + |setLabelValue| |epilogue| |sup| |basisOfRightAnnihilator| |radPoly| + |OMReadError?| |polyred| |d01apf| |real?| |logGamma| |OMopenString| + |elliptic?| |cardinality| |checkPrecision| |asech| |besselK| |bright| + |inrootof| |trapezoidalo| |norm| |baseRDE| |polCase| |ord| |randomR| + |comp| |physicalLength!| |rubiksGroup| |d01amf| |minIndex| + |numberOfVariables| |multiple| |OMputSymbol| + |lastSubResultantEuclidean| |edf2ef| |splitConstant| |trivialIdeal?| + |represents| |applyQuote| |axes| |curry| |tanIfCan| + |noncommutativeJordanAlgebra?| |hasHi| |weight| |traverse| |safeFloor| + |lyndonIfCan| |recip| |OMputApp| |eval| |green| |iiGamma| |setClosed| + |leftMinimalPolynomial| |any| |in?| |primaryDecomp| |OMputBVar| + |reduceLODE| |doubleResultant| |selectNonFiniteRoutines| + |integralMatrix| |permutationRepresentation| |ruleset| |zCoord| + |makeViewport3D| |wreath| |leftCharacteristicPolynomial| |innerSolve1| + |bipolar| |#| |rowEchelonLocal| |adaptive?| |inHallBasis?| |lowerCase| + |transcendenceDegree| |nullary| |setOfMinN| |indicialEquations| + |ODESolve| |OMsetEncoding| |ellipticCylindrical| |cyclotomic| + |randnum| |semiResultantEuclidean2| |limitPlus| |primitivePart!| + |curveColor| |innerEigenvectors| |e02ddf| |frobenius| |suchThat| + |stiffnessAndStabilityFactor| |iitan| |eigenvector| |invmod| |search| + |solveLinear| |variationOfParameters| |rightDivide| |minPoints3D| + |close!| |center| |char| |sinhIfCan| |acoshIfCan| |compdegd| + |OMmakeConn| |resetAttributeButtons| |rightLcm| |leftZero| |maxdeg| + |principal?| |integerIfCan| |partialQuotients| |e04ycf| |lazyEvaluate| + |mainCoefficients| |sin2csc| |unitVector| |imagE| |permutation| + |debug3D| |intPatternMatch| |fixPredicate| |genericRightTraceForm| + |iCompose| |extension| |badValues| |swapColumns!| |prod| |makeSUP| + |LyndonWordsList| |setProperty| |discriminantEuclidean| |graeffe| + |reduced?| |rischDEsys| |e02bbf| |sylvesterSequence| |areEquivalent?| + |rk4qc| |changeNameToObjf| |complexElementary| |generic?| |qqq| + |radicalSolve| |mapUp!| |semiDiscriminantEuclidean| |d01asf| + |makeYoungTableau| |bumprow| |redPo| |e02akf| |leadingIndex| + |alternatingGroup| |currentSubProgram| |d02bhf| |measure| |numerator| + |Zero| |processTemplate| |appendPoint| |taylorIfCan| |discreteLog| + |iiabs| |gcdPrimitive| ~ |lazyIntegrate| |mergeDifference| + |branchIfCan| |compactFraction| |One| |toroidal| |cn| |adaptive3D?| + |lintgcd| |polynomialZeros| |outputMeasure| |PollardSmallFactor| |ran| + |pack!| |digits| |notelem| |members| |point?| |create3Space| |pole?| + |cyclotomicFactorization| |algDsolve| |oddInfiniteProduct| |edf2efi| + |realSolve| |simplifyPower| |multiple?| |quasiMonicPolynomials| + |rightOne| |basis| |endSubProgram| |primextintfrac| |s19aaf| + |asechIfCan| |resetVariableOrder| |UP2ifCan| |mapSolve| + |rightDiscriminant| |laguerre| |stronglyReduce| |polygon| |mainValue| + |cycleRagits| |getGraph| |normal?| |normalizedAssociate| + |OMsupportsCD?| |createPrimitiveElement| |createPrimitiveNormalPoly| + |symmetricGroup| |mulmod| |seriesSolve| |open| |normalizeIfCan| |mat| + |setValue!| |rational| |length| |rootRadius| |s18dcf| |is?| + |univariatePolynomials| |whatInfinity| |eyeDistance| + |representationType| |conjug| |ode| |scripts| |bivariatePolynomials| + |redPol| |associatorDependence| |leftUnits| |mantissa| |integer?| + |symmetricPower| |besselY| |terms| |rational?| |trueEqual| + |generalPosition| |omError| |subTriSet?| |s17aff| |wholeRadix| + |specialTrigs| |expr| |components| |leadingTerm| |hclf| |typeLists| + |f01qcf| |quoted?| |s21baf| |roughBase?| |clipSurface| |critpOrder| + |divideExponents| |append| |s17dhf| |subResultantChain| + |factorGroebnerBasis| |reducedContinuedFraction| + |parabolicCylindrical| |fullPartialFraction| |clearFortranOutputStack| + NOT |scaleRoots| |rank| |delete| |countRealRootsMultiple| |cSec| + |expextendedint| |printCode| |twist| |padecf| OR |setMaxPoints| + |branchPoint?| |copy!| |queue| |variable| |romberg| |lineColorDefault| + |fortranComplex| |addMatch| AND |reverse!| |e02ahf| + |nextsousResultant2| |characteristicSerie| |mainSquareFreePart| + |cAsech| |numberOfCycles| |medialSet| |readLineIfCan!| |style| + |localReal?| |dictionary| |genericRightMinimalPolynomial| + |rationalPoints| |sturmSequence| |removeSuperfluousQuasiComponents| + |critBonD| |leadingBasisTerm| |log2| |mainCharacterization| |eq| + |internalInfRittWu?| |janko2| |cyclicGroup| + |rewriteIdealWithHeadRemainder| |idealiser| |lazyGintegrate| |merge| + |removeSuperfluousCases| |musserTrials| |iter| |LazardQuotient2| + |complexNumericIfCan| |approxNthRoot| |showAll?| |e02agf| + |superHeight| |leaf?| |factorSquareFreePolynomial| |iifact| + |exponents| |/\\| |obj| |imagK| |elem?| |semiResultantReduitEuclidean| + |every?| |string?| |createGenericMatrix| |initials| |explicitEntries?| + |characteristicPolynomial| |\\/| |nullity| |cache| |e02zaf| |s14baf| + |operators| |reducedQPowers| |curryLeft| |numericalOptimization| + |numer| |setTopPredicate| |monicLeftDivide| |conditionsForIdempotents| + |solveLinearPolynomialEquation| |setAdaptive| |tower| + |createPrimitivePoly| |cRationalPower| |satisfy?| |distance| + |primPartElseUnitCanonical| |OMconnOutDevice| |putGraph| + |divisorCascade| |subset?| |powerAssociative?| |acschIfCan| + |dimensions| |headReduce| |makeFR| |semiSubResultantGcdEuclidean2| + |repeatUntilLoop| |rationalPoint?| |vark| * |df2st| |OMencodingXML| + |numFunEvals3D| |tanh2trigh| |extractClosed| |decimal| |internal?| + |generalizedContinuumHypothesisAssumed| |extendedResultant| + |coerceListOfPairs| |OMputEndBVar| |lazyVariations| |factor| |c02aff| + |exp| |balancedBinaryTree| |distdfact| |purelyTranscendental?| + |rootOfIrreduciblePoly| |declare!| |zero| |linearAssociatedOrder| + |viewPhiDefault| |moduloP| |sqrt| |setEmpty!| |f01brf| |setRow!| |dot| + |complex| |bringDown| |expintfldpoly| |complexExpand| |null| + |ScanFloatIgnoreSpaces| |real| |divideIfCan| UP2UTS |invmultisect| + |rootNormalize| |groebnerIdeal| |bracket| |curveColorPalette| |And| + |rightRankPolynomial| |coth2tanh| |removeRedundantFactorsInPols| + |imag| |showAllElements| |rules| |s19acf| |directProduct| |makeTerm| + |d01gbf| |showRegion| |subst| |Or| |adaptive| |minimumDegree| + |unaryFunction| |startTableInvSet!| |numFunEvals| |youngGroup| + |normalizeAtInfinity| |f01bsf| |factorFraction| |Not| |increment| + |powers| |ridHack1| |stoseInvertibleSet| |trigs| + |halfExtendedResultant1| |subNode?| |rotatex| |incrementKthElement| + |bezoutResultant| |expint| |clearTheIFTable| |universe| |destruct| + |unary?| |fractionFreeGauss!| |lfintegrate| |rightMult| |f04asf| + |coerceP| |sumSquares| |groebSolve| |diag| |weights| |coerceImages| + |cCosh| |rightScalarTimes!| |f01mcf| |iiacsc| |infieldIntegrate| + |OMParseError?| |makeFloatFunction| |patternVariable| |rootSplit| + |coercePreimagesImages| |iroot| |biRank| |critM| |laplacian| |f04qaf| + |objects| |ScanArabic| |SturmHabichtCoefficients| |asecIfCan| + |scanOneDimSubspaces| |choosemon| |overlap| |conical| |setPrologue!| + |f2df| |triangular?| |fglmIfCan| |base| |f02aff| |OMgetObject| + |s18aef| |lex| |d01anf| |double| |OMgetEndError| |or| + |symmetricSquare| |insertTop!| |realEigenvalues| |var1Steps| + |lieAlgebra?| |c06fqf| |s18def| |ParCondList| |symmetricDifference| + |quotientByP| |inc| |changeName| |and| |diagonalMatrix| |someBasis| + |rarrow| |regularRepresentation| |btwFact| |matrixDimensions| + |OMUnknownSymbol?| |argscript| |tubePlot| |dAndcExp| |iicoth| + |charClass| |OMgetEndApp| |removeConstantTerm| |e04jaf| |minset| + |prefix| |yCoord| |stoseSquareFreePart| |leftRegularRepresentation| + |hcrf| |checkForZero| |messagePrint| |degreePartition| |triangulate| + |toScale| |iiasin| |monomialIntPoly| |super| |mathieu11| |build| + |comment| F |hasoln| |extendIfCan| |freeOf?| |e02aef| + |brillhartIrreducible?| |nthFlag| |f07adf| |selectPolynomials| + |f04jgf| |getExplanations| |subResultantGcd| |test| + |algebraicVariables| |edf2df| |euclideanGroebner| |singleFactorBound| + |meshPar1Var| |divideIfCan!| |SturmHabicht| |compose| |chebyshevU| + |LyndonCoordinates| |OMputInteger| |startPolynomial| |whileLoop| + |returnType!| |airyAi| |graphCurves| |iiacot| |OMsupportsSymbol?| + |abelianGroup| |fractRagits| |mkAnswer| |orthonormalBasis| + |showFortranOutputStack| |RittWuCompare| |content| |max| |denomRicDE| + |Gamma| |radicalOfLeftTraceForm| |isAbsolutelyIrreducible?| |ignore?| + |neglist| |jordanAdmissible?| |unrankImproperPartitions0| |bat1| + |lexico| |socf2socdf| |csch2sinh| |axesColorDefault| |sort!| + |permutationGroup| |supersub| |atom?| |airyBi| |mindeg| |Frobenius| + |belong?| |concat| |fprindINFO| |leftPower| |top!| + |viewWriteAvailable| |selectsecond| |nonQsign| |quatern| + |SturmHabichtSequence| |partition| |froot| |setEpilogue!| |previous| + |hash| |clipBoolean| |rightNorm| |roughBasicSet| |closeComponent| + |rootSimp| |iisec| |genericRightTrace| |numberOfDivisors| |tab| + |count| |algint| |reduceByQuasiMonic| |setStatus| |extractIfCan| + |preprocess| |positiveRemainder| |PDESolve| |innerSolve| |setStatus!| + |composite| |ref| |updatF| |genericLeftTraceForm| |shade| + |cycleSplit!| |intermediateResultsIF| |physicalLength| + |collectQuasiMonic| |safetyMargin| |var2Steps| |lookup| |ideal| + |createNormalPoly| |harmonic| |lllip| |parent| |leftOne| |contains?| + |primitiveElement| |unmakeSUP| |newLine| |primitivePart| |cTan| + |setleft!| |primlimitedint| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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(-725)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-33) . T) ((-37 |#2|) |has| |#2| (-156)) ((-97) -3747 (|has| |#2| (-1005)) (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-338)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-106 |#2| |#2|) -3747 (|has| |#2| (-963)) (|has| |#2| (-333)) (|has| |#2| (-156))) ((-106 $ $) |has| |#2| (-156)) ((-123) -3747 (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-123))) ((-557 (-787)) -3747 (|has| |#2| (-1005)) (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-338)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-557 (-787))) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-557 (-1157 |#2|)) . T) ((-156) |has| |#2| (-156)) ((-205 |#2|) |has| |#2| (-963)) ((-207) -12 (|has| |#2| (-207)) (|has| |#2| (-963))) ((-258 #0=(-517) |#2|) . T) ((-260 #0# |#2|) . T) ((-280 |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1005))) ((-338) |has| |#2| (-338)) ((-347 |#2|) |has| |#2| (-963)) ((-381 |#2|) |has| |#2| (-1005)) ((-456 |#2|) . T) ((-550 #0# |#2|) . T) ((-478 |#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1005))) ((-585 |#2|) -3747 (|has| |#2| (-963)) (|has| |#2| (-333)) (|has| |#2| (-156))) ((-585 $) -3747 (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-579 (-517)) -12 (|has| |#2| (-579 (-517))) (|has| |#2| (-963))) ((-579 |#2|) |has| |#2| (-963)) ((-650 |#2|) -3747 (|has| |#2| (-333)) (|has| |#2| (-156))) ((-659) -3747 (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-723) |has| |#2| (-777)) ((-724) -3747 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-725) |has| |#2| (-725)) ((-726) -3747 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-727) -3747 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-777) |has| |#2| (-777)) ((-779) -3747 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-823 (-1076)) -12 (|has| |#2| (-823 (-1076))) (|has| |#2| (-963))) ((-954 (-377 (-517))) -12 (|has| |#2| (-954 (-377 (-517)))) (|has| |#2| (-1005))) ((-954 (-517)) -12 (|has| |#2| (-954 (-517))) (|has| |#2| (-1005))) ((-954 |#2|) |has| |#2| (-1005)) ((-969 |#2|) -3747 (|has| |#2| (-963)) (|has| |#2| (-333)) (|has| |#2| (-156))) ((-969 $) |has| |#2| (-156)) ((-963) -3747 (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-970) -3747 (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-1017) -3747 (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-1005) -3747 (|has| |#2| (-1005)) (|has| |#2| (-963)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-338)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-1111) . T) ((-1164 |#2|) |has| |#2| (-333))) -((-1532 (((-214 |#1| |#3|) (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|) 21)) (-1522 ((|#3| (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|) 23)) (-3310 (((-214 |#1| |#3|) (-1 |#3| |#2|) (-214 |#1| |#2|)) 18))) -(((-213 |#1| |#2| |#3|) (-10 -7 (-15 -1532 ((-214 |#1| |#3|) (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|)) (-15 -1522 (|#3| (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|)) (-15 -3310 ((-214 |#1| |#3|) (-1 |#3| |#2|) (-214 |#1| |#2|)))) (-703) (-1111) (-1111)) (T -213)) -((-3310 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-214 *5 *6)) (-14 *5 (-703)) (-4 *6 (-1111)) (-4 *7 (-1111)) (-5 *2 (-214 *5 *7)) (-5 *1 (-213 *5 *6 *7)))) (-1522 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-214 *5 *6)) (-14 *5 (-703)) (-4 *6 (-1111)) (-4 *2 (-1111)) (-5 *1 (-213 *5 *6 *2)))) (-1532 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-214 *6 *7)) (-14 *6 (-703)) (-4 *7 (-1111)) (-4 *5 (-1111)) (-5 *2 (-214 *6 *5)) (-5 *1 (-213 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-478 |#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1006))) ((-585 |#2|) -3786 (|has| |#2| (-964)) (|has| |#2| (-333)) (|has| |#2| (-156))) ((-585 $) -3786 (|has| |#2| (-964)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-579 (-517)) -12 (|has| |#2| (-579 (-517))) (|has| |#2| (-964))) ((-579 |#2|) |has| |#2| (-964)) ((-650 |#2|) -3786 (|has| |#2| (-333)) (|has| |#2| (-156))) ((-659) -3786 (|has| |#2| (-964)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-723) |has| |#2| (-777)) ((-724) -3786 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-725) |has| |#2| (-725)) ((-726) -3786 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-727) -3786 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-777) |has| |#2| (-777)) ((-779) -3786 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-824 (-1077)) -12 (|has| |#2| (-824 (-1077))) (|has| |#2| (-964))) ((-955 (-377 (-517))) -12 (|has| |#2| (-955 (-377 (-517)))) (|has| |#2| (-1006))) ((-955 (-517)) -12 (|has| |#2| (-955 (-517))) (|has| |#2| (-1006))) ((-955 |#2|) |has| |#2| (-1006)) ((-970 |#2|) -3786 (|has| |#2| (-964)) (|has| |#2| (-333)) (|has| |#2| (-156))) ((-970 $) |has| |#2| (-156)) ((-964) -3786 (|has| |#2| (-964)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-971) -3786 (|has| |#2| (-964)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-1018) -3786 (|has| |#2| (-964)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-1006) -3786 (|has| |#2| (-1006)) (|has| |#2| (-964)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-338)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-1112) . 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"STREAM2" 2657371 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1054 2656228 2656280 2656373 "STREAM1" 2656482 NIL STREAM1 (NIL T) -7 NIL NIL) (-1053 2655244 2655425 2655656 "STINPROD" 2656044 NIL STINPROD (NIL T) -7 NIL NIL) (-1052 2654822 2655006 2655037 "STEP" 2655117 T STEP (NIL) -9 NIL 2655195) (-1051 2648365 2654721 2654798 "STBL" 2654803 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1050 2643540 2647587 2647631 "STAGG" 2647784 NIL STAGG (NIL T) -9 NIL 2647873) (-1049 2641242 2641844 2642716 "STAGG-" 2642721 NIL STAGG- (NIL T T) -8 NIL NIL) (-1048 2639437 2641012 2641104 "STACK" 2641185 NIL STACK (NIL T) -8 NIL NIL) (-1047 2632168 2637584 2638039 "SREGSET" 2639067 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1046 2624608 2625976 2627488 "SRDCMPK" 2630774 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1045 2617575 2622048 2622079 "SRAGG" 2623382 T SRAGG (NIL) -9 NIL 2623990) (-1044 2616592 2616847 2617226 "SRAGG-" 2617231 NIL SRAGG- (NIL T) -8 NIL NIL) (-1043 2611041 2615511 2615938 "SQMATRIX" 2616211 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1042 2604793 2607761 2608487 "SPLTREE" 2610387 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1041 2600783 2601449 2602095 "SPLNODE" 2604219 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1040 2599829 2600062 2600093 "SPFCAT" 2600537 T SPFCAT (NIL) -9 NIL NIL) (-1039 2598566 2598776 2599040 "SPECOUT" 2599587 T SPECOUT (NIL) -7 NIL NIL) (-1038 2598327 2598367 2598436 "SPADPRSR" 2598519 T SPADPRSR (NIL) -7 NIL NIL) (-1037 2590349 2592096 2592139 "SPACEC" 2596462 NIL SPACEC (NIL T) -9 NIL 2598278) (-1036 2588521 2590282 2590330 "SPACE3" 2590335 NIL SPACE3 (NIL T) -8 NIL NIL) (-1035 2587273 2587444 2587735 "SORTPAK" 2588326 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1034 2585329 2585632 2586050 "SOLVETRA" 2586937 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1033 2584340 2584562 2584836 "SOLVESER" 2585102 NIL SOLVESER (NIL T) -7 NIL NIL) (-1032 2579560 2580441 2581443 "SOLVERAD" 2583392 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1031 2575375 2575984 2576713 "SOLVEFOR" 2578927 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1030 2569674 2574726 2574823 "SNTSCAT" 2574828 NIL SNTSCAT (NIL T T T T) -9 NIL 2574898) (-1029 2563779 2568005 2568395 "SMTS" 2569364 NIL SMTS (NIL T T T) -8 NIL NIL) (-1028 2558190 2563668 2563744 "SMP" 2563749 NIL SMP (NIL T T) -8 NIL NIL) (-1027 2556349 2556650 2557048 "SMITH" 2557887 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1026 2549313 2553509 2553612 "SMATCAT" 2554952 NIL SMATCAT (NIL NIL T T T) -9 NIL 2555501) (-1025 2546254 2547077 2548254 "SMATCAT-" 2548259 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1024 2543967 2545490 2545534 "SKAGG" 2545795 NIL SKAGG (NIL T) -9 NIL 2545930) (-1023 2540025 2543071 2543349 "SINT" 2543711 T SINT (NIL) -8 NIL NIL) (-1022 2539797 2539835 2539901 "SIMPAN" 2539981 T SIMPAN (NIL) -7 NIL NIL) (-1021 2538635 2538856 2539131 "SIGNRF" 2539556 NIL SIGNRF (NIL T) -7 NIL NIL) (-1020 2537444 2537595 2537885 "SIGNEF" 2538464 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1019 2535134 2535588 2536094 "SHP" 2536985 NIL SHP (NIL T NIL) -7 NIL NIL) (-1018 2528987 2535035 2535111 "SHDP" 2535116 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1017 2528476 2528668 2528699 "SGROUP" 2528851 T SGROUP (NIL) -9 NIL 2528938) (-1016 2528246 2528298 2528402 "SGROUP-" 2528407 NIL SGROUP- (NIL T) -8 NIL NIL) (-1015 2525082 2525779 2526502 "SGCF" 2527545 T SGCF (NIL) -7 NIL NIL) (-1014 2519480 2524532 2524629 "SFRTCAT" 2524634 NIL SFRTCAT (NIL T T T T) -9 NIL 2524672) (-1013 2512940 2513955 2515089 "SFRGCD" 2518463 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1012 2506106 2507177 2508361 "SFQCMPK" 2511873 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1011 2505728 2505817 2505927 "SFORT" 2506047 NIL SFORT (NIL T T) -8 NIL NIL) (-1010 2504873 2505568 2505689 "SEXOF" 2505694 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1009 2504007 2504754 2504822 "SEX" 2504827 T SEX (NIL) -8 NIL NIL) (-1008 2498783 2499472 2499568 "SEXCAT" 2503339 NIL SEXCAT (NIL T T T T T) -9 NIL 2503958) (-1007 2495963 2498717 2498765 "SET" 2498770 NIL SET (NIL T) -8 NIL NIL) (-1006 2494214 2494676 2494981 "SETMN" 2495704 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1005 2493821 2493947 2493978 "SETCAT" 2494095 T SETCAT (NIL) -9 NIL 2494179) (-1004 2493601 2493653 2493752 "SETCAT-" 2493757 NIL SETCAT- (NIL T) -8 NIL NIL) (-1003 2489988 2492062 2492106 "SETAGG" 2492976 NIL SETAGG (NIL T) -9 NIL 2493316) (-1002 2489446 2489562 2489799 "SETAGG-" 2489804 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1001 2488651 2488944 2489006 "SEGXCAT" 2489292 NIL SEGXCAT (NIL T T) -9 NIL 2489411) (-1000 2487709 2488319 2488500 "SEG" 2488505 NIL SEG (NIL T) -8 NIL NIL) (-999 2486626 2486839 2486881 "SEGCAT" 2487454 NIL SEGCAT (NIL T) -9 NIL 2487692) (-998 2485680 2486010 2486208 "SEGBIND" 2486461 NIL SEGBIND (NIL T) -8 NIL NIL) (-997 2485312 2485369 2485478 "SEGBIND2" 2485617 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-996 2484535 2484661 2484863 "SEG2" 2485156 NIL SEG2 (NIL T T) -7 NIL NIL) (-995 2483974 2484472 2484517 "SDVAR" 2484522 NIL SDVAR (NIL T) -8 NIL NIL) (-994 2476280 2483753 2483877 "SDPOL" 2483882 NIL SDPOL (NIL T) -8 NIL NIL) (-993 2474879 2475145 2475462 "SCPKG" 2475995 NIL SCPKG (NIL T) -7 NIL NIL) (-992 2474106 2474239 2474416 "SCACHE" 2474734 NIL SCACHE (NIL T) -7 NIL NIL) (-991 2473549 2473870 2473953 "SAOS" 2474043 T SAOS (NIL) -8 NIL NIL) (-990 2473117 2473152 2473323 "SAERFFC" 2473508 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-989 2467013 2473016 2473094 "SAE" 2473099 NIL SAE (NIL T T NIL) -8 NIL NIL) (-988 2466609 2466644 2466801 "SAEFACT" 2466972 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-987 2464935 2465249 2465648 "RURPK" 2466275 NIL RURPK (NIL T NIL) -7 NIL NIL) (-986 2463588 2463865 2464172 "RULESET" 2464771 NIL RULESET (NIL T T T) -8 NIL NIL) (-985 2460796 2461299 2461760 "RULE" 2463270 NIL RULE (NIL T T T) -8 NIL NIL) (-984 2460438 2460593 2460674 "RULECOLD" 2460748 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-983 2455330 2456124 2457040 "RSETGCD" 2459637 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-982 2444644 2449696 2449791 "RSETCAT" 2453856 NIL RSETCAT (NIL T T T T) -9 NIL 2454953) (-981 2442575 2443114 2443934 "RSETCAT-" 2443939 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-980 2435005 2436380 2437896 "RSDCMPK" 2441174 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-979 2433022 2433463 2433536 "RRCC" 2434612 NIL RRCC (NIL T T) -9 NIL 2434956) (-978 2432376 2432550 2432826 "RRCC-" 2432831 NIL RRCC- (NIL T T T) -8 NIL NIL) (-977 2406742 2416367 2416432 "RPOLCAT" 2426934 NIL RPOLCAT (NIL T T T) -9 NIL 2430092) (-976 2398246 2400584 2403702 "RPOLCAT-" 2403707 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-975 2389312 2396476 2396956 "ROUTINE" 2397786 T ROUTINE (NIL) -8 NIL NIL) (-974 2386017 2388868 2389015 "ROMAN" 2389185 T ROMAN (NIL) -8 NIL NIL) (-973 2384303 2384888 2385145 "ROIRC" 2385823 NIL ROIRC (NIL T T) -8 NIL NIL) (-972 2380707 2383011 2383040 "RNS" 2383336 T RNS (NIL) -9 NIL 2383606) (-971 2379221 2379604 2380135 "RNS-" 2380208 NIL RNS- (NIL T) -8 NIL NIL) (-970 2378646 2379054 2379083 "RNG" 2379088 T RNG (NIL) -9 NIL 2379109) (-969 2378043 2378405 2378446 "RMODULE" 2378506 NIL RMODULE (NIL T) -9 NIL 2378548) (-968 2376895 2376989 2377319 "RMCAT2" 2377944 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-967 2373609 2376078 2376399 "RMATRIX" 2376630 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-966 2366605 2368839 2368952 "RMATCAT" 2372261 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2373243) (-965 2365984 2366131 2366434 "RMATCAT-" 2366439 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-964 2365554 2365629 2365755 "RINTERP" 2365903 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-963 2364604 2365168 2365197 "RING" 2365307 T RING (NIL) -9 NIL 2365401) (-962 2364399 2364443 2364537 "RING-" 2364542 NIL RING- (NIL T) -8 NIL NIL) (-961 2363247 2363484 2363740 "RIDIST" 2364163 T RIDIST (NIL) -7 NIL NIL) (-960 2354569 2362721 2362924 "RGCHAIN" 2363096 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-959 2351574 2352188 2352856 "RF" 2353933 NIL RF (NIL T) -7 NIL NIL) (-958 2351223 2351286 2351387 "RFFACTOR" 2351505 NIL RFFACTOR (NIL T) -7 NIL NIL) (-957 2350951 2350986 2351081 "RFFACT" 2351182 NIL RFFACT (NIL T) -7 NIL NIL) (-956 2349081 2349445 2349825 "RFDIST" 2350591 T RFDIST (NIL) -7 NIL NIL) (-955 2348539 2348631 2348791 "RETSOL" 2348983 NIL RETSOL (NIL T T) -7 NIL NIL) (-954 2348131 2348211 2348253 "RETRACT" 2348443 NIL RETRACT (NIL T) -9 NIL NIL) (-953 2347983 2348008 2348092 "RETRACT-" 2348097 NIL RETRACT- (NIL T T) -8 NIL NIL) (-952 2340841 2347640 2347765 "RESULT" 2347878 T RESULT (NIL) -8 NIL NIL) (-951 2339426 2340115 2340312 "RESRING" 2340744 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-950 2339066 2339115 2339211 "RESLATC" 2339363 NIL RESLATC (NIL T) -7 NIL NIL) (-949 2338775 2338809 2338914 "REPSQ" 2339025 NIL REPSQ (NIL T) -7 NIL NIL) (-948 2336206 2336786 2337386 "REP" 2338195 T REP (NIL) -7 NIL NIL) (-947 2335907 2335941 2336050 "REPDB" 2336165 NIL REPDB (NIL T) -7 NIL NIL) (-946 2329852 2331231 2332451 "REP2" 2334719 NIL REP2 (NIL T) -7 NIL NIL) (-945 2326258 2326939 2327744 "REP1" 2329079 NIL REP1 (NIL T) -7 NIL NIL) (-944 2319004 2324419 2324871 "REGSET" 2325889 NIL REGSET (NIL T T T T) -8 NIL NIL) (-943 2317825 2318160 2318408 "REF" 2318789 NIL REF (NIL T) -8 NIL NIL) (-942 2317206 2317309 2317474 "REDORDER" 2317709 NIL REDORDER (NIL T T) -7 NIL NIL) (-941 2313175 2316440 2316661 "RECLOS" 2317037 NIL RECLOS (NIL T) -8 NIL NIL) (-940 2312232 2312413 2312626 "REALSOLV" 2312982 T REALSOLV (NIL) -7 NIL NIL) (-939 2312079 2312120 2312149 "REAL" 2312154 T REAL (NIL) -9 NIL 2312189) (-938 2308570 2309372 2310254 "REAL0Q" 2311244 NIL REAL0Q (NIL T) -7 NIL NIL) (-937 2304181 2305169 2306228 "REAL0" 2307551 NIL REAL0 (NIL T) -7 NIL NIL) (-936 2303589 2303661 2303866 "RDIV" 2304103 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-935 2302662 2302836 2303047 "RDIST" 2303411 NIL RDIST (NIL T) -7 NIL NIL) (-934 2301266 2301553 2301922 "RDETRS" 2302370 NIL RDETRS (NIL T T) -7 NIL NIL) (-933 2299087 2299541 2300076 "RDETR" 2300808 NIL RDETR (NIL T T) -7 NIL NIL) (-932 2297703 2297981 2298382 "RDEEFS" 2298803 NIL RDEEFS (NIL T T) -7 NIL NIL) (-931 2296203 2296509 2296938 "RDEEF" 2297391 NIL RDEEF (NIL T T) -7 NIL NIL) (-930 2290487 2293419 2293448 "RCFIELD" 2294725 T RCFIELD (NIL) -9 NIL 2295455) (-929 2288556 2289060 2289753 "RCFIELD-" 2289826 NIL RCFIELD- (NIL T) -8 NIL NIL) (-928 2284887 2286672 2286714 "RCAGG" 2287785 NIL RCAGG (NIL T) -9 NIL 2288250) (-927 2284518 2284612 2284772 "RCAGG-" 2284777 NIL RCAGG- (NIL T T) -8 NIL NIL) (-926 2283863 2283974 2284136 "RATRET" 2284402 NIL RATRET (NIL T) -7 NIL NIL) (-925 2283420 2283487 2283606 "RATFACT" 2283791 NIL RATFACT (NIL T) -7 NIL NIL) (-924 2282735 2282855 2283005 "RANDSRC" 2283290 T RANDSRC (NIL) -7 NIL NIL) (-923 2282472 2282516 2282587 "RADUTIL" 2282684 T RADUTIL (NIL) -7 NIL NIL) (-922 2275479 2281215 2281532 "RADIX" 2282187 NIL RADIX (NIL NIL) -8 NIL NIL) (-921 2267049 2275323 2275451 "RADFF" 2275456 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-920 2266700 2266775 2266804 "RADCAT" 2266961 T RADCAT (NIL) -9 NIL NIL) (-919 2266485 2266533 2266630 "RADCAT-" 2266635 NIL RADCAT- (NIL T) -8 NIL NIL) (-918 2264636 2266260 2266349 "QUEUE" 2266429 NIL QUEUE (NIL T) -8 NIL NIL) (-917 2261133 2264573 2264618 "QUAT" 2264623 NIL QUAT (NIL T) -8 NIL NIL) (-916 2260771 2260814 2260941 "QUATCT2" 2261084 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-915 2254564 2257944 2257985 "QUATCAT" 2258764 NIL QUATCAT (NIL T) -9 NIL 2259529) (-914 2250708 2251745 2253132 "QUATCAT-" 2253226 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-913 2248228 2249792 2249834 "QUAGG" 2250209 NIL QUAGG (NIL T) -9 NIL 2250384) (-912 2247153 2247626 2247798 "QFORM" 2248100 NIL QFORM (NIL NIL T) -8 NIL NIL) (-911 2238449 2243707 2243748 "QFCAT" 2244406 NIL QFCAT (NIL T) -9 NIL 2245399) (-910 2234021 2235222 2236813 "QFCAT-" 2236907 NIL QFCAT- (NIL T T) -8 NIL NIL) (-909 2233659 2233702 2233829 "QFCAT2" 2233972 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-908 2233119 2233229 2233359 "QEQUAT" 2233549 T QEQUAT (NIL) -8 NIL NIL) (-907 2226305 2227376 2228558 "QCMPACK" 2232052 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-906 2223881 2224302 2224730 "QALGSET" 2225960 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-905 2223126 2223300 2223532 "QALGSET2" 2223701 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-904 2221817 2222040 2222357 "PWFFINTB" 2222899 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-903 2220005 2220173 2220526 "PUSHVAR" 2221631 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-902 2215922 2216976 2217018 "PTRANFN" 2218902 NIL PTRANFN (NIL T) -9 NIL NIL) (-901 2214334 2214625 2214946 "PTPACK" 2215633 NIL PTPACK (NIL T) -7 NIL NIL) (-900 2213970 2214027 2214134 "PTFUNC2" 2214271 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-899 2208446 2212787 2212828 "PTCAT" 2213196 NIL PTCAT (NIL T) -9 NIL 2213358) (-898 2208104 2208139 2208263 "PSQFR" 2208405 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-897 2206699 2206997 2207331 "PSEUDLIN" 2207802 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-896 2193507 2195871 2198194 "PSETPK" 2204459 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-895 2186593 2189307 2189402 "PSETCAT" 2192383 NIL PSETCAT (NIL T T T T) -9 NIL 2193197) (-894 2184431 2185065 2185884 "PSETCAT-" 2185889 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-893 2183779 2183944 2183973 "PSCURVE" 2184241 T PSCURVE (NIL) -9 NIL 2184408) (-892 2180230 2181756 2181821 "PSCAT" 2182657 NIL PSCAT (NIL T T T) -9 NIL 2182897) (-891 2179294 2179510 2179909 "PSCAT-" 2179914 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-890 2177947 2178579 2178793 "PRTITION" 2179100 T PRTITION (NIL) -8 NIL NIL) (-889 2167045 2169251 2171439 "PRS" 2175809 NIL PRS (NIL T T) -7 NIL NIL) (-888 2164903 2166395 2166436 "PRQAGG" 2166619 NIL PRQAGG (NIL T) -9 NIL 2166721) (-887 2164473 2164575 2164604 "PROPLOG" 2164789 T PROPLOG (NIL) -9 NIL NIL) (-886 2158247 2162639 2163459 "PRODUCT" 2163699 NIL PRODUCT (NIL T T) -8 NIL NIL) (-885 2155523 2157707 2157940 "PR" 2158058 NIL PR (NIL T T) -8 NIL NIL) (-884 2155319 2155351 2155410 "PRINT" 2155484 T PRINT (NIL) -7 NIL NIL) (-883 2154659 2154776 2154928 "PRIMES" 2155199 NIL PRIMES (NIL T) -7 NIL NIL) (-882 2152724 2153125 2153591 "PRIMELT" 2154238 NIL PRIMELT (NIL T) -7 NIL NIL) (-881 2152455 2152503 2152532 "PRIMCAT" 2152655 T PRIMCAT (NIL) -9 NIL NIL) (-880 2148616 2152393 2152438 "PRIMARR" 2152443 NIL PRIMARR (NIL T) -8 NIL NIL) (-879 2147623 2147801 2148029 "PRIMARR2" 2148434 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-878 2147266 2147322 2147433 "PREASSOC" 2147561 NIL PREASSOC (NIL T T) -7 NIL NIL) (-877 2146740 2146873 2146902 "PPCURVE" 2147107 T PPCURVE (NIL) -9 NIL 2147243) (-876 2144099 2144498 2145090 "POLYROOT" 2146321 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-875 2138005 2143705 2143864 "POLY" 2143972 NIL POLY (NIL T) -8 NIL NIL) (-874 2137390 2137448 2137681 "POLYLIFT" 2137941 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-873 2133675 2134124 2134752 "POLYCATQ" 2136935 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-872 2120715 2126112 2126177 "POLYCAT" 2129662 NIL POLYCAT (NIL T T T) -9 NIL 2131589) (-871 2114166 2116027 2118410 "POLYCAT-" 2118415 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-870 2113755 2113823 2113942 "POLY2UP" 2114092 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-869 2113391 2113448 2113555 "POLY2" 2113692 NIL POLY2 (NIL T T) -7 NIL NIL) (-868 2112076 2112315 2112591 "POLUTIL" 2113165 NIL POLUTIL (NIL T T) -7 NIL NIL) (-867 2110438 2110715 2111045 "POLTOPOL" 2111798 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-866 2105961 2110375 2110420 "POINT" 2110425 NIL POINT (NIL T) -8 NIL NIL) (-865 2104148 2104505 2104880 "PNTHEORY" 2105606 T PNTHEORY (NIL) -7 NIL NIL) (-864 2102576 2102873 2103282 "PMTOOLS" 2103846 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-863 2102169 2102247 2102364 "PMSYM" 2102492 NIL PMSYM (NIL T) -7 NIL NIL) (-862 2101679 2101748 2101922 "PMQFCAT" 2102094 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-861 2101034 2101144 2101300 "PMPRED" 2101556 NIL PMPRED (NIL T) -7 NIL NIL) (-860 2100430 2100516 2100677 "PMPREDFS" 2100935 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-859 2099076 2099284 2099668 "PMPLCAT" 2100192 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-858 2098608 2098687 2098839 "PMLSAGG" 2098991 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-857 2098085 2098161 2098341 "PMKERNEL" 2098526 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-856 2097702 2097777 2097890 "PMINS" 2098004 NIL PMINS (NIL T) -7 NIL NIL) (-855 2097132 2097201 2097416 "PMFS" 2097627 NIL PMFS (NIL T T T) -7 NIL NIL) (-854 2096363 2096481 2096685 "PMDOWN" 2097009 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-853 2095526 2095685 2095867 "PMASS" 2096201 T PMASS (NIL) -7 NIL NIL) (-852 2094800 2094911 2095074 "PMASSFS" 2095412 NIL PMASSFS (NIL T T) -7 NIL NIL) (-851 2094455 2094523 2094617 "PLOTTOOL" 2094726 T PLOTTOOL (NIL) -7 NIL NIL) (-850 2089077 2090266 2091414 "PLOT" 2093327 T PLOT (NIL) -8 NIL NIL) (-849 2084891 2085925 2086846 "PLOT3D" 2088176 T PLOT3D (NIL) -8 NIL NIL) (-848 2083803 2083980 2084215 "PLOT1" 2084695 NIL PLOT1 (NIL T) -7 NIL NIL) (-847 2059198 2063869 2068720 "PLEQN" 2079069 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-846 2058516 2058638 2058818 "PINTERP" 2059063 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-845 2058209 2058256 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2035197 "PFECAT" 2035782 T PFECAT (NIL) -9 NIL 2036166) (-831 2033332 2033486 2033700 "PFECAT-" 2033705 NIL PFECAT- (NIL T) -8 NIL NIL) (-830 2031936 2032187 2032488 "PFBRU" 2033081 NIL PFBRU (NIL T T) -7 NIL NIL) (-829 2029803 2030154 2030586 "PFBR" 2031587 NIL PFBR (NIL T T T T) -7 NIL NIL) (-828 2025655 2027179 2027855 "PERM" 2029160 NIL PERM (NIL T) -8 NIL NIL) (-827 2020921 2021862 2022732 "PERMGRP" 2024818 NIL PERMGRP (NIL T) -8 NIL NIL) (-826 2018991 2019984 2020026 "PERMCAT" 2020472 NIL PERMCAT (NIL T) -9 NIL 2020777) (-825 2018646 2018687 2018810 "PERMAN" 2018944 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-824 2016086 2018215 2018346 "PENDTREE" 2018548 NIL PENDTREE (NIL T) -8 NIL NIL) (-823 2014158 2014936 2014978 "PDRING" 2015635 NIL PDRING (NIL T) -9 NIL 2015920) (-822 2013261 2013479 2013841 "PDRING-" 2013846 NIL PDRING- (NIL T T) -8 NIL NIL) (-821 2010403 2011153 2011844 "PDEPROB" 2012590 T PDEPROB (NIL) -8 NIL NIL) (-820 2007974 2008470 2009019 "PDEPACK" 2009874 T PDEPACK (NIL) -7 NIL NIL) (-819 2006886 2007076 2007327 "PDECOMP" 2007773 NIL PDECOMP (NIL T T) -7 NIL NIL) (-818 2004497 2005312 2005341 "PDECAT" 2006126 T PDECAT (NIL) -9 NIL 2006837) (-817 2004250 2004283 2004372 "PCOMP" 2004458 NIL PCOMP (NIL T T) -7 NIL NIL) (-816 2002457 2003053 2003349 "PBWLB" 2003980 NIL PBWLB (NIL T) -8 NIL NIL) (-815 1994966 1996534 1997870 "PATTERN" 2001142 NIL PATTERN (NIL T) -8 NIL NIL) (-814 1994598 1994655 1994764 "PATTERN2" 1994903 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-813 1992355 1992743 1993200 "PATTERN1" 1994187 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-812 1989750 1990304 1990785 "PATRES" 1991920 NIL PATRES (NIL T T) -8 NIL NIL) (-811 1989314 1989381 1989513 "PATRES2" 1989677 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-810 1987211 1987611 1988016 "PATMATCH" 1988983 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-809 1986747 1986930 1986972 "PATMAB" 1987079 NIL PATMAB (NIL T) -9 NIL 1987162) (-808 1985292 1985601 1985859 "PATLRES" 1986552 NIL PATLRES (NIL T T T) -8 NIL NIL) (-807 1984837 1984960 1985002 "PATAB" 1985007 NIL PATAB (NIL T) -9 NIL 1985179) (-806 1982318 1982850 1983423 "PARTPERM" 1984284 T PARTPERM (NIL) -7 NIL NIL) (-805 1981939 1982002 1982104 "PARSURF" 1982249 NIL PARSURF (NIL T) -8 NIL NIL) (-804 1981571 1981628 1981737 "PARSU2" 1981876 NIL PARSU2 (NIL T T) -7 NIL NIL) (-803 1981335 1981375 1981442 "PARSER" 1981524 T PARSER (NIL) -7 NIL NIL) (-802 1980956 1981019 1981121 "PARSCURV" 1981266 NIL PARSCURV (NIL T) -8 NIL NIL) (-801 1980588 1980645 1980754 "PARSC2" 1980893 NIL PARSC2 (NIL T T) -7 NIL NIL) (-800 1980227 1980285 1980382 "PARPCURV" 1980524 NIL PARPCURV (NIL T) -8 NIL NIL) (-799 1979859 1979916 1980025 "PARPC2" 1980164 NIL PARPC2 (NIL T T) -7 NIL NIL) (-798 1979379 1979465 1979584 "PAN2EXPR" 1979760 T PAN2EXPR (NIL) -7 NIL NIL) (-797 1978185 1978500 1978728 "PALETTE" 1979171 T PALETTE (NIL) -8 NIL NIL) (-796 1972035 1977444 1977638 "PADICRC" 1978040 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-795 1965243 1971381 1971565 "PADICRAT" 1971883 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-794 1963547 1965180 1965225 "PADIC" 1965230 NIL PADIC (NIL NIL) -8 NIL NIL) (-793 1960751 1962325 1962366 "PADICCT" 1962947 NIL PADICCT (NIL NIL) -9 NIL 1963229) (-792 1959708 1959908 1960176 "PADEPAC" 1960538 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-791 1958920 1959053 1959259 "PADE" 1959570 NIL PADE (NIL T T T) -7 NIL NIL) (-790 1956931 1957763 1958078 "OWP" 1958688 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-789 1956040 1956536 1956708 "OVAR" 1956799 NIL OVAR (NIL NIL) -8 NIL NIL) (-788 1955304 1955425 1955586 "OUT" 1955899 T OUT (NIL) -7 NIL NIL) (-787 1944350 1946529 1948699 "OUTFORM" 1953154 T OUTFORM (NIL) -8 NIL NIL) (-786 1943758 1944079 1944168 "OSI" 1944281 T OSI (NIL) -8 NIL NIL) (-785 1942503 1942730 1943015 "ORTHPOL" 1943505 NIL ORTHPOL (NIL T) -7 NIL NIL) (-784 1939874 1942164 1942302 "OREUP" 1942446 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-783 1937270 1939567 1939693 "ORESUP" 1939816 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-782 1934805 1935305 1935865 "OREPCTO" 1936759 NIL OREPCTO (NIL T T) -7 NIL NIL) (-781 1928714 1930920 1930961 "OREPCAT" 1933282 NIL OREPCAT (NIL T) -9 NIL 1934385) (-780 1925862 1926644 1927701 "OREPCAT-" 1927706 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-779 1925039 1925311 1925340 "ORDSET" 1925649 T ORDSET (NIL) -9 NIL 1925813) (-778 1924558 1924680 1924873 "ORDSET-" 1924878 NIL ORDSET- (NIL T) -8 NIL NIL) (-777 1923171 1923972 1924001 "ORDRING" 1924203 T ORDRING (NIL) -9 NIL 1924327) (-776 1922816 1922910 1923054 "ORDRING-" 1923059 NIL ORDRING- (NIL T) -8 NIL NIL) (-775 1922191 1922672 1922701 "ORDMON" 1922706 T ORDMON (NIL) -9 NIL 1922727) (-774 1921353 1921500 1921695 "ORDFUNS" 1922040 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-773 1920864 1921223 1921252 "ORDFIN" 1921257 T ORDFIN (NIL) -9 NIL 1921278) (-772 1917376 1919450 1919859 "ORDCOMP" 1920488 NIL ORDCOMP (NIL T) -8 NIL NIL) (-771 1916642 1916769 1916955 "ORDCOMP2" 1917236 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-770 1913150 1914032 1914869 "OPTPROB" 1915825 T OPTPROB (NIL) -8 NIL NIL) (-769 1909992 1910621 1911315 "OPTPACK" 1912476 T OPTPACK (NIL) -7 NIL NIL) (-768 1907717 1908453 1908482 "OPTCAT" 1909297 T OPTCAT (NIL) -9 NIL 1909943) (-767 1907485 1907524 1907590 "OPQUERY" 1907671 T OPQUERY (NIL) -7 NIL NIL) (-766 1904621 1905812 1906312 "OP" 1907017 NIL OP (NIL T) -8 NIL NIL) (-765 1901386 1903418 1903787 "ONECOMP" 1904285 NIL ONECOMP (NIL T) -8 NIL NIL) (-764 1900691 1900806 1900980 "ONECOMP2" 1901258 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-763 1900110 1900216 1900346 "OMSERVER" 1900581 T OMSERVER (NIL) -7 NIL NIL) (-762 1896998 1899550 1899591 "OMSAGG" 1899652 NIL OMSAGG (NIL T) -9 NIL 1899716) (-761 1895621 1895884 1896166 "OMPKG" 1896736 T OMPKG (NIL) -7 NIL NIL) (-760 1895050 1895153 1895182 "OM" 1895481 T OM (NIL) -9 NIL NIL) (-759 1893589 1894602 1894770 "OMLO" 1894931 NIL OMLO (NIL T T) -8 NIL NIL) (-758 1892519 1892666 1892892 "OMEXPR" 1893415 NIL OMEXPR (NIL T) -7 NIL NIL) (-757 1891837 1892065 1892201 "OMERR" 1892403 T OMERR (NIL) -8 NIL NIL) (-756 1891015 1891258 1891418 "OMERRK" 1891697 T OMERRK (NIL) -8 NIL NIL) (-755 1890493 1890692 1890800 "OMENC" 1890927 T OMENC (NIL) -8 NIL NIL) (-754 1884388 1885573 1886744 "OMDEV" 1889342 T OMDEV (NIL) -8 NIL NIL) (-753 1883457 1883628 1883822 "OMCONN" 1884214 T OMCONN (NIL) -8 NIL NIL) (-752 1882072 1883058 1883087 "OINTDOM" 1883092 T OINTDOM (NIL) -9 NIL 1883113) (-751 1877834 1879064 1879779 "OFMONOID" 1881389 NIL OFMONOID (NIL T) -8 NIL NIL) (-750 1877272 1877771 1877816 "ODVAR" 1877821 NIL ODVAR (NIL T) -8 NIL NIL) (-749 1874397 1876769 1876954 "ODR" 1877147 NIL ODR (NIL T T NIL) -8 NIL NIL) (-748 1866703 1874176 1874300 "ODPOL" 1874305 NIL ODPOL (NIL T) -8 NIL NIL) (-747 1860526 1866575 1866680 "ODP" 1866685 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-746 1859292 1859507 1859782 "ODETOOLS" 1860300 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-745 1856261 1856917 1857633 "ODESYS" 1858625 NIL ODESYS (NIL T T) -7 NIL NIL) (-744 1851165 1852073 1853096 "ODERTRIC" 1855336 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-743 1850591 1850673 1850867 "ODERED" 1851077 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-742 1847493 1848041 1848716 "ODERAT" 1850014 NIL ODERAT (NIL T T) -7 NIL NIL) (-741 1844461 1844925 1845521 "ODEPRRIC" 1847022 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-740 1842332 1842899 1843408 "ODEPROB" 1843972 T ODEPROB (NIL) -8 NIL NIL) (-739 1838864 1839347 1839993 "ODEPRIM" 1841811 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-738 1838117 1838219 1838477 "ODEPAL" 1838756 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-737 1834319 1835100 1835954 "ODEPACK" 1837283 T ODEPACK (NIL) -7 NIL NIL) (-736 1833356 1833463 1833691 "ODEINT" 1834208 NIL ODEINT (NIL T T) -7 NIL NIL) (-735 1827457 1828882 1830329 "ODEIFTBL" 1831929 T ODEIFTBL (NIL) -8 NIL NIL) (-734 1822801 1823587 1824545 "ODEEF" 1826616 NIL ODEEF (NIL T T) -7 NIL NIL) (-733 1822138 1822227 1822456 "ODECONST" 1822706 NIL ODECONST (NIL T T T) -7 NIL NIL) (-732 1820295 1820928 1820957 "ODECAT" 1821560 T ODECAT (NIL) -9 NIL 1822089) (-731 1817167 1820007 1820126 "OCT" 1820208 NIL OCT (NIL T) -8 NIL NIL) (-730 1816805 1816848 1816975 "OCTCT2" 1817118 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-729 1811638 1814076 1814117 "OC" 1815213 NIL OC (NIL T) -9 NIL 1816070) (-728 1808865 1809613 1810603 "OC-" 1810697 NIL OC- (NIL T T) -8 NIL NIL) (-727 1808243 1808685 1808714 "OCAMON" 1808719 T OCAMON (NIL) -9 NIL 1808740) (-726 1807696 1808103 1808132 "OASGP" 1808137 T OASGP (NIL) -9 NIL 1808157) (-725 1806983 1807446 1807475 "OAMONS" 1807515 T OAMONS (NIL) -9 NIL 1807558) (-724 1806423 1806830 1806859 "OAMON" 1806864 T OAMON (NIL) -9 NIL 1806884) (-723 1805727 1806219 1806248 "OAGROUP" 1806253 T OAGROUP (NIL) -9 NIL 1806273) (-722 1805417 1805467 1805555 "NUMTUBE" 1805671 NIL NUMTUBE (NIL T) -7 NIL NIL) (-721 1798990 1800508 1802044 "NUMQUAD" 1803901 T NUMQUAD (NIL) -7 NIL NIL) (-720 1794746 1795734 1796759 "NUMODE" 1797985 T NUMODE (NIL) -7 NIL NIL) (-719 1792149 1792995 1793024 "NUMINT" 1793941 T NUMINT (NIL) -9 NIL 1794697) (-718 1791097 1791294 1791512 "NUMFMT" 1791951 T NUMFMT (NIL) -7 NIL NIL) (-717 1777479 1780413 1782943 "NUMERIC" 1788606 NIL NUMERIC (NIL T) -7 NIL NIL) (-716 1771879 1776931 1777026 "NTSCAT" 1777031 NIL NTSCAT (NIL T T T T) -9 NIL 1777069) (-715 1771073 1771238 1771431 "NTPOLFN" 1771718 NIL NTPOLFN (NIL T) -7 NIL NIL) (-714 1758929 1767915 1768725 "NSUP" 1770295 NIL NSUP (NIL T) -8 NIL NIL) (-713 1758565 1758622 1758729 "NSUP2" 1758866 NIL NSUP2 (NIL T T) -7 NIL NIL) (-712 1748527 1758344 1758474 "NSMP" 1758479 NIL NSMP (NIL T T) -8 NIL NIL) (-711 1746959 1747260 1747617 "NREP" 1748215 NIL NREP (NIL T) -7 NIL NIL) (-710 1745550 1745802 1746160 "NPCOEF" 1746702 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-709 1744616 1744731 1744947 "NORMRETR" 1745431 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-708 1742669 1742959 1743366 "NORMPK" 1744324 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-707 1742354 1742382 1742506 "NORMMA" 1742635 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-706 1742181 1742311 1742340 "NONE" 1742345 T NONE (NIL) -8 NIL NIL) (-705 1741970 1741999 1742068 "NONE1" 1742145 NIL NONE1 (NIL T) -7 NIL NIL) (-704 1741455 1741517 1741702 "NODE1" 1741902 NIL NODE1 (NIL T T) -7 NIL NIL) (-703 1739748 1740618 1740873 "NNI" 1741220 T NNI (NIL) -8 NIL NIL) (-702 1738168 1738481 1738845 "NLINSOL" 1739416 NIL NLINSOL (NIL T) -7 NIL NIL) (-701 1734336 1735303 1736225 "NIPROB" 1737266 T NIPROB (NIL) -8 NIL NIL) (-700 1733093 1733327 1733629 "NFINTBAS" 1734098 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-699 1731801 1732032 1732313 "NCODIV" 1732861 NIL NCODIV (NIL T T) -7 NIL NIL) (-698 1731563 1731600 1731675 "NCNTFRAC" 1731758 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-697 1729743 1730107 1730527 "NCEP" 1731188 NIL NCEP (NIL T) -7 NIL NIL) (-696 1728654 1729393 1729422 "NASRING" 1729532 T NASRING (NIL) -9 NIL 1729606) (-695 1728449 1728493 1728587 "NASRING-" 1728592 NIL NASRING- (NIL T) -8 NIL NIL) (-694 1727602 1728101 1728130 "NARNG" 1728247 T NARNG (NIL) -9 NIL 1728338) (-693 1727294 1727361 1727495 "NARNG-" 1727500 NIL NARNG- (NIL T) -8 NIL NIL) (-692 1726173 1726380 1726615 "NAGSP" 1727079 T NAGSP (NIL) -7 NIL NIL) (-691 1717597 1719243 1720878 "NAGS" 1724558 T NAGS (NIL) -7 NIL NIL) (-690 1716161 1716465 1716792 "NAGF07" 1717290 T NAGF07 (NIL) -7 NIL NIL) (-689 1710743 1712023 1713319 "NAGF04" 1714885 T NAGF04 (NIL) -7 NIL NIL) (-688 1703775 1705373 1706990 "NAGF02" 1709146 T NAGF02 (NIL) -7 NIL NIL) (-687 1699039 1700129 1701236 "NAGF01" 1702688 T NAGF01 (NIL) -7 NIL NIL) (-686 1692699 1694257 1695834 "NAGE04" 1697482 T NAGE04 (NIL) -7 NIL NIL) (-685 1683940 1686043 1688155 "NAGE02" 1690607 T NAGE02 (NIL) -7 NIL NIL) (-684 1679933 1680870 1681824 "NAGE01" 1683006 T NAGE01 (NIL) -7 NIL NIL) (-683 1677740 1678271 1678826 "NAGD03" 1679398 T NAGD03 (NIL) -7 NIL NIL) (-682 1669526 1671445 1673390 "NAGD02" 1675815 T NAGD02 (NIL) -7 NIL NIL) (-681 1663385 1664798 1666226 "NAGD01" 1668118 T NAGD01 (NIL) -7 NIL NIL) (-680 1659642 1660452 1661277 "NAGC06" 1662580 T NAGC06 (NIL) -7 NIL NIL) (-679 1658119 1658448 1658801 "NAGC05" 1659309 T NAGC05 (NIL) -7 NIL NIL) (-678 1657503 1657620 1657762 "NAGC02" 1657997 T NAGC02 (NIL) -7 NIL NIL) (-677 1656564 1657121 1657162 "NAALG" 1657241 NIL NAALG (NIL T) -9 NIL 1657302) (-676 1656399 1656428 1656518 "NAALG-" 1656523 NIL NAALG- (NIL T T) -8 NIL NIL) (-675 1650349 1651457 1652644 "MULTSQFR" 1655295 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-674 1649668 1649743 1649927 "MULTFACT" 1650261 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-673 1642861 1646772 1646825 "MTSCAT" 1647885 NIL MTSCAT (NIL T T) -9 NIL 1648399) (-672 1642573 1642627 1642719 "MTHING" 1642801 NIL MTHING (NIL T) -7 NIL NIL) (-671 1642365 1642398 1642458 "MSYSCMD" 1642533 T MSYSCMD (NIL) -7 NIL NIL) (-670 1638477 1641120 1641440 "MSET" 1642078 NIL MSET (NIL T) -8 NIL NIL) (-669 1635572 1638038 1638080 "MSETAGG" 1638085 NIL MSETAGG (NIL T) -9 NIL 1638119) (-668 1631428 1632970 1633711 "MRING" 1634875 NIL MRING (NIL T T) -8 NIL NIL) (-667 1630998 1631065 1631194 "MRF2" 1631355 NIL MRF2 (NIL T T T) -7 NIL NIL) (-666 1630616 1630651 1630795 "MRATFAC" 1630957 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-665 1628228 1628523 1628954 "MPRFF" 1630321 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-664 1622248 1628083 1628179 "MPOLY" 1628184 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-663 1621738 1621773 1621981 "MPCPF" 1622207 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-662 1621254 1621297 1621480 "MPC3" 1621689 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-661 1620455 1620536 1620755 "MPC2" 1621169 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-660 1618756 1619093 1619483 "MONOTOOL" 1620115 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-659 1617880 1618215 1618244 "MONOID" 1618521 T MONOID (NIL) -9 NIL 1618693) (-658 1617258 1617421 1617664 "MONOID-" 1617669 NIL MONOID- (NIL T) -8 NIL NIL) (-657 1608238 1614224 1614284 "MONOGEN" 1614958 NIL MONOGEN (NIL T T) -9 NIL 1615414) (-656 1605456 1606191 1607191 "MONOGEN-" 1607310 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-655 1604315 1604735 1604764 "MONADWU" 1605156 T MONADWU (NIL) -9 NIL 1605394) (-654 1603687 1603846 1604094 "MONADWU-" 1604099 NIL MONADWU- (NIL T) -8 NIL NIL) (-653 1603072 1603290 1603319 "MONAD" 1603526 T MONAD (NIL) -9 NIL 1603638) (-652 1602757 1602835 1602967 "MONAD-" 1602972 NIL MONAD- (NIL T) -8 NIL NIL) (-651 1601008 1601670 1601949 "MOEBIUS" 1602510 NIL MOEBIUS (NIL T) -8 NIL NIL) (-650 1600401 1600779 1600820 "MODULE" 1600825 NIL MODULE (NIL T) -9 NIL 1600851) (-649 1599969 1600065 1600255 "MODULE-" 1600260 NIL MODULE- (NIL T T) -8 NIL NIL) (-648 1597640 1598335 1598661 "MODRING" 1599794 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1594596 1595761 1596278 "MODOP" 1597172 NIL MODOP (NIL T T) -8 NIL NIL) (-646 1592783 1593235 1593576 "MODMONOM" 1594395 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-645 1582501 1590987 1591409 "MODMON" 1592411 NIL MODMON (NIL T T) -8 NIL NIL) (-644 1579627 1581345 1581621 "MODFIELD" 1582376 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-643 1579153 1579196 1579375 "MMAP" 1579578 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-642 1577389 1578166 1578207 "MLO" 1578624 NIL MLO (NIL T) -9 NIL 1578865) (-641 1574756 1575271 1575873 "MLIFT" 1576870 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-640 1574147 1574231 1574385 "MKUCFUNC" 1574667 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-639 1573746 1573816 1573939 "MKRECORD" 1574070 NIL MKRECORD (NIL T T) -7 NIL NIL) (-638 1572794 1572955 1573183 "MKFUNC" 1573557 NIL MKFUNC (NIL T) -7 NIL NIL) (-637 1572182 1572286 1572442 "MKFLCFN" 1572677 NIL MKFLCFN (NIL T) -7 NIL NIL) (-636 1571608 1571975 1572064 "MKCHSET" 1572126 NIL MKCHSET (NIL T) -8 NIL NIL) (-635 1570885 1570987 1571172 "MKBCFUNC" 1571501 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-634 1567569 1570439 1570575 "MINT" 1570769 T MINT (NIL) -8 NIL NIL) (-633 1566381 1566624 1566901 "MHROWRED" 1567324 NIL MHROWRED (NIL T) -7 NIL NIL) (-632 1561652 1564826 1565250 "MFLOAT" 1565977 T MFLOAT (NIL) -8 NIL NIL) (-631 1561009 1561085 1561256 "MFINFACT" 1561564 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-630 1557324 1558172 1559056 "MESH" 1560145 T MESH (NIL) -7 NIL NIL) (-629 1555714 1556026 1556379 "MDDFACT" 1557011 NIL MDDFACT (NIL T) -7 NIL NIL) (-628 1552556 1554873 1554915 "MDAGG" 1555170 NIL MDAGG (NIL T) -9 NIL 1555313) (-627 1542254 1551849 1552056 "MCMPLX" 1552369 T MCMPLX (NIL) -8 NIL NIL) (-626 1541395 1541541 1541741 "MCDEN" 1542103 NIL MCDEN (NIL T T) -7 NIL NIL) (-625 1539285 1539555 1539935 "MCALCFN" 1541125 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-624 1536907 1537430 1537991 "MATSTOR" 1538756 NIL MATSTOR (NIL T) -7 NIL NIL) (-623 1532915 1536282 1536529 "MATRIX" 1536692 NIL MATRIX (NIL T) -8 NIL NIL) (-622 1528685 1529388 1530124 "MATLIN" 1532272 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-621 1518882 1522020 1522097 "MATCAT" 1526935 NIL MATCAT (NIL T T T) -9 NIL 1528352) (-620 1515247 1516260 1517615 "MATCAT-" 1517620 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-619 1513849 1514002 1514333 "MATCAT2" 1515082 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1511961 1512285 1512669 "MAPPKG3" 1513524 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-617 1510942 1511115 1511337 "MAPPKG2" 1511785 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-616 1509441 1509725 1510052 "MAPPKG1" 1510648 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-615 1509052 1509110 1509233 "MAPHACK3" 1509377 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-614 1508644 1508705 1508819 "MAPHACK2" 1508984 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-613 1508082 1508185 1508327 "MAPHACK1" 1508535 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-612 1506190 1506784 1507087 "MAGMA" 1507811 NIL MAGMA (NIL T) -8 NIL NIL) (-611 1502664 1504434 1504894 "M3D" 1505763 NIL M3D (NIL T) -8 NIL NIL) (-610 1496819 1501034 1501076 "LZSTAGG" 1501858 NIL LZSTAGG (NIL T) -9 NIL 1502153) (-609 1492792 1493950 1495407 "LZSTAGG-" 1495412 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-608 1489908 1490685 1491171 "LWORD" 1492338 NIL LWORD (NIL T) -8 NIL NIL) (-607 1483068 1489679 1489813 "LSQM" 1489818 NIL LSQM (NIL NIL T) -8 NIL NIL) (-606 1482292 1482431 1482659 "LSPP" 1482923 NIL LSPP (NIL T T T T) -7 NIL NIL) (-605 1480104 1480405 1480861 "LSMP" 1481981 NIL LSMP (NIL T T T T) -7 NIL NIL) (-604 1476883 1477557 1478287 "LSMP1" 1479406 NIL LSMP1 (NIL T) -7 NIL NIL) (-603 1470809 1476051 1476093 "LSAGG" 1476155 NIL LSAGG (NIL T) -9 NIL 1476233) (-602 1467504 1468428 1469641 "LSAGG-" 1469646 NIL LSAGG- (NIL T T) -8 NIL NIL) (-601 1465130 1466648 1466897 "LPOLY" 1467299 NIL LPOLY (NIL T T) -8 NIL NIL) (-600 1464712 1464797 1464920 "LPEFRAC" 1465039 NIL LPEFRAC (NIL T) -7 NIL NIL) (-599 1463059 1463806 1464059 "LO" 1464544 NIL LO (NIL T T T) -8 NIL NIL) (-598 1462712 1462824 1462853 "LOGIC" 1462964 T LOGIC (NIL) -9 NIL 1463044) (-597 1462574 1462597 1462668 "LOGIC-" 1462673 NIL LOGIC- (NIL T) -8 NIL NIL) (-596 1461767 1461907 1462100 "LODOOPS" 1462430 NIL LODOOPS (NIL T T) -7 NIL NIL) (-595 1459185 1461684 1461749 "LODO" 1461754 NIL LODO (NIL T NIL) -8 NIL NIL) (-594 1457731 1457966 1458317 "LODOF" 1458932 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1454150 1456586 1456627 "LODOCAT" 1457059 NIL LODOCAT (NIL T) -9 NIL 1457270) (-592 1453884 1453942 1454068 "LODOCAT-" 1454073 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1451198 1453725 1453843 "LODO2" 1453848 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1448627 1451135 1451180 "LODO1" 1451185 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1447490 1447655 1447966 "LODEEF" 1448450 NIL LODEEF (NIL T T T) -7 NIL NIL) (-588 1442776 1445620 1445662 "LNAGG" 1446609 NIL LNAGG (NIL T) -9 NIL 1447053) (-587 1441923 1442137 1442479 "LNAGG-" 1442484 NIL LNAGG- (NIL T T) -8 NIL NIL) (-586 1438088 1438850 1439488 "LMOPS" 1441339 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-585 1437485 1437847 1437888 "LMODULE" 1437948 NIL LMODULE (NIL T) -9 NIL 1437990) (-584 1434731 1437130 1437253 "LMDICT" 1437395 NIL LMDICT (NIL T) -8 NIL NIL) (-583 1427958 1433677 1433975 "LIST" 1434466 NIL LIST (NIL T) -8 NIL NIL) (-582 1427483 1427557 1427696 "LIST3" 1427878 NIL LIST3 (NIL T T T) -7 NIL NIL) (-581 1426490 1426668 1426896 "LIST2" 1427301 NIL LIST2 (NIL T T) -7 NIL NIL) (-580 1424624 1424936 1425335 "LIST2MAP" 1426137 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1423336 1424016 1424057 "LINEXP" 1424310 NIL LINEXP (NIL T) -9 NIL 1424458) (-578 1421983 1422243 1422540 "LINDEP" 1423088 NIL LINDEP (NIL T T) -7 NIL NIL) (-577 1418750 1419469 1420246 "LIMITRF" 1421238 NIL LIMITRF (NIL T) -7 NIL NIL) (-576 1417030 1417325 1417740 "LIMITPS" 1418445 NIL LIMITPS (NIL T T) -7 NIL NIL) (-575 1411485 1416541 1416769 "LIE" 1416851 NIL LIE (NIL T T) -8 NIL NIL) (-574 1410535 1410978 1411019 "LIECAT" 1411159 NIL LIECAT (NIL T) -9 NIL 1411310) (-573 1410376 1410403 1410491 "LIECAT-" 1410496 NIL LIECAT- (NIL T T) -8 NIL NIL) (-572 1402988 1409825 1409990 "LIB" 1410231 T LIB (NIL) -8 NIL NIL) (-571 1398625 1399506 1400441 "LGROBP" 1402105 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-570 1396495 1396768 1397129 "LF" 1398347 NIL LF (NIL T T) -7 NIL NIL) (-569 1395335 1396026 1396055 "LFCAT" 1396262 T LFCAT (NIL) -9 NIL 1396401) (-568 1392247 1392873 1393559 "LEXTRIPK" 1394701 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-567 1388953 1389817 1390320 "LEXP" 1391827 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-566 1387351 1387664 1388065 "LEADCDET" 1388635 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-565 1386547 1386621 1386848 "LAZM3PK" 1387272 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-564 1381463 1384626 1385163 "LAUPOL" 1386060 NIL LAUPOL (NIL T T) -8 NIL NIL) (-563 1381030 1381074 1381241 "LAPLACE" 1381413 NIL LAPLACE (NIL T T) -7 NIL NIL) (-562 1378958 1380131 1380382 "LA" 1380863 NIL LA (NIL T T T) -8 NIL NIL) (-561 1378020 1378614 1378655 "LALG" 1378716 NIL LALG (NIL T) -9 NIL 1378774) (-560 1377735 1377794 1377929 "LALG-" 1377934 NIL LALG- (NIL T T) -8 NIL NIL) (-559 1376645 1376832 1377129 "KOVACIC" 1377535 NIL KOVACIC (NIL T T) -7 NIL NIL) (-558 1376479 1376503 1376545 "KONVERT" 1376607 NIL KONVERT (NIL T) -9 NIL NIL) (-557 1376313 1376337 1376379 "KOERCE" 1376441 NIL KOERCE (NIL T) -9 NIL NIL) (-556 1374047 1374807 1375200 "KERNEL" 1375952 NIL KERNEL (NIL T) -8 NIL NIL) (-555 1373549 1373630 1373760 "KERNEL2" 1373961 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-554 1367400 1372088 1372143 "KDAGG" 1372520 NIL KDAGG (NIL T T) -9 NIL 1372726) (-553 1366929 1367053 1367258 "KDAGG-" 1367263 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-552 1360104 1366590 1366745 "KAFILE" 1366807 NIL KAFILE (NIL T) -8 NIL NIL) (-551 1354559 1359615 1359843 "JORDAN" 1359925 NIL JORDAN (NIL T T) -8 NIL NIL) (-550 1350858 1352764 1352819 "IXAGG" 1353748 NIL IXAGG (NIL T T) -9 NIL 1354207) (-549 1349777 1350083 1350502 "IXAGG-" 1350507 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-548 1345362 1349699 1349758 "IVECTOR" 1349763 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-547 1344128 1344365 1344631 "ITUPLE" 1345129 NIL ITUPLE (NIL T) -8 NIL NIL) (-546 1342564 1342741 1343047 "ITRIGMNP" 1343950 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-545 1341309 1341513 1341796 "ITFUN3" 1342340 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-544 1340941 1340998 1341107 "ITFUN2" 1341246 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-543 1338743 1339814 1340111 "ITAYLOR" 1340676 NIL ITAYLOR (NIL T) -8 NIL NIL) (-542 1327734 1332929 1334088 "ISUPS" 1337616 NIL ISUPS (NIL T) -8 NIL NIL) (-541 1326838 1326978 1327214 "ISUMP" 1327581 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-540 1322102 1326639 1326718 "ISTRING" 1326791 NIL ISTRING (NIL NIL) -8 NIL NIL) (-539 1321315 1321396 1321611 "IRURPK" 1322016 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-538 1320251 1320452 1320692 "IRSN" 1321095 T IRSN (NIL) -7 NIL NIL) (-537 1318286 1318641 1319076 "IRRF2F" 1319889 NIL IRRF2F (NIL T) -7 NIL NIL) (-536 1318033 1318071 1318147 "IRREDFFX" 1318242 NIL IRREDFFX (NIL T) -7 NIL NIL) (-535 1316648 1316907 1317206 "IROOT" 1317766 NIL IROOT (NIL T) -7 NIL NIL) (-534 1313286 1314337 1315027 "IR" 1315990 NIL IR (NIL T) -8 NIL NIL) (-533 1310899 1311394 1311960 "IR2" 1312764 NIL IR2 (NIL T T) -7 NIL NIL) (-532 1309975 1310088 1310308 "IR2F" 1310782 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1309766 1309800 1309860 "IPRNTPK" 1309935 T IPRNTPK (NIL) -7 NIL NIL) (-530 1306320 1309655 1309724 "IPF" 1309729 NIL IPF (NIL NIL) -8 NIL NIL) (-529 1304637 1306245 1306302 "IPADIC" 1306307 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-528 1304136 1304194 1304383 "INVLAPLA" 1304573 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-527 1293785 1296138 1298524 "INTTR" 1301800 NIL INTTR (NIL T T) -7 NIL NIL) (-526 1290133 1290874 1291737 "INTTOOLS" 1292971 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-525 1289719 1289810 1289927 "INTSLPE" 1290036 T INTSLPE (NIL) -7 NIL NIL) (-524 1287669 1289642 1289701 "INTRVL" 1289706 NIL INTRVL (NIL T) -8 NIL NIL) (-523 1285276 1285788 1286362 "INTRF" 1287154 NIL INTRF (NIL T) -7 NIL NIL) (-522 1284691 1284788 1284929 "INTRET" 1285174 NIL INTRET (NIL T) -7 NIL NIL) (-521 1282693 1283082 1283551 "INTRAT" 1284299 NIL INTRAT (NIL T T) -7 NIL NIL) (-520 1279926 1280509 1281134 "INTPM" 1282178 NIL INTPM (NIL T T) -7 NIL NIL) (-519 1276635 1277234 1277978 "INTPAF" 1279312 NIL INTPAF (NIL T T T) -7 NIL NIL) (-518 1271886 1272830 1273863 "INTPACK" 1275622 T INTPACK (NIL) -7 NIL NIL) (-517 1268740 1271615 1271742 "INT" 1271779 T INT (NIL) -8 NIL NIL) (-516 1267992 1268144 1268352 "INTHERTR" 1268582 NIL INTHERTR (NIL T T) -7 NIL NIL) (-515 1267431 1267511 1267699 "INTHERAL" 1267906 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-514 1265277 1265720 1266177 "INTHEORY" 1266994 T INTHEORY (NIL) -7 NIL NIL) (-513 1256600 1258220 1259998 "INTG0" 1263629 NIL INTG0 (NIL T T T) -7 NIL NIL) (-512 1237173 1241963 1246773 "INTFTBL" 1251810 T INTFTBL (NIL) -8 NIL NIL) (-511 1236422 1236560 1236733 "INTFACT" 1237032 NIL INTFACT (NIL T) -7 NIL NIL) (-510 1233813 1234259 1234822 "INTEF" 1235976 NIL INTEF (NIL T T) -7 NIL NIL) (-509 1232274 1233023 1233052 "INTDOM" 1233353 T INTDOM (NIL) -9 NIL 1233560) (-508 1231643 1231817 1232059 "INTDOM-" 1232064 NIL INTDOM- (NIL T) -8 NIL NIL) (-507 1228135 1230067 1230122 "INTCAT" 1230921 NIL INTCAT (NIL T) -9 NIL 1231240) (-506 1227608 1227710 1227838 "INTBIT" 1228027 T INTBIT (NIL) -7 NIL NIL) (-505 1226283 1226437 1226750 "INTALG" 1227453 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-504 1225740 1225830 1226000 "INTAF" 1226187 NIL INTAF (NIL T T) -7 NIL NIL) (-503 1219194 1225550 1225690 "INTABL" 1225695 NIL INTABL (NIL T T T) -8 NIL NIL) (-502 1214144 1216873 1216902 "INS" 1217870 T INS (NIL) -9 NIL 1218551) (-501 1211384 1212155 1213129 "INS-" 1213202 NIL INS- (NIL T) -8 NIL NIL) (-500 1210163 1210390 1210687 "INPSIGN" 1211137 NIL INPSIGN (NIL T T) -7 NIL NIL) (-499 1209281 1209398 1209595 "INPRODPF" 1210043 NIL INPRODPF (NIL T T) -7 NIL NIL) (-498 1208175 1208292 1208529 "INPRODFF" 1209161 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-497 1207175 1207327 1207587 "INNMFACT" 1208011 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-496 1206372 1206469 1206657 "INMODGCD" 1207074 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-495 1204881 1205125 1205449 "INFSP" 1206117 NIL INFSP (NIL T T T) -7 NIL NIL) (-494 1204065 1204182 1204365 "INFPROD0" 1204761 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-493 1201075 1202234 1202725 "INFORM" 1203582 T INFORM (NIL) -8 NIL NIL) (-492 1200685 1200745 1200843 "INFORM1" 1201010 NIL INFORM1 (NIL T) -7 NIL NIL) (-491 1200208 1200297 1200411 "INFINITY" 1200591 T INFINITY (NIL) -7 NIL NIL) (-490 1198826 1199074 1199395 "INEP" 1199956 NIL INEP (NIL T T T) -7 NIL NIL) (-489 1198102 1198723 1198788 "INDE" 1198793 NIL INDE (NIL T) -8 NIL NIL) (-488 1197666 1197734 1197851 "INCRMAPS" 1198029 NIL INCRMAPS (NIL T) -7 NIL NIL) (-487 1192977 1193902 1194846 "INBFF" 1196754 NIL INBFF (NIL T) -7 NIL NIL) (-486 1189472 1192822 1192925 "IMATRIX" 1192930 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-485 1188184 1188307 1188622 "IMATQF" 1189328 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-484 1186404 1186631 1186968 "IMATLIN" 1187940 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-483 1181030 1186328 1186386 "ILIST" 1186391 NIL ILIST (NIL T NIL) -8 NIL NIL) (-482 1178983 1180890 1181003 "IIARRAY2" 1181008 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-481 1174351 1178894 1178958 "IFF" 1178963 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-480 1169394 1173643 1173831 "IFARRAY" 1174208 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-479 1168601 1169298 1169371 "IFAMON" 1169376 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-478 1168184 1168249 1168304 "IEVALAB" 1168511 NIL IEVALAB (NIL T T) -9 NIL NIL) (-477 1167859 1167927 1168087 "IEVALAB-" 1168092 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-476 1167517 1167773 1167836 "IDPO" 1167841 NIL IDPO (NIL T T) -8 NIL NIL) (-475 1166794 1167406 1167481 "IDPOAMS" 1167486 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-474 1166128 1166683 1166758 "IDPOAM" 1166763 NIL IDPOAM (NIL T T) -8 NIL NIL) (-473 1165213 1165463 1165517 "IDPC" 1165930 NIL IDPC (NIL T T) -9 NIL 1166079) (-472 1164709 1165105 1165178 "IDPAM" 1165183 NIL IDPAM (NIL T T) -8 NIL NIL) (-471 1164112 1164601 1164674 "IDPAG" 1164679 NIL IDPAG (NIL T T) -8 NIL NIL) (-470 1160367 1161215 1162110 "IDECOMP" 1163269 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-469 1153241 1154290 1155337 "IDEAL" 1159403 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-468 1152405 1152517 1152716 "ICDEN" 1153125 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-467 1151504 1151885 1152032 "ICARD" 1152278 T ICARD (NIL) -8 NIL NIL) (-466 1149576 1149889 1150292 "IBPTOOLS" 1151181 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-465 1145190 1149196 1149309 "IBITS" 1149495 NIL IBITS (NIL NIL) -8 NIL NIL) (-464 1141913 1142489 1143184 "IBATOOL" 1144607 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-463 1139693 1140154 1140687 "IBACHIN" 1141448 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-462 1137570 1139539 1139642 "IARRAY2" 1139647 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-461 1133723 1137496 1137553 "IARRAY1" 1137558 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-460 1127662 1132141 1132619 "IAN" 1133265 T IAN (NIL) -8 NIL NIL) (-459 1127173 1127230 1127403 "IALGFACT" 1127599 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-458 1126700 1126813 1126842 "HYPCAT" 1127049 T HYPCAT (NIL) -9 NIL NIL) (-457 1126238 1126355 1126541 "HYPCAT-" 1126546 NIL HYPCAT- (NIL T) -8 NIL NIL) (-456 1122917 1124248 1124290 "HOAGG" 1125271 NIL HOAGG (NIL T) -9 NIL 1125950) (-455 1121511 1121910 1122436 "HOAGG-" 1122441 NIL HOAGG- (NIL T T) -8 NIL NIL) (-454 1115342 1120952 1121118 "HEXADEC" 1121365 T HEXADEC (NIL) -8 NIL NIL) (-453 1114090 1114312 1114575 "HEUGCD" 1115119 NIL HEUGCD (NIL T) -7 NIL NIL) (-452 1113193 1113927 1114057 "HELLFDIV" 1114062 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-451 1111421 1112970 1113058 "HEAP" 1113137 NIL HEAP (NIL T) -8 NIL NIL) (-450 1105288 1111336 1111398 "HDP" 1111403 NIL HDP (NIL NIL T) -8 NIL NIL) (-449 1099000 1104925 1105076 "HDMP" 1105189 NIL HDMP (NIL NIL T) -8 NIL NIL) (-448 1098325 1098464 1098628 "HB" 1098856 T HB (NIL) -7 NIL NIL) (-447 1091822 1098171 1098275 "HASHTBL" 1098280 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-446 1089575 1091450 1091629 "HACKPI" 1091663 T HACKPI (NIL) -8 NIL NIL) (-445 1085271 1089429 1089541 "GTSET" 1089546 NIL GTSET (NIL T T T T) -8 NIL NIL) (-444 1078797 1085149 1085247 "GSTBL" 1085252 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-443 1071033 1077833 1078097 "GSERIES" 1078588 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-442 1070055 1070508 1070537 "GROUP" 1070798 T GROUP (NIL) -9 NIL 1070957) (-441 1069171 1069394 1069738 "GROUP-" 1069743 NIL GROUP- (NIL T) -8 NIL NIL) (-440 1067540 1067859 1068246 "GROEBSOL" 1068848 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-439 1066480 1066742 1066794 "GRMOD" 1067323 NIL GRMOD (NIL T T) -9 NIL 1067491) (-438 1066248 1066284 1066412 "GRMOD-" 1066417 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-437 1061576 1062602 1063602 "GRIMAGE" 1065268 T GRIMAGE (NIL) -8 NIL NIL) (-436 1060043 1060303 1060627 "GRDEF" 1061272 T GRDEF (NIL) -7 NIL NIL) (-435 1059487 1059603 1059744 "GRAY" 1059922 T GRAY (NIL) -7 NIL NIL) (-434 1058720 1059100 1059152 "GRALG" 1059305 NIL GRALG (NIL T T) -9 NIL 1059397) (-433 1058381 1058454 1058617 "GRALG-" 1058622 NIL GRALG- (NIL T T T) -8 NIL NIL) (-432 1055189 1057970 1058146 "GPOLSET" 1058288 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-431 1054545 1054602 1054859 "GOSPER" 1055126 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-430 1050304 1050983 1051509 "GMODPOL" 1054244 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-429 1049309 1049493 1049731 "GHENSEL" 1050116 NIL GHENSEL (NIL T T) -7 NIL NIL) (-428 1043375 1044218 1045244 "GENUPS" 1048393 NIL GENUPS (NIL T T) -7 NIL NIL) (-427 1043072 1043123 1043212 "GENUFACT" 1043318 NIL GENUFACT (NIL T) -7 NIL NIL) (-426 1042484 1042561 1042726 "GENPGCD" 1042990 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-425 1041958 1041993 1042206 "GENMFACT" 1042443 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-424 1040526 1040781 1041088 "GENEEZ" 1041701 NIL GENEEZ (NIL T T) -7 NIL NIL) (-423 1034400 1040139 1040300 "GDMP" 1040449 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-422 1023782 1028171 1029277 "GCNAALG" 1033383 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-421 1022203 1023075 1023104 "GCDDOM" 1023359 T GCDDOM (NIL) -9 NIL 1023516) (-420 1021673 1021800 1022015 "GCDDOM-" 1022020 NIL GCDDOM- (NIL T) -8 NIL NIL) (-419 1020345 1020530 1020834 "GB" 1021452 NIL GB (NIL T T T T) -7 NIL NIL) (-418 1008965 1011291 1013683 "GBINTERN" 1018036 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-417 1006802 1007094 1007515 "GBF" 1008640 NIL GBF (NIL T T T T) -7 NIL NIL) (-416 1005583 1005748 1006015 "GBEUCLID" 1006618 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-415 1004932 1005057 1005206 "GAUSSFAC" 1005454 T GAUSSFAC (NIL) -7 NIL NIL) (-414 1003309 1003611 1003924 "GALUTIL" 1004651 NIL GALUTIL (NIL T) -7 NIL NIL) (-413 1001626 1001900 1002223 "GALPOLYU" 1003036 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-412 999015 999305 999710 "GALFACTU" 1001323 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-411 990821 992320 993928 "GALFACT" 997447 NIL GALFACT (NIL T) -7 NIL NIL) (-410 988208 988866 988895 "FVFUN" 990051 T FVFUN (NIL) -9 NIL 990771) (-409 987473 987655 987684 "FVC" 987975 T FVC (NIL) -9 NIL 988158) (-408 987115 987270 987351 "FUNCTION" 987425 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-407 984785 985336 985825 "FT" 986646 T FT (NIL) -8 NIL NIL) (-406 983603 984086 984289 "FTEM" 984602 T FTEM (NIL) -8 NIL NIL) (-405 981868 982156 982558 "FSUPFACT" 983295 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-404 980265 980554 980886 "FST" 981556 T FST (NIL) -8 NIL NIL) (-403 979440 979546 979740 "FSRED" 980147 NIL FSRED (NIL T T) -7 NIL NIL) (-402 978119 978374 978728 "FSPRMELT" 979155 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-401 975204 975642 976141 "FSPECF" 977682 NIL FSPECF (NIL T T) -7 NIL NIL) (-400 957577 966134 966175 "FS" 970013 NIL FS (NIL T) -9 NIL 972295) (-399 946227 949217 953273 "FS-" 953570 NIL FS- (NIL T T) -8 NIL NIL) (-398 945743 945797 945973 "FSINT" 946168 NIL FSINT (NIL T T) -7 NIL NIL) (-397 944024 944736 945039 "FSERIES" 945522 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 943042 943158 943388 "FSCINT" 943904 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 939276 941986 942028 "FSAGG" 942398 NIL FSAGG (NIL T) -9 NIL 942657) (-394 937038 937639 938435 "FSAGG-" 938530 NIL FSAGG- (NIL T T) -8 NIL NIL) (-393 936080 936223 936450 "FSAGG2" 936891 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-392 933739 934018 934571 "FS2UPS" 935798 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 933325 933368 933521 "FS2" 933690 NIL FS2 (NIL T T T T) -7 NIL NIL) (-390 932185 932356 932664 "FS2EXPXP" 933150 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-389 931611 931726 931878 "FRUTIL" 932065 NIL FRUTIL (NIL T) -7 NIL NIL) (-388 923032 927110 928466 "FR" 930287 NIL FR (NIL T) -8 NIL NIL) (-387 918108 920751 920792 "FRNAALG" 922188 NIL FRNAALG (NIL T) -9 NIL 922795) (-386 913787 914857 916132 "FRNAALG-" 916882 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-385 913425 913468 913595 "FRNAAF2" 913738 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-384 911790 912282 912576 "FRMOD" 913238 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-383 909513 910181 910497 "FRIDEAL" 911581 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-382 908712 908799 909086 "FRIDEAL2" 909420 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 907969 908377 908419 "FRETRCT" 908424 NIL FRETRCT (NIL T) -9 NIL 908595) (-380 907081 907312 907663 "FRETRCT-" 907668 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-379 904290 905510 905570 "FRAMALG" 906452 NIL FRAMALG (NIL T T) -9 NIL 906744) (-378 902423 902879 903509 "FRAMALG-" 903732 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-377 896325 901898 902174 "FRAC" 902179 NIL FRAC (NIL T) -8 NIL NIL) (-376 895961 896018 896125 "FRAC2" 896262 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 895597 895654 895761 "FR2" 895898 NIL FR2 (NIL T T) -7 NIL NIL) (-374 890270 893183 893212 "FPS" 894331 T FPS (NIL) -9 NIL 894887) (-373 889719 889828 889992 "FPS-" 890138 NIL FPS- (NIL T) -8 NIL NIL) (-372 887167 888864 888893 "FPC" 889118 T FPC (NIL) -9 NIL 889260) (-371 886960 887000 887097 "FPC-" 887102 NIL FPC- (NIL T) -8 NIL NIL) (-370 885838 886448 886490 "FPATMAB" 886495 NIL FPATMAB (NIL T) -9 NIL 886647) (-369 883538 884014 884440 "FPARFRAC" 885475 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-368 878933 879430 880112 "FORTRAN" 882970 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-367 876649 877149 877688 "FORT" 878414 T FORT (NIL) -7 NIL NIL) (-366 874324 874886 874915 "FORTFN" 875975 T FORTFN (NIL) -9 NIL 876599) (-365 874087 874137 874166 "FORTCAT" 874225 T FORTCAT (NIL) -9 NIL 874287) (-364 872147 872630 873029 "FORMULA" 873708 T FORMULA (NIL) -8 NIL NIL) (-363 871935 871965 872034 "FORMULA1" 872111 NIL FORMULA1 (NIL T) -7 NIL NIL) (-362 871458 871510 871683 "FORDER" 871877 NIL FORDER (NIL T T T T) -7 NIL NIL) (-361 870554 870718 870911 "FOP" 871285 T FOP (NIL) -7 NIL NIL) (-360 869162 869834 870008 "FNLA" 870436 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-359 867830 868219 868248 "FNCAT" 868820 T FNCAT (NIL) -9 NIL 869113) (-358 867396 867789 867817 "FNAME" 867822 T FNAME (NIL) -8 NIL NIL) (-357 866055 867028 867057 "FMTC" 867062 T FMTC (NIL) -9 NIL 867097) (-356 862373 863580 864208 "FMONOID" 865460 NIL FMONOID (NIL T) -8 NIL NIL) (-355 861593 862116 862264 "FM" 862269 NIL FM (NIL T T) -8 NIL NIL) (-354 859016 859662 859691 "FMFUN" 860835 T FMFUN (NIL) -9 NIL 861543) (-353 858284 858465 858494 "FMC" 858784 T FMC (NIL) -9 NIL 858966) (-352 855513 856347 856401 "FMCAT" 857583 NIL FMCAT (NIL T T) -9 NIL 858077) (-351 854408 855281 855380 "FM1" 855458 NIL FM1 (NIL T T) -8 NIL NIL) (-350 852182 852598 853092 "FLOATRP" 853959 NIL FLOATRP (NIL T) -7 NIL NIL) (-349 845668 849838 850468 "FLOAT" 851572 T FLOAT (NIL) -8 NIL NIL) (-348 843106 843606 844184 "FLOATCP" 845135 NIL FLOATCP (NIL T) -7 NIL NIL) (-347 841894 842742 842783 "FLINEXP" 842788 NIL FLINEXP (NIL T) -9 NIL 842881) (-346 841049 841284 841611 "FLINEXP-" 841616 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-345 840125 840269 840493 "FLASORT" 840901 NIL FLASORT (NIL T T) -7 NIL NIL) (-344 837343 838185 838238 "FLALG" 839465 NIL FLALG (NIL T T) -9 NIL 839932) (-343 831127 834829 834871 "FLAGG" 836133 NIL FLAGG (NIL T) -9 NIL 836785) (-342 829853 830192 830682 "FLAGG-" 830687 NIL FLAGG- (NIL T T) -8 NIL NIL) (-341 828895 829038 829265 "FLAGG2" 829706 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 825867 826885 826945 "FINRALG" 828073 NIL FINRALG (NIL T T) -9 NIL 828581) (-339 825027 825256 825595 "FINRALG-" 825600 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-338 824433 824646 824675 "FINITE" 824871 T FINITE (NIL) -9 NIL 824978) (-337 816892 819053 819094 "FINAALG" 822761 NIL FINAALG (NIL T) -9 NIL 824214) (-336 812233 813274 814418 "FINAALG-" 815797 NIL FINAALG- (NIL T T) -8 NIL NIL) (-335 811628 811988 812091 "FILE" 812163 NIL FILE (NIL T) -8 NIL NIL) (-334 810312 810624 810679 "FILECAT" 811363 NIL FILECAT (NIL T T) -9 NIL 811579) (-333 808174 809730 809759 "FIELD" 809799 T FIELD (NIL) -9 NIL 809879) (-332 806794 807179 807690 "FIELD-" 807695 NIL FIELD- (NIL T) -8 NIL NIL) (-331 804609 805431 805777 "FGROUP" 806481 NIL FGROUP (NIL T) -8 NIL NIL) (-330 803699 803863 804083 "FGLMICPK" 804441 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-329 799501 803624 803681 "FFX" 803686 NIL FFX (NIL T NIL) -8 NIL NIL) (-328 799102 799163 799298 "FFSLPE" 799434 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-327 795097 795874 796670 "FFPOLY" 798338 NIL FFPOLY (NIL T) -7 NIL NIL) (-326 794601 794637 794846 "FFPOLY2" 795055 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-325 790423 794520 794583 "FFP" 794588 NIL FFP (NIL T NIL) -8 NIL NIL) (-324 785791 790334 790398 "FF" 790403 NIL FF (NIL NIL NIL) -8 NIL NIL) (-323 780887 785134 785324 "FFNBX" 785645 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-322 775797 780022 780280 "FFNBP" 780741 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-321 770400 775081 775292 "FFNB" 775630 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-320 769232 769430 769745 "FFINTBAS" 770197 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-319 765455 767695 767724 "FFIELDC" 768344 T FFIELDC (NIL) -9 NIL 768720) (-318 764118 764488 764985 "FFIELDC-" 764990 NIL FFIELDC- (NIL T) -8 NIL NIL) (-317 763688 763733 763857 "FFHOM" 764060 NIL FFHOM (NIL T T T) -7 NIL NIL) (-316 761386 761870 762387 "FFF" 763203 NIL FFF (NIL T) -7 NIL NIL) (-315 756974 761128 761229 "FFCGX" 761329 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-314 752576 756706 756813 "FFCGP" 756917 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-313 747729 752303 752411 "FFCG" 752512 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-312 729674 738797 738884 "FFCAT" 744049 NIL FFCAT (NIL T T T) -9 NIL 745536) (-311 724872 725919 727233 "FFCAT-" 728463 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-310 724283 724326 724561 "FFCAT2" 724823 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-309 713483 717273 718490 "FEXPR" 723138 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-308 712482 712917 712959 "FEVALAB" 713043 NIL FEVALAB (NIL T) -9 NIL 713304) (-307 711641 711851 712189 "FEVALAB-" 712194 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-306 710234 711024 711227 "FDIV" 711540 NIL FDIV (NIL T T T T) -8 NIL NIL) (-305 707300 708015 708131 "FDIVCAT" 709699 NIL FDIVCAT (NIL T T T T) -9 NIL 710136) (-304 707062 707089 707259 "FDIVCAT-" 707264 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-303 706282 706369 706646 "FDIV2" 706969 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-302 704975 705232 705519 "FCPAK1" 706015 T FCPAK1 (NIL) -7 NIL NIL) (-301 704103 704475 704616 "FCOMP" 704866 NIL FCOMP (NIL T) -8 NIL NIL) (-300 687743 691155 694715 "FC" 700563 T FC (NIL) -8 NIL NIL) (-299 680338 684384 684425 "FAXF" 686227 NIL FAXF (NIL T) -9 NIL 686918) (-298 677617 678272 679097 "FAXF-" 679562 NIL FAXF- (NIL T T) -8 NIL NIL) (-297 672717 676993 677169 "FARRAY" 677474 NIL FARRAY (NIL T) -8 NIL NIL) (-296 668107 670178 670231 "FAMR" 671243 NIL FAMR (NIL T T) -9 NIL 671703) (-295 666998 667300 667734 "FAMR-" 667739 NIL FAMR- (NIL T T T) -8 NIL NIL) (-294 666194 666920 666973 "FAMONOID" 666978 NIL FAMONOID (NIL T) -8 NIL NIL) (-293 664026 664710 664764 "FAMONC" 665705 NIL FAMONC (NIL T T) -9 NIL 666090) (-292 662718 663780 663917 "FAGROUP" 663922 NIL FAGROUP (NIL T) -8 NIL NIL) (-291 660521 660840 661242 "FACUTIL" 662399 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-290 659620 659805 660027 "FACTFUNC" 660331 NIL FACTFUNC (NIL T) -7 NIL NIL) (-289 651943 658871 659083 "EXPUPXS" 659476 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-288 649426 649966 650552 "EXPRTUBE" 651377 T EXPRTUBE (NIL) -7 NIL NIL) (-287 645620 646212 646949 "EXPRODE" 648765 NIL EXPRODE (NIL T T) -7 NIL NIL) (-286 630782 644279 644705 "EXPR" 645226 NIL EXPR (NIL T) -8 NIL NIL) (-285 625210 625797 626609 "EXPR2UPS" 630080 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-284 624846 624903 625010 "EXPR2" 625147 NIL EXPR2 (NIL T T) -7 NIL NIL) (-283 616200 623983 624278 "EXPEXPAN" 624684 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-282 616027 616157 616186 "EXIT" 616191 T EXIT (NIL) -8 NIL NIL) (-281 615654 615716 615829 "EVALCYC" 615959 NIL EVALCYC (NIL T) -7 NIL NIL) (-280 615194 615312 615354 "EVALAB" 615524 NIL EVALAB (NIL T) -9 NIL 615628) (-279 614675 614797 615018 "EVALAB-" 615023 NIL EVALAB- (NIL T T) -8 NIL NIL) (-278 612137 613449 613478 "EUCDOM" 614033 T EUCDOM (NIL) -9 NIL 614383) (-277 610542 610984 611574 "EUCDOM-" 611579 NIL EUCDOM- (NIL T) -8 NIL NIL) (-276 598120 600868 603608 "ESTOOLS" 607822 T ESTOOLS (NIL) -7 NIL NIL) (-275 597756 597813 597920 "ESTOOLS2" 598057 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-274 597507 597549 597629 "ESTOOLS1" 597708 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-273 591444 593168 593197 "ES" 595961 T ES (NIL) -9 NIL 597367) (-272 586392 587678 589495 "ES-" 589659 NIL ES- (NIL T) -8 NIL NIL) (-271 582767 583527 584307 "ESCONT" 585632 T ESCONT (NIL) -7 NIL NIL) (-270 582512 582544 582626 "ESCONT1" 582729 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-269 582187 582237 582337 "ES2" 582456 NIL ES2 (NIL T T) -7 NIL NIL) (-268 581817 581875 581984 "ES1" 582123 NIL ES1 (NIL T T) -7 NIL NIL) (-267 581033 581162 581338 "ERROR" 581661 T ERROR (NIL) -7 NIL NIL) (-266 574536 580892 580983 "EQTBL" 580988 NIL EQTBL (NIL T T) -8 NIL NIL) (-265 566973 569854 571301 "EQ" 573122 NIL -3221 (NIL T) -8 NIL NIL) (-264 566605 566662 566771 "EQ2" 566910 NIL EQ2 (NIL T T) -7 NIL NIL) (-263 561897 562943 564036 "EP" 565544 NIL EP (NIL T) -7 NIL NIL) (-262 561056 561620 561649 "ENTIRER" 561654 T ENTIRER (NIL) -9 NIL 561699) (-261 557512 559011 559381 "EMR" 560855 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-260 556655 556840 556895 "ELTAGG" 557275 NIL ELTAGG (NIL T T) -9 NIL 557486) (-259 556374 556436 556577 "ELTAGG-" 556582 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-258 556162 556191 556246 "ELTAB" 556330 NIL ELTAB (NIL T T) -9 NIL NIL) (-257 555288 555434 555633 "ELFUTS" 556013 NIL ELFUTS (NIL T T) -7 NIL NIL) (-256 555029 555085 555114 "ELEMFUN" 555219 T ELEMFUN (NIL) -9 NIL NIL) (-255 554899 554920 554988 "ELEMFUN-" 554993 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-254 549790 552999 553041 "ELAGG" 553981 NIL ELAGG (NIL T) -9 NIL 554444) (-253 548075 548509 549172 "ELAGG-" 549177 NIL ELAGG- (NIL T T) -8 NIL NIL) (-252 540943 542742 543569 "EFUPXS" 547351 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-251 534393 536194 537004 "EFULS" 540219 NIL EFULS (NIL T T T) -8 NIL NIL) (-250 531824 532182 532660 "EFSTRUC" 534025 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-249 520896 522461 524021 "EF" 530339 NIL EF (NIL T T) -7 NIL NIL) (-248 519997 520381 520530 "EAB" 520767 T EAB (NIL) -8 NIL NIL) (-247 519210 519956 519984 "E04UCFA" 519989 T E04UCFA (NIL) -8 NIL NIL) (-246 518423 519169 519197 "E04NAFA" 519202 T E04NAFA (NIL) -8 NIL NIL) (-245 517636 518382 518410 "E04MBFA" 518415 T E04MBFA (NIL) -8 NIL NIL) (-244 516849 517595 517623 "E04JAFA" 517628 T E04JAFA (NIL) -8 NIL NIL) (-243 516064 516808 516836 "E04GCFA" 516841 T E04GCFA (NIL) -8 NIL NIL) (-242 515279 516023 516051 "E04FDFA" 516056 T E04FDFA (NIL) -8 NIL NIL) (-241 514492 515238 515266 "E04DGFA" 515271 T E04DGFA (NIL) -8 NIL NIL) (-240 508677 510022 511384 "E04AGNT" 513150 T E04AGNT (NIL) -7 NIL NIL) (-239 507403 507883 507924 "DVARCAT" 508399 NIL DVARCAT (NIL T) -9 NIL 508597) (-238 506607 506819 507133 "DVARCAT-" 507138 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-237 499469 506409 506536 "DSMP" 506541 NIL DSMP (NIL T T T) -8 NIL NIL) (-236 494279 495414 496482 "DROPT" 498421 T DROPT (NIL) -8 NIL NIL) (-235 493944 494003 494101 "DROPT1" 494214 NIL DROPT1 (NIL T) -7 NIL NIL) (-234 489059 490185 491322 "DROPT0" 492827 T DROPT0 (NIL) -7 NIL NIL) (-233 487404 487729 488115 "DRAWPT" 488693 T DRAWPT (NIL) -7 NIL NIL) (-232 482079 482978 484033 "DRAW" 486402 NIL DRAW (NIL T) -7 NIL NIL) (-231 481720 481771 481887 "DRAWHACK" 482022 NIL DRAWHACK (NIL T) -7 NIL NIL) (-230 480451 480720 481011 "DRAWCX" 481449 T DRAWCX (NIL) -7 NIL NIL) (-229 479969 480037 480187 "DRAWCURV" 480377 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-228 470441 472399 474514 "DRAWCFUN" 477874 T DRAWCFUN (NIL) -7 NIL NIL) (-227 467254 469136 469178 "DQAGG" 469807 NIL DQAGG (NIL T) -9 NIL 470080) (-226 455760 462498 462581 "DPOLCAT" 464419 NIL DPOLCAT (NIL T T T T) -9 NIL 464963) (-225 450600 451946 453903 "DPOLCAT-" 453908 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-224 444684 450462 450559 "DPMO" 450564 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-223 438671 444465 444631 "DPMM" 444636 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-222 438304 438380 438478 "DOMAIN" 438593 T DOMAIN (NIL) -8 NIL NIL) (-221 432016 437941 438092 "DMP" 438205 NIL DMP (NIL NIL T) -8 NIL NIL) (-220 431616 431672 431816 "DLP" 431954 NIL DLP (NIL T) -7 NIL NIL) (-219 425260 430717 430944 "DLIST" 431421 NIL DLIST (NIL T) -8 NIL NIL) (-218 422106 424115 424157 "DLAGG" 424707 NIL DLAGG (NIL T) -9 NIL 424936) (-217 420815 421507 421536 "DIVRING" 421686 T DIVRING (NIL) -9 NIL 421794) (-216 419803 420056 420449 "DIVRING-" 420454 NIL DIVRING- (NIL T) -8 NIL NIL) (-215 417905 418262 418668 "DISPLAY" 419417 T DISPLAY (NIL) -7 NIL NIL) (-214 411794 417819 417882 "DIRPROD" 417887 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-213 410642 410845 411110 "DIRPROD2" 411587 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 400272 406277 406331 "DIRPCAT" 406739 NIL DIRPCAT (NIL NIL T) -9 NIL 407566) (-211 397598 398240 399121 "DIRPCAT-" 399458 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-210 396885 397045 397231 "DIOSP" 397432 T DIOSP (NIL) -7 NIL NIL) (-209 393587 395797 395839 "DIOPS" 396273 NIL DIOPS (NIL T) -9 NIL 396502) (-208 393136 393250 393441 "DIOPS-" 393446 NIL DIOPS- (NIL T T) -8 NIL NIL) (-207 392007 392645 392674 "DIFRING" 392861 T DIFRING (NIL) -9 NIL 392970) (-206 391653 391730 391882 "DIFRING-" 391887 NIL DIFRING- (NIL T) -8 NIL NIL) (-205 389442 390724 390765 "DIFEXT" 391124 NIL DIFEXT (NIL T) -9 NIL 391417) (-204 387728 388156 388821 "DIFEXT-" 388826 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-203 385050 387260 387302 "DIAGG" 387307 NIL DIAGG (NIL T) -9 NIL 387327) (-202 384434 384591 384843 "DIAGG-" 384848 NIL DIAGG- (NIL T T) -8 NIL NIL) (-201 379899 383393 383670 "DHMATRIX" 384203 NIL DHMATRIX (NIL T) -8 NIL NIL) (-200 375511 376420 377430 "DFSFUN" 378909 T DFSFUN (NIL) -7 NIL NIL) (-199 370297 374225 374590 "DFLOAT" 375166 T DFLOAT (NIL) -8 NIL NIL) (-198 368530 368811 369206 "DFINTTLS" 370005 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 365563 366565 366963 "DERHAM" 368197 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363412 365338 365427 "DEQUEUE" 365507 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 362630 362763 362958 "DEGRED" 363274 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 359046 359787 360635 "DEFINTRF" 361862 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 356585 357052 357648 "DEFINTEF" 358567 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350416 356026 356192 "DECIMAL" 356439 T DECIMAL (NIL) -8 NIL NIL) (-191 347928 348386 348892 "DDFACT" 349960 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 347524 347567 347718 "DBLRESP" 347879 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 345234 345568 345937 "DBASE" 347282 NIL DBASE (NIL T) -8 NIL NIL) (-188 344369 345193 345221 "D03FAFA" 345226 T D03FAFA (NIL) -8 NIL NIL) (-187 343505 344328 344356 "D03EEFA" 344361 T D03EEFA (NIL) -8 NIL NIL) (-186 341455 341921 342410 "D03AGNT" 343036 T D03AGNT (NIL) -7 NIL NIL) (-185 340773 341414 341442 "D02EJFA" 341447 T D02EJFA (NIL) -8 NIL NIL) (-184 340091 340732 340760 "D02CJFA" 340765 T D02CJFA (NIL) -8 NIL NIL) (-183 339409 340050 340078 "D02BHFA" 340083 T D02BHFA (NIL) -8 NIL NIL) (-182 338727 339368 339396 "D02BBFA" 339401 T D02BBFA (NIL) -8 NIL NIL) (-181 331925 333513 335119 "D02AGNT" 337141 T D02AGNT (NIL) -7 NIL NIL) (-180 329694 330216 330762 "D01WGTS" 331399 T D01WGTS (NIL) -7 NIL NIL) (-179 328797 329653 329681 "D01TRNS" 329686 T D01TRNS (NIL) -8 NIL NIL) (-178 327900 328756 328784 "D01GBFA" 328789 T D01GBFA (NIL) -8 NIL NIL) (-177 327003 327859 327887 "D01FCFA" 327892 T D01FCFA (NIL) -8 NIL NIL) (-176 326106 326962 326990 "D01ASFA" 326995 T D01ASFA (NIL) -8 NIL NIL) (-175 325209 326065 326093 "D01AQFA" 326098 T D01AQFA (NIL) -8 NIL NIL) (-174 324312 325168 325196 "D01APFA" 325201 T D01APFA (NIL) -8 NIL NIL) (-173 323415 324271 324299 "D01ANFA" 324304 T D01ANFA (NIL) -8 NIL NIL) (-172 322518 323374 323402 "D01AMFA" 323407 T D01AMFA (NIL) -8 NIL NIL) (-171 321621 322477 322505 "D01ALFA" 322510 T D01ALFA (NIL) -8 NIL NIL) (-170 320724 321580 321608 "D01AKFA" 321613 T D01AKFA (NIL) -8 NIL NIL) (-169 319827 320683 320711 "D01AJFA" 320716 T D01AJFA (NIL) -8 NIL NIL) (-168 313131 314680 316239 "D01AGNT" 318288 T D01AGNT (NIL) -7 NIL NIL) (-167 312468 312596 312748 "CYCLOTOM" 312999 T CYCLOTOM (NIL) -7 NIL NIL) (-166 309203 309916 310643 "CYCLES" 311761 T CYCLES (NIL) -7 NIL NIL) (-165 308515 308649 308820 "CVMP" 309064 NIL CVMP (NIL T) -7 NIL NIL) (-164 306297 306554 306929 "CTRIGMNP" 308243 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 305671 305770 305923 "CSTTOOLS" 306194 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 301470 302127 302885 "CRFP" 304983 NIL CRFP (NIL T T) -7 NIL NIL) (-161 300517 300702 300930 "CRAPACK" 301274 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 299901 300002 300206 "CPMATCH" 300393 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 299626 299654 299760 "CPIMA" 299867 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 295990 296662 297380 "COORDSYS" 298961 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 291851 293993 294485 "CONTFRAC" 295530 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 291004 291568 291597 "COMRING" 291602 T COMRING (NIL) -9 NIL 291653) (-155 290085 290362 290546 "COMPPROP" 290840 T COMPPROP (NIL) -8 NIL NIL) (-154 289746 289781 289909 "COMPLPAT" 290044 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 279727 289555 289664 "COMPLEX" 289669 NIL COMPLEX (NIL T) -8 NIL NIL) (-152 279363 279420 279527 "COMPLEX2" 279664 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-151 279081 279116 279214 "COMPFACT" 279322 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263415 273709 273750 "COMPCAT" 274752 NIL COMPCAT (NIL T) -9 NIL 276145) (-149 252930 255854 259481 "COMPCAT-" 259837 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 252661 252689 252791 "COMMUPC" 252896 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 252456 252489 252548 "COMMONOP" 252622 T COMMONOP (NIL) -7 NIL NIL) (-146 252039 252207 252294 "COMM" 252389 T COMM (NIL) -8 NIL NIL) (-145 251293 251485 251514 "COMBOPC" 251850 T COMBOPC (NIL) -9 NIL 252023) (-144 250189 250399 250641 "COMBINAT" 251083 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246395 246966 247604 "COMBF" 249613 NIL COMBF (NIL T T) -7 NIL NIL) (-142 245181 245511 245746 "COLOR" 246180 T COLOR (NIL) -8 NIL NIL) (-141 244821 244868 244993 "CMPLXRT" 245128 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240323 241351 242431 "CLIP" 243761 T CLIP (NIL) -7 NIL NIL) (-139 238661 239431 239669 "CLIF" 240151 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 234883 236807 236849 "CLAGG" 237778 NIL CLAGG (NIL T) -9 NIL 238314) (-137 233305 233762 234345 "CLAGG-" 234350 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 232849 232934 233074 "CINTSLPE" 233214 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230350 230821 231369 "CHVAR" 232377 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 229572 230136 230165 "CHARZ" 230170 T CHARZ (NIL) -9 NIL 230184) (-133 229326 229366 229444 "CHARPOL" 229526 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 228432 229029 229058 "CHARNZ" 229105 T CHARNZ (NIL) -9 NIL 229160) (-131 226455 227122 227457 "CHAR" 228117 T CHAR (NIL) -8 NIL NIL) (-130 226180 226241 226270 "CFCAT" 226381 T CFCAT (NIL) -9 NIL NIL) (-129 225425 225536 225718 "CDEN" 226064 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 221417 224578 224858 "CCLASS" 225165 T CCLASS (NIL) -8 NIL NIL) (-127 216470 217446 218199 "CARTEN" 220720 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-126 215578 215726 215947 "CARTEN2" 216317 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-125 213875 214730 214986 "CARD" 215342 T CARD (NIL) -8 NIL NIL) (-124 213247 213575 213604 "CACHSET" 213736 T CACHSET (NIL) -9 NIL 213813) (-123 212743 213039 213068 "CABMON" 213118 T CABMON (NIL) -9 NIL 213174) (-122 210300 212435 212542 "BTREE" 212669 NIL BTREE (NIL T) -8 NIL NIL) (-121 207798 209948 210070 "BTOURN" 210210 NIL BTOURN (NIL T) -8 NIL NIL) (-120 205216 207269 207311 "BTCAT" 207379 NIL BTCAT (NIL T) -9 NIL 207456) (-119 204883 204963 205112 "BTCAT-" 205117 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 200103 203974 204003 "BTAGG" 204259 T BTAGG (NIL) -9 NIL 204438) (-117 199526 199670 199900 "BTAGG-" 199905 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 196570 198804 199019 "BSTREE" 199343 NIL BSTREE (NIL T) -8 NIL NIL) (-115 195708 195834 196018 "BRILL" 196426 NIL BRILL (NIL T) -7 NIL NIL) (-114 192409 194436 194478 "BRAGG" 195127 NIL BRAGG (NIL T) -9 NIL 195384) (-113 190938 191344 191899 "BRAGG-" 191904 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 184146 190284 190468 "BPADICRT" 190786 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 182450 184083 184128 "BPADIC" 184133 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 182150 182180 182293 "BOUNDZRO" 182414 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-109 177665 178756 179623 "BOP" 181303 T BOP (NIL) -8 NIL NIL) (-108 175286 175730 176250 "BOP1" 177178 NIL BOP1 (NIL T) -7 NIL NIL) (-107 173639 174329 174623 "BOOLEAN" 175012 T BOOLEAN (NIL) -8 NIL NIL) (-106 173005 173383 173436 "BMODULE" 173441 NIL BMODULE (NIL T T) -9 NIL 173505) (-105 168815 172803 172876 "BITS" 172952 T BITS (NIL) -8 NIL NIL) (-104 167912 168347 168499 "BINFILE" 168683 T BINFILE (NIL) -8 NIL NIL) (-103 161747 167356 167521 "BINARY" 167767 T BINARY (NIL) -8 NIL NIL) (-102 159574 161002 161044 "BGAGG" 161304 NIL BGAGG (NIL T) -9 NIL 161441) (-101 159405 159437 159528 "BGAGG-" 159533 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158503 158789 158994 "BFUNCT" 159220 T BFUNCT (NIL) -8 NIL NIL) (-99 157204 157382 157667 "BEZOUT" 158327 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 153729 156064 156392 "BBTREE" 156907 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153466 153519 153546 "BASTYPE" 153663 T BASTYPE (NIL) -9 NIL NIL) (-96 153321 153350 153420 "BASTYPE-" 153425 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 152759 152835 152985 "BALFACT" 153232 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151581 152178 152363 "AUTOMOR" 152604 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151306 151311 151338 "ATTREG" 151343 T ATTREG (NIL) -9 NIL NIL) (-92 149585 150003 150355 "ATTRBUT" 150972 T ATTRBUT (NIL) -8 NIL NIL) (-91 149120 149233 149260 "ATRIG" 149461 T ATRIG (NIL) -9 NIL NIL) (-90 148929 148970 149057 "ATRIG-" 149062 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147126 148705 148793 "ASTACK" 148872 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145631 145928 146293 "ASSOCEQ" 146808 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144663 145290 145414 "ASP9" 145538 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144427 144611 144650 "ASP8" 144655 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143297 144032 144174 "ASP80" 144316 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142196 142932 143064 "ASP7" 143196 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141152 141873 141991 "ASP78" 142109 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140123 140832 140949 "ASP77" 141066 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139038 139761 139892 "ASP74" 140023 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 137939 138673 138805 "ASP73" 138937 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 136894 137616 137734 "ASP6" 137852 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 135843 136571 136689 "ASP55" 136807 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 134793 135517 135636 "ASP50" 135755 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 133881 134494 134604 "ASP4" 134714 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 132969 133582 133692 "ASP49" 133802 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 131754 132508 132676 "ASP42" 132858 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130532 131287 131457 "ASP41" 131641 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129484 130209 130327 "ASP35" 130445 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129249 129432 129471 "ASP34" 129476 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 128986 129053 129129 "ASP33" 129204 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 127882 128621 128753 "ASP31" 128885 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127647 127830 127869 "ASP30" 127874 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127382 127451 127527 "ASP29" 127602 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127147 127330 127369 "ASP28" 127374 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 126912 127095 127134 "ASP27" 127139 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 125996 126610 126721 "ASP24" 126832 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 124913 125637 125767 "ASP20" 125897 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124001 124614 124724 "ASP1" 124834 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 122945 123675 123794 "ASP19" 123913 NIL ASP19 (NIL 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"STREAM2" 2658652 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1055 2657509 2657561 2657654 "STREAM1" 2657763 NIL STREAM1 (NIL T) -7 NIL NIL) (-1054 2656525 2656706 2656937 "STINPROD" 2657325 NIL STINPROD (NIL T) -7 NIL NIL) (-1053 2656103 2656287 2656318 "STEP" 2656398 T STEP (NIL) -9 NIL 2656476) (-1052 2649646 2656002 2656079 "STBL" 2656084 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1051 2644821 2648868 2648912 "STAGG" 2649065 NIL STAGG (NIL T) -9 NIL 2649154) (-1050 2642523 2643125 2643997 "STAGG-" 2644002 NIL STAGG- (NIL T T) -8 NIL NIL) (-1049 2640718 2642293 2642385 "STACK" 2642466 NIL STACK (NIL T) -8 NIL NIL) (-1048 2633449 2638865 2639320 "SREGSET" 2640348 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1047 2625889 2627257 2628769 "SRDCMPK" 2632055 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1046 2618856 2623329 2623360 "SRAGG" 2624663 T SRAGG (NIL) -9 NIL 2625271) (-1045 2617873 2618128 2618507 "SRAGG-" 2618512 NIL SRAGG- (NIL T) -8 NIL NIL) (-1044 2612322 2616792 2617219 "SQMATRIX" 2617492 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1043 2606074 2609042 2609768 "SPLTREE" 2611668 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1042 2602064 2602730 2603376 "SPLNODE" 2605500 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1041 2601110 2601343 2601374 "SPFCAT" 2601818 T SPFCAT (NIL) -9 NIL NIL) (-1040 2599847 2600057 2600321 "SPECOUT" 2600868 T SPECOUT (NIL) -7 NIL NIL) (-1039 2599608 2599648 2599717 "SPADPRSR" 2599800 T SPADPRSR (NIL) -7 NIL NIL) (-1038 2591630 2593377 2593420 "SPACEC" 2597743 NIL SPACEC (NIL T) -9 NIL 2599559) (-1037 2589802 2591563 2591611 "SPACE3" 2591616 NIL SPACE3 (NIL T) -8 NIL NIL) (-1036 2588554 2588725 2589016 "SORTPAK" 2589607 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1035 2586610 2586913 2587331 "SOLVETRA" 2588218 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1034 2585621 2585843 2586117 "SOLVESER" 2586383 NIL SOLVESER (NIL T) -7 NIL NIL) (-1033 2580841 2581722 2582724 "SOLVERAD" 2584673 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1032 2576656 2577265 2577994 "SOLVEFOR" 2580208 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1031 2570955 2576007 2576104 "SNTSCAT" 2576109 NIL SNTSCAT (NIL T T T T) -9 NIL 2576179) (-1030 2565060 2569286 2569676 "SMTS" 2570645 NIL SMTS (NIL T T T) -8 NIL NIL) (-1029 2559471 2564949 2565025 "SMP" 2565030 NIL SMP (NIL T T) -8 NIL NIL) (-1028 2557630 2557931 2558329 "SMITH" 2559168 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1027 2550594 2554790 2554893 "SMATCAT" 2556233 NIL SMATCAT (NIL NIL T T T) -9 NIL 2556782) (-1026 2547535 2548358 2549535 "SMATCAT-" 2549540 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1025 2545248 2546771 2546815 "SKAGG" 2547076 NIL SKAGG (NIL T) -9 NIL 2547211) (-1024 2541306 2544352 2544630 "SINT" 2544992 T SINT (NIL) -8 NIL NIL) (-1023 2541078 2541116 2541182 "SIMPAN" 2541262 T SIMPAN (NIL) -7 NIL NIL) (-1022 2539916 2540137 2540412 "SIGNRF" 2540837 NIL SIGNRF (NIL T) -7 NIL NIL) (-1021 2538725 2538876 2539166 "SIGNEF" 2539745 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1020 2536415 2536869 2537375 "SHP" 2538266 NIL SHP (NIL T NIL) -7 NIL NIL) (-1019 2530268 2536316 2536392 "SHDP" 2536397 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1018 2529757 2529949 2529980 "SGROUP" 2530132 T SGROUP (NIL) -9 NIL 2530219) (-1017 2529527 2529579 2529683 "SGROUP-" 2529688 NIL SGROUP- (NIL T) -8 NIL NIL) (-1016 2526363 2527060 2527783 "SGCF" 2528826 T SGCF (NIL) -7 NIL NIL) (-1015 2520761 2525813 2525910 "SFRTCAT" 2525915 NIL SFRTCAT (NIL T T T T) -9 NIL 2525953) (-1014 2514221 2515236 2516370 "SFRGCD" 2519744 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1013 2507387 2508458 2509642 "SFQCMPK" 2513154 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1012 2507009 2507098 2507208 "SFORT" 2507328 NIL SFORT (NIL T T) -8 NIL NIL) (-1011 2506154 2506849 2506970 "SEXOF" 2506975 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1010 2505288 2506035 2506103 "SEX" 2506108 T SEX (NIL) -8 NIL NIL) (-1009 2500064 2500753 2500849 "SEXCAT" 2504620 NIL SEXCAT (NIL T T T T T) -9 NIL 2505239) (-1008 2497244 2499998 2500046 "SET" 2500051 NIL SET (NIL T) -8 NIL NIL) (-1007 2495495 2495957 2496262 "SETMN" 2496985 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1006 2495102 2495228 2495259 "SETCAT" 2495376 T SETCAT (NIL) -9 NIL 2495460) (-1005 2494882 2494934 2495033 "SETCAT-" 2495038 NIL SETCAT- (NIL T) -8 NIL NIL) (-1004 2491269 2493343 2493387 "SETAGG" 2494257 NIL SETAGG (NIL T) -9 NIL 2494597) (-1003 2490727 2490843 2491080 "SETAGG-" 2491085 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1002 2489930 2490223 2490285 "SEGXCAT" 2490571 NIL SEGXCAT (NIL T T) -9 NIL 2490691) (-1001 2488986 2489596 2489778 "SEG" 2489783 NIL SEG (NIL T) -8 NIL NIL) (-1000 2487892 2488105 2488149 "SEGCAT" 2488731 NIL SEGCAT (NIL T) -9 NIL 2488969) (-999 2486946 2487276 2487474 "SEGBIND" 2487727 NIL SEGBIND (NIL T) -8 NIL NIL) (-998 2486578 2486635 2486744 "SEGBIND2" 2486883 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-997 2485801 2485927 2486129 "SEG2" 2486422 NIL SEG2 (NIL T T) -7 NIL NIL) (-996 2485240 2485738 2485783 "SDVAR" 2485788 NIL SDVAR (NIL T) -8 NIL NIL) (-995 2477546 2485019 2485143 "SDPOL" 2485148 NIL SDPOL (NIL T) -8 NIL NIL) (-994 2476145 2476411 2476728 "SCPKG" 2477261 NIL SCPKG (NIL T) -7 NIL NIL) (-993 2475372 2475505 2475682 "SCACHE" 2476000 NIL SCACHE (NIL T) -7 NIL NIL) (-992 2474815 2475136 2475219 "SAOS" 2475309 T SAOS (NIL) -8 NIL NIL) (-991 2474383 2474418 2474589 "SAERFFC" 2474774 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-990 2468279 2474282 2474360 "SAE" 2474365 NIL SAE (NIL T T NIL) -8 NIL NIL) (-989 2467875 2467910 2468067 "SAEFACT" 2468238 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-988 2466201 2466515 2466914 "RURPK" 2467541 NIL RURPK (NIL T NIL) -7 NIL NIL) (-987 2464854 2465131 2465438 "RULESET" 2466037 NIL RULESET (NIL T T T) -8 NIL NIL) (-986 2462062 2462565 2463026 "RULE" 2464536 NIL RULE (NIL T T T) -8 NIL NIL) (-985 2461704 2461859 2461940 "RULECOLD" 2462014 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-984 2456596 2457390 2458306 "RSETGCD" 2460903 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-983 2445910 2450962 2451057 "RSETCAT" 2455122 NIL RSETCAT (NIL T T T T) -9 NIL 2456219) (-982 2443841 2444380 2445200 "RSETCAT-" 2445205 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-981 2436271 2437646 2439162 "RSDCMPK" 2442440 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-980 2434288 2434729 2434802 "RRCC" 2435878 NIL RRCC (NIL T T) -9 NIL 2436222) (-979 2433642 2433816 2434092 "RRCC-" 2434097 NIL RRCC- (NIL T T T) -8 NIL NIL) (-978 2408008 2417633 2417698 "RPOLCAT" 2428200 NIL RPOLCAT (NIL T T T) -9 NIL 2431358) (-977 2399512 2401850 2404968 "RPOLCAT-" 2404973 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-976 2390578 2397742 2398222 "ROUTINE" 2399052 T ROUTINE (NIL) -8 NIL NIL) (-975 2387283 2390134 2390281 "ROMAN" 2390451 T ROMAN (NIL) -8 NIL NIL) (-974 2385569 2386154 2386411 "ROIRC" 2387089 NIL ROIRC (NIL T T) -8 NIL NIL) (-973 2381973 2384277 2384306 "RNS" 2384602 T RNS (NIL) -9 NIL 2384872) (-972 2380487 2380870 2381401 "RNS-" 2381474 NIL RNS- (NIL T) -8 NIL NIL) (-971 2379912 2380320 2380349 "RNG" 2380354 T RNG (NIL) -9 NIL 2380375) (-970 2379309 2379671 2379712 "RMODULE" 2379772 NIL RMODULE (NIL T) -9 NIL 2379814) (-969 2378161 2378255 2378585 "RMCAT2" 2379210 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-968 2374875 2377344 2377665 "RMATRIX" 2377896 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-967 2367871 2370105 2370218 "RMATCAT" 2373527 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2374509) (-966 2367250 2367397 2367700 "RMATCAT-" 2367705 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-965 2366820 2366895 2367021 "RINTERP" 2367169 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-964 2365870 2366434 2366463 "RING" 2366573 T RING (NIL) -9 NIL 2366667) (-963 2365665 2365709 2365803 "RING-" 2365808 NIL RING- (NIL T) -8 NIL NIL) (-962 2364513 2364750 2365006 "RIDIST" 2365429 T RIDIST (NIL) -7 NIL NIL) (-961 2355835 2363987 2364190 "RGCHAIN" 2364362 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-960 2352840 2353454 2354122 "RF" 2355199 NIL RF (NIL T) -7 NIL NIL) (-959 2352489 2352552 2352653 "RFFACTOR" 2352771 NIL RFFACTOR (NIL T) -7 NIL NIL) (-958 2352217 2352252 2352347 "RFFACT" 2352448 NIL RFFACT (NIL T) -7 NIL NIL) (-957 2350347 2350711 2351091 "RFDIST" 2351857 T RFDIST (NIL) -7 NIL NIL) (-956 2349805 2349897 2350057 "RETSOL" 2350249 NIL RETSOL (NIL T T) -7 NIL NIL) (-955 2349397 2349477 2349519 "RETRACT" 2349709 NIL RETRACT (NIL T) -9 NIL NIL) (-954 2349249 2349274 2349358 "RETRACT-" 2349363 NIL RETRACT- (NIL T T) -8 NIL NIL) (-953 2342107 2348906 2349031 "RESULT" 2349144 T RESULT (NIL) -8 NIL NIL) (-952 2340692 2341381 2341578 "RESRING" 2342010 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-951 2340332 2340381 2340477 "RESLATC" 2340629 NIL RESLATC (NIL T) -7 NIL NIL) (-950 2340041 2340075 2340180 "REPSQ" 2340291 NIL REPSQ (NIL T) -7 NIL NIL) (-949 2337472 2338052 2338652 "REP" 2339461 T REP (NIL) -7 NIL NIL) (-948 2337173 2337207 2337316 "REPDB" 2337431 NIL REPDB (NIL T) -7 NIL NIL) (-947 2331118 2332497 2333717 "REP2" 2335985 NIL REP2 (NIL T) -7 NIL NIL) (-946 2327524 2328205 2329010 "REP1" 2330345 NIL REP1 (NIL T) -7 NIL NIL) (-945 2320270 2325685 2326137 "REGSET" 2327155 NIL REGSET (NIL T T T T) -8 NIL NIL) (-944 2319091 2319426 2319674 "REF" 2320055 NIL REF (NIL T) -8 NIL NIL) (-943 2318472 2318575 2318740 "REDORDER" 2318975 NIL REDORDER (NIL T T) -7 NIL NIL) (-942 2314441 2317706 2317927 "RECLOS" 2318303 NIL RECLOS (NIL T) -8 NIL NIL) (-941 2313498 2313679 2313892 "REALSOLV" 2314248 T REALSOLV (NIL) -7 NIL NIL) (-940 2313345 2313386 2313415 "REAL" 2313420 T REAL (NIL) -9 NIL 2313455) (-939 2309836 2310638 2311520 "REAL0Q" 2312510 NIL REAL0Q (NIL T) -7 NIL NIL) (-938 2305447 2306435 2307494 "REAL0" 2308817 NIL REAL0 (NIL T) -7 NIL NIL) (-937 2304855 2304927 2305132 "RDIV" 2305369 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-936 2303928 2304102 2304313 "RDIST" 2304677 NIL RDIST (NIL T) -7 NIL NIL) (-935 2302532 2302819 2303188 "RDETRS" 2303636 NIL RDETRS (NIL T T) -7 NIL NIL) (-934 2300353 2300807 2301342 "RDETR" 2302074 NIL RDETR (NIL T T) -7 NIL NIL) (-933 2298969 2299247 2299648 "RDEEFS" 2300069 NIL RDEEFS (NIL T T) -7 NIL NIL) (-932 2297469 2297775 2298204 "RDEEF" 2298657 NIL RDEEF (NIL T T) -7 NIL NIL) (-931 2291753 2294685 2294714 "RCFIELD" 2295991 T RCFIELD (NIL) -9 NIL 2296721) (-930 2289822 2290326 2291019 "RCFIELD-" 2291092 NIL RCFIELD- (NIL T) -8 NIL NIL) (-929 2286153 2287938 2287980 "RCAGG" 2289051 NIL RCAGG (NIL T) -9 NIL 2289516) (-928 2285784 2285878 2286038 "RCAGG-" 2286043 NIL RCAGG- (NIL T T) -8 NIL NIL) (-927 2285129 2285240 2285402 "RATRET" 2285668 NIL RATRET (NIL T) -7 NIL NIL) (-926 2284686 2284753 2284872 "RATFACT" 2285057 NIL RATFACT (NIL T) -7 NIL NIL) (-925 2284001 2284121 2284271 "RANDSRC" 2284556 T RANDSRC (NIL) -7 NIL NIL) (-924 2283738 2283782 2283853 "RADUTIL" 2283950 T RADUTIL (NIL) -7 NIL NIL) (-923 2276745 2282481 2282798 "RADIX" 2283453 NIL RADIX (NIL NIL) -8 NIL NIL) (-922 2268315 2276589 2276717 "RADFF" 2276722 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-921 2267966 2268041 2268070 "RADCAT" 2268227 T RADCAT (NIL) -9 NIL NIL) (-920 2267751 2267799 2267896 "RADCAT-" 2267901 NIL RADCAT- (NIL T) -8 NIL NIL) (-919 2265902 2267526 2267615 "QUEUE" 2267695 NIL QUEUE (NIL T) -8 NIL NIL) (-918 2262399 2265839 2265884 "QUAT" 2265889 NIL QUAT (NIL T) -8 NIL NIL) (-917 2262037 2262080 2262207 "QUATCT2" 2262350 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-916 2255830 2259210 2259251 "QUATCAT" 2260030 NIL QUATCAT (NIL T) -9 NIL 2260795) (-915 2251974 2253011 2254398 "QUATCAT-" 2254492 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-914 2249494 2251058 2251100 "QUAGG" 2251475 NIL QUAGG (NIL T) -9 NIL 2251650) (-913 2248419 2248892 2249064 "QFORM" 2249366 NIL QFORM (NIL NIL T) -8 NIL NIL) (-912 2239715 2244973 2245014 "QFCAT" 2245672 NIL QFCAT (NIL T) -9 NIL 2246665) (-911 2235287 2236488 2238079 "QFCAT-" 2238173 NIL QFCAT- (NIL T T) -8 NIL NIL) (-910 2234925 2234968 2235095 "QFCAT2" 2235238 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-909 2234385 2234495 2234625 "QEQUAT" 2234815 T QEQUAT (NIL) -8 NIL NIL) (-908 2227571 2228642 2229824 "QCMPACK" 2233318 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-907 2225147 2225568 2225996 "QALGSET" 2227226 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-906 2224392 2224566 2224798 "QALGSET2" 2224967 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-905 2223083 2223306 2223623 "PWFFINTB" 2224165 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-904 2221271 2221439 2221792 "PUSHVAR" 2222897 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-903 2217188 2218242 2218284 "PTRANFN" 2220168 NIL PTRANFN (NIL T) -9 NIL NIL) (-902 2215600 2215891 2216212 "PTPACK" 2216899 NIL PTPACK (NIL T) -7 NIL NIL) (-901 2215236 2215293 2215400 "PTFUNC2" 2215537 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-900 2209712 2214053 2214094 "PTCAT" 2214462 NIL PTCAT (NIL T) -9 NIL 2214624) (-899 2209370 2209405 2209529 "PSQFR" 2209671 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-898 2207965 2208263 2208597 "PSEUDLIN" 2209068 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-897 2194773 2197137 2199460 "PSETPK" 2205725 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-896 2187859 2190573 2190668 "PSETCAT" 2193649 NIL PSETCAT (NIL T T T T) -9 NIL 2194463) (-895 2185697 2186331 2187150 "PSETCAT-" 2187155 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-894 2185045 2185210 2185239 "PSCURVE" 2185507 T PSCURVE (NIL) -9 NIL 2185674) (-893 2181496 2183022 2183087 "PSCAT" 2183923 NIL PSCAT (NIL T T T) -9 NIL 2184163) (-892 2180560 2180776 2181175 "PSCAT-" 2181180 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-891 2179213 2179845 2180059 "PRTITION" 2180366 T PRTITION (NIL) -8 NIL NIL) (-890 2168311 2170517 2172705 "PRS" 2177075 NIL PRS (NIL T T) -7 NIL NIL) (-889 2166169 2167661 2167702 "PRQAGG" 2167885 NIL PRQAGG (NIL T) -9 NIL 2167987) (-888 2165739 2165841 2165870 "PROPLOG" 2166055 T PROPLOG (NIL) -9 NIL NIL) (-887 2159513 2163905 2164725 "PRODUCT" 2164965 NIL PRODUCT (NIL T T) -8 NIL NIL) (-886 2156789 2158973 2159206 "PR" 2159324 NIL PR (NIL T T) -8 NIL NIL) (-885 2156585 2156617 2156676 "PRINT" 2156750 T PRINT (NIL) -7 NIL NIL) (-884 2155925 2156042 2156194 "PRIMES" 2156465 NIL PRIMES (NIL T) -7 NIL NIL) (-883 2153990 2154391 2154857 "PRIMELT" 2155504 NIL PRIMELT (NIL T) -7 NIL NIL) (-882 2153721 2153769 2153798 "PRIMCAT" 2153921 T PRIMCAT (NIL) -9 NIL NIL) (-881 2149882 2153659 2153704 "PRIMARR" 2153709 NIL PRIMARR (NIL T) -8 NIL NIL) (-880 2148889 2149067 2149295 "PRIMARR2" 2149700 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-879 2148532 2148588 2148699 "PREASSOC" 2148827 NIL PREASSOC (NIL T T) -7 NIL NIL) (-878 2148006 2148139 2148168 "PPCURVE" 2148373 T PPCURVE (NIL) -9 NIL 2148509) (-877 2145365 2145764 2146356 "POLYROOT" 2147587 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-876 2139271 2144971 2145130 "POLY" 2145238 NIL POLY (NIL T) -8 NIL NIL) (-875 2138656 2138714 2138947 "POLYLIFT" 2139207 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-874 2134941 2135390 2136018 "POLYCATQ" 2138201 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-873 2121981 2127378 2127443 "POLYCAT" 2130928 NIL POLYCAT (NIL T T T) -9 NIL 2132855) (-872 2115432 2117293 2119676 "POLYCAT-" 2119681 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-871 2115021 2115089 2115208 "POLY2UP" 2115358 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-870 2114657 2114714 2114821 "POLY2" 2114958 NIL POLY2 (NIL T T) -7 NIL NIL) (-869 2113342 2113581 2113857 "POLUTIL" 2114431 NIL POLUTIL (NIL T T) -7 NIL NIL) (-868 2111704 2111981 2112311 "POLTOPOL" 2113064 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-867 2107227 2111641 2111686 "POINT" 2111691 NIL POINT (NIL T) -8 NIL NIL) (-866 2105414 2105771 2106146 "PNTHEORY" 2106872 T PNTHEORY (NIL) -7 NIL NIL) (-865 2103842 2104139 2104548 "PMTOOLS" 2105112 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-864 2103435 2103513 2103630 "PMSYM" 2103758 NIL PMSYM (NIL T) -7 NIL NIL) (-863 2102945 2103014 2103188 "PMQFCAT" 2103360 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-862 2102300 2102410 2102566 "PMPRED" 2102822 NIL PMPRED (NIL T) -7 NIL NIL) (-861 2101696 2101782 2101943 "PMPREDFS" 2102201 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-860 2100342 2100550 2100934 "PMPLCAT" 2101458 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-859 2099874 2099953 2100105 "PMLSAGG" 2100257 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-858 2099351 2099427 2099607 "PMKERNEL" 2099792 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-857 2098968 2099043 2099156 "PMINS" 2099270 NIL PMINS (NIL T) -7 NIL NIL) (-856 2098398 2098467 2098682 "PMFS" 2098893 NIL PMFS (NIL T T T) -7 NIL NIL) (-855 2097629 2097747 2097951 "PMDOWN" 2098275 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-854 2096792 2096951 2097133 "PMASS" 2097467 T PMASS (NIL) -7 NIL NIL) (-853 2096066 2096177 2096340 "PMASSFS" 2096678 NIL PMASSFS (NIL T T) -7 NIL NIL) (-852 2095721 2095789 2095883 "PLOTTOOL" 2095992 T PLOTTOOL (NIL) -7 NIL NIL) (-851 2090343 2091532 2092680 "PLOT" 2094593 T PLOT (NIL) -8 NIL NIL) (-850 2086157 2087191 2088112 "PLOT3D" 2089442 T PLOT3D (NIL) -8 NIL NIL) (-849 2085069 2085246 2085481 "PLOT1" 2085961 NIL PLOT1 (NIL T) -7 NIL NIL) (-848 2060464 2065135 2069986 "PLEQN" 2080335 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-847 2059782 2059904 2060084 "PINTERP" 2060329 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-846 2059475 2059522 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2036463 "PFECAT" 2037048 T PFECAT (NIL) -9 NIL 2037432) (-832 2034598 2034752 2034966 "PFECAT-" 2034971 NIL PFECAT- (NIL T) -8 NIL NIL) (-831 2033202 2033453 2033754 "PFBRU" 2034347 NIL PFBRU (NIL T T) -7 NIL NIL) (-830 2031069 2031420 2031852 "PFBR" 2032853 NIL PFBR (NIL T T T T) -7 NIL NIL) (-829 2026921 2028445 2029121 "PERM" 2030426 NIL PERM (NIL T) -8 NIL NIL) (-828 2022187 2023128 2023998 "PERMGRP" 2026084 NIL PERMGRP (NIL T) -8 NIL NIL) (-827 2020257 2021250 2021292 "PERMCAT" 2021738 NIL PERMCAT (NIL T) -9 NIL 2022043) (-826 2019912 2019953 2020076 "PERMAN" 2020210 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-825 2017352 2019481 2019612 "PENDTREE" 2019814 NIL PENDTREE (NIL T) -8 NIL NIL) (-824 2015424 2016202 2016244 "PDRING" 2016901 NIL PDRING (NIL T) -9 NIL 2017186) (-823 2014527 2014745 2015107 "PDRING-" 2015112 NIL PDRING- (NIL T T) -8 NIL NIL) (-822 2011669 2012419 2013110 "PDEPROB" 2013856 T PDEPROB (NIL) -8 NIL NIL) (-821 2009240 2009736 2010285 "PDEPACK" 2011140 T PDEPACK (NIL) -7 NIL NIL) (-820 2008152 2008342 2008593 "PDECOMP" 2009039 NIL PDECOMP (NIL T T) -7 NIL NIL) (-819 2005763 2006578 2006607 "PDECAT" 2007392 T PDECAT (NIL) -9 NIL 2008103) (-818 2005516 2005549 2005638 "PCOMP" 2005724 NIL PCOMP (NIL T T) -7 NIL NIL) (-817 2003723 2004319 2004615 "PBWLB" 2005246 NIL PBWLB (NIL T) -8 NIL NIL) (-816 1996232 1997800 1999136 "PATTERN" 2002408 NIL PATTERN (NIL T) -8 NIL NIL) (-815 1995864 1995921 1996030 "PATTERN2" 1996169 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-814 1993621 1994009 1994466 "PATTERN1" 1995453 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-813 1991016 1991570 1992051 "PATRES" 1993186 NIL PATRES (NIL T T) -8 NIL NIL) (-812 1990580 1990647 1990779 "PATRES2" 1990943 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-811 1988477 1988877 1989282 "PATMATCH" 1990249 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-810 1988013 1988196 1988238 "PATMAB" 1988345 NIL PATMAB (NIL T) -9 NIL 1988428) (-809 1986558 1986867 1987125 "PATLRES" 1987818 NIL PATLRES (NIL T T T) -8 NIL NIL) (-808 1986103 1986226 1986268 "PATAB" 1986273 NIL PATAB (NIL T) -9 NIL 1986445) (-807 1983584 1984116 1984689 "PARTPERM" 1985550 T PARTPERM (NIL) -7 NIL NIL) (-806 1983205 1983268 1983370 "PARSURF" 1983515 NIL PARSURF (NIL T) -8 NIL NIL) (-805 1982837 1982894 1983003 "PARSU2" 1983142 NIL PARSU2 (NIL T T) -7 NIL NIL) (-804 1982601 1982641 1982708 "PARSER" 1982790 T PARSER (NIL) -7 NIL NIL) (-803 1982222 1982285 1982387 "PARSCURV" 1982532 NIL PARSCURV (NIL T) -8 NIL NIL) (-802 1981854 1981911 1982020 "PARSC2" 1982159 NIL PARSC2 (NIL T T) -7 NIL NIL) (-801 1981493 1981551 1981648 "PARPCURV" 1981790 NIL PARPCURV (NIL T) -8 NIL NIL) (-800 1981125 1981182 1981291 "PARPC2" 1981430 NIL PARPC2 (NIL T T) -7 NIL NIL) (-799 1980645 1980731 1980850 "PAN2EXPR" 1981026 T PAN2EXPR (NIL) -7 NIL NIL) (-798 1979451 1979766 1979994 "PALETTE" 1980437 T PALETTE (NIL) -8 NIL NIL) (-797 1977919 1978456 1978816 "PAIR" 1979137 NIL PAIR (NIL T T) -8 NIL NIL) (-796 1971769 1977178 1977372 "PADICRC" 1977774 NIL PADICRC 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1939427 "ORESUP" 1939550 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-782 1934539 1935039 1935599 "OREPCTO" 1936493 NIL OREPCTO (NIL T T) -7 NIL NIL) (-781 1928448 1930654 1930695 "OREPCAT" 1933016 NIL OREPCAT (NIL T) -9 NIL 1934119) (-780 1925596 1926378 1927435 "OREPCAT-" 1927440 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-779 1924773 1925045 1925074 "ORDSET" 1925383 T ORDSET (NIL) -9 NIL 1925547) (-778 1924292 1924414 1924607 "ORDSET-" 1924612 NIL ORDSET- (NIL T) -8 NIL NIL) (-777 1922905 1923706 1923735 "ORDRING" 1923937 T ORDRING (NIL) -9 NIL 1924061) (-776 1922550 1922644 1922788 "ORDRING-" 1922793 NIL ORDRING- (NIL T) -8 NIL NIL) (-775 1921925 1922406 1922435 "ORDMON" 1922440 T ORDMON (NIL) -9 NIL 1922461) (-774 1921087 1921234 1921429 "ORDFUNS" 1921774 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-773 1920598 1920957 1920986 "ORDFIN" 1920991 T ORDFIN (NIL) -9 NIL 1921012) (-772 1917110 1919184 1919593 "ORDCOMP" 1920222 NIL ORDCOMP (NIL T) -8 NIL NIL) (-771 1916376 1916503 1916689 "ORDCOMP2" 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1893149 NIL OMEXPR (NIL T) -7 NIL NIL) (-757 1891571 1891799 1891935 "OMERR" 1892137 T OMERR (NIL) -8 NIL NIL) (-756 1890749 1890992 1891152 "OMERRK" 1891431 T OMERRK (NIL) -8 NIL NIL) (-755 1890227 1890426 1890534 "OMENC" 1890661 T OMENC (NIL) -8 NIL NIL) (-754 1884122 1885307 1886478 "OMDEV" 1889076 T OMDEV (NIL) -8 NIL NIL) (-753 1883191 1883362 1883556 "OMCONN" 1883948 T OMCONN (NIL) -8 NIL NIL) (-752 1881806 1882792 1882821 "OINTDOM" 1882826 T OINTDOM (NIL) -9 NIL 1882847) (-751 1877568 1878798 1879513 "OFMONOID" 1881123 NIL OFMONOID (NIL T) -8 NIL NIL) (-750 1877006 1877505 1877550 "ODVAR" 1877555 NIL ODVAR (NIL T) -8 NIL NIL) (-749 1874131 1876503 1876688 "ODR" 1876881 NIL ODR (NIL T T NIL) -8 NIL NIL) (-748 1866437 1873910 1874034 "ODPOL" 1874039 NIL ODPOL (NIL T) -8 NIL NIL) (-747 1860260 1866309 1866414 "ODP" 1866419 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-746 1859026 1859241 1859516 "ODETOOLS" 1860034 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-745 1855995 1856651 1857367 "ODESYS" 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(NIL T T T) -7 NIL NIL) (-732 1820029 1820662 1820691 "ODECAT" 1821294 T ODECAT (NIL) -9 NIL 1821823) (-731 1816901 1819741 1819860 "OCT" 1819942 NIL OCT (NIL T) -8 NIL NIL) (-730 1816539 1816582 1816709 "OCTCT2" 1816852 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-729 1811372 1813810 1813851 "OC" 1814947 NIL OC (NIL T) -9 NIL 1815804) (-728 1808599 1809347 1810337 "OC-" 1810431 NIL OC- (NIL T T) -8 NIL NIL) (-727 1807977 1808419 1808448 "OCAMON" 1808453 T OCAMON (NIL) -9 NIL 1808474) (-726 1807430 1807837 1807866 "OASGP" 1807871 T OASGP (NIL) -9 NIL 1807891) (-725 1806717 1807180 1807209 "OAMONS" 1807249 T OAMONS (NIL) -9 NIL 1807292) (-724 1806157 1806564 1806593 "OAMON" 1806598 T OAMON (NIL) -9 NIL 1806618) (-723 1805461 1805953 1805982 "OAGROUP" 1805987 T OAGROUP (NIL) -9 NIL 1806007) (-722 1805151 1805201 1805289 "NUMTUBE" 1805405 NIL NUMTUBE (NIL T) -7 NIL NIL) (-721 1798724 1800242 1801778 "NUMQUAD" 1803635 T NUMQUAD (NIL) -7 NIL NIL) (-720 1794480 1795468 1796493 "NUMODE" 1797719 T NUMODE (NIL) -7 NIL NIL) (-719 1791883 1792729 1792758 "NUMINT" 1793675 T NUMINT (NIL) -9 NIL 1794431) (-718 1790831 1791028 1791246 "NUMFMT" 1791685 T NUMFMT (NIL) -7 NIL NIL) (-717 1777213 1780147 1782677 "NUMERIC" 1788340 NIL NUMERIC (NIL T) -7 NIL NIL) (-716 1771613 1776665 1776760 "NTSCAT" 1776765 NIL NTSCAT (NIL T T T T) -9 NIL 1776803) (-715 1770807 1770972 1771165 "NTPOLFN" 1771452 NIL NTPOLFN (NIL T) -7 NIL NIL) (-714 1758663 1767649 1768459 "NSUP" 1770029 NIL NSUP (NIL T) -8 NIL NIL) (-713 1758299 1758356 1758463 "NSUP2" 1758600 NIL NSUP2 (NIL T T) -7 NIL NIL) (-712 1748261 1758078 1758208 "NSMP" 1758213 NIL NSMP (NIL T T) -8 NIL NIL) (-711 1746693 1746994 1747351 "NREP" 1747949 NIL NREP (NIL T) -7 NIL NIL) (-710 1745284 1745536 1745894 "NPCOEF" 1746436 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-709 1744350 1744465 1744681 "NORMRETR" 1745165 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-708 1742403 1742693 1743100 "NORMPK" 1744058 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-707 1742088 1742116 1742240 "NORMMA" 1742369 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-706 1741915 1742045 1742074 "NONE" 1742079 T NONE (NIL) -8 NIL NIL) (-705 1741704 1741733 1741802 "NONE1" 1741879 NIL NONE1 (NIL T) -7 NIL NIL) (-704 1741189 1741251 1741436 "NODE1" 1741636 NIL NODE1 (NIL T T) -7 NIL NIL) (-703 1739482 1740352 1740607 "NNI" 1740954 T NNI (NIL) -8 NIL NIL) (-702 1737902 1738215 1738579 "NLINSOL" 1739150 NIL NLINSOL (NIL T) -7 NIL NIL) (-701 1734070 1735037 1735959 "NIPROB" 1737000 T NIPROB (NIL) -8 NIL NIL) (-700 1732827 1733061 1733363 "NFINTBAS" 1733832 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-699 1731535 1731766 1732047 "NCODIV" 1732595 NIL NCODIV (NIL T T) -7 NIL NIL) (-698 1731297 1731334 1731409 "NCNTFRAC" 1731492 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-697 1729477 1729841 1730261 "NCEP" 1730922 NIL NCEP (NIL T) -7 NIL NIL) (-696 1728388 1729127 1729156 "NASRING" 1729266 T NASRING (NIL) -9 NIL 1729340) (-695 1728183 1728227 1728321 "NASRING-" 1728326 NIL NASRING- (NIL T) -8 NIL 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"NAGD01" 1667852 T NAGD01 (NIL) -7 NIL NIL) (-680 1659376 1660186 1661011 "NAGC06" 1662314 T NAGC06 (NIL) -7 NIL NIL) (-679 1657853 1658182 1658535 "NAGC05" 1659043 T NAGC05 (NIL) -7 NIL NIL) (-678 1657237 1657354 1657496 "NAGC02" 1657731 T NAGC02 (NIL) -7 NIL NIL) (-677 1656298 1656855 1656896 "NAALG" 1656975 NIL NAALG (NIL T) -9 NIL 1657036) (-676 1656133 1656162 1656252 "NAALG-" 1656257 NIL NAALG- (NIL T T) -8 NIL NIL) (-675 1650083 1651191 1652378 "MULTSQFR" 1655029 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-674 1649402 1649477 1649661 "MULTFACT" 1649995 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-673 1642595 1646506 1646559 "MTSCAT" 1647619 NIL MTSCAT (NIL T T) -9 NIL 1648133) (-672 1642307 1642361 1642453 "MTHING" 1642535 NIL MTHING (NIL T) -7 NIL NIL) (-671 1642099 1642132 1642192 "MSYSCMD" 1642267 T MSYSCMD (NIL) -7 NIL NIL) (-670 1638211 1640854 1641174 "MSET" 1641812 NIL MSET (NIL T) -8 NIL NIL) (-669 1635306 1637772 1637814 "MSETAGG" 1637819 NIL MSETAGG (NIL T) -9 NIL 1637853) (-668 1631162 1632704 1633445 "MRING" 1634609 NIL MRING (NIL T T) -8 NIL NIL) (-667 1630732 1630799 1630928 "MRF2" 1631089 NIL MRF2 (NIL T T T) -7 NIL NIL) (-666 1630350 1630385 1630529 "MRATFAC" 1630691 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-665 1627962 1628257 1628688 "MPRFF" 1630055 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-664 1621982 1627817 1627913 "MPOLY" 1627918 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-663 1621472 1621507 1621715 "MPCPF" 1621941 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-662 1620988 1621031 1621214 "MPC3" 1621423 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-661 1620189 1620270 1620489 "MPC2" 1620903 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-660 1618490 1618827 1619217 "MONOTOOL" 1619849 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-659 1617614 1617949 1617978 "MONOID" 1618255 T MONOID (NIL) -9 NIL 1618427) (-658 1616992 1617155 1617398 "MONOID-" 1617403 NIL MONOID- (NIL T) -8 NIL NIL) (-657 1607972 1613958 1614018 "MONOGEN" 1614692 NIL MONOGEN (NIL T T) -9 NIL 1615148) (-656 1605190 1605925 1606925 "MONOGEN-" 1607044 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-655 1604049 1604469 1604498 "MONADWU" 1604890 T MONADWU (NIL) -9 NIL 1605128) (-654 1603421 1603580 1603828 "MONADWU-" 1603833 NIL MONADWU- (NIL T) -8 NIL NIL) (-653 1602806 1603024 1603053 "MONAD" 1603260 T MONAD (NIL) -9 NIL 1603372) (-652 1602491 1602569 1602701 "MONAD-" 1602706 NIL MONAD- (NIL T) -8 NIL NIL) (-651 1600742 1601404 1601683 "MOEBIUS" 1602244 NIL MOEBIUS (NIL T) -8 NIL NIL) (-650 1600135 1600513 1600554 "MODULE" 1600559 NIL MODULE (NIL T) -9 NIL 1600585) (-649 1599703 1599799 1599989 "MODULE-" 1599994 NIL MODULE- (NIL T T) -8 NIL NIL) (-648 1597374 1598069 1598395 "MODRING" 1599528 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1594330 1595495 1596012 "MODOP" 1596906 NIL MODOP (NIL T T) -8 NIL NIL) (-646 1592517 1592969 1593310 "MODMONOM" 1594129 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-645 1582235 1590721 1591143 "MODMON" 1592145 NIL MODMON (NIL T T) -8 NIL NIL) (-644 1579361 1581079 1581355 "MODFIELD" 1582110 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-643 1578887 1578930 1579109 "MMAP" 1579312 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-642 1577123 1577900 1577941 "MLO" 1578358 NIL MLO (NIL T) -9 NIL 1578599) (-641 1574490 1575005 1575607 "MLIFT" 1576604 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-640 1573881 1573965 1574119 "MKUCFUNC" 1574401 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-639 1573480 1573550 1573673 "MKRECORD" 1573804 NIL MKRECORD (NIL T T) -7 NIL NIL) (-638 1572528 1572689 1572917 "MKFUNC" 1573291 NIL MKFUNC (NIL T) -7 NIL NIL) (-637 1571916 1572020 1572176 "MKFLCFN" 1572411 NIL MKFLCFN (NIL T) -7 NIL NIL) (-636 1571342 1571709 1571798 "MKCHSET" 1571860 NIL MKCHSET (NIL T) -8 NIL NIL) (-635 1570619 1570721 1570906 "MKBCFUNC" 1571235 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-634 1567303 1570173 1570309 "MINT" 1570503 T MINT (NIL) -8 NIL NIL) (-633 1566115 1566358 1566635 "MHROWRED" 1567058 NIL MHROWRED (NIL T) -7 NIL NIL) (-632 1561386 1564560 1564984 "MFLOAT" 1565711 T MFLOAT (NIL) -8 NIL NIL) (-631 1560743 1560819 1560990 "MFINFACT" 1561298 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-630 1557058 1557906 1558790 "MESH" 1559879 T MESH (NIL) -7 NIL NIL) (-629 1555448 1555760 1556113 "MDDFACT" 1556745 NIL MDDFACT (NIL T) -7 NIL NIL) (-628 1552290 1554607 1554649 "MDAGG" 1554904 NIL MDAGG (NIL T) -9 NIL 1555047) (-627 1541988 1551583 1551790 "MCMPLX" 1552103 T MCMPLX (NIL) -8 NIL NIL) (-626 1541129 1541275 1541475 "MCDEN" 1541837 NIL MCDEN (NIL T T) -7 NIL NIL) (-625 1539019 1539289 1539669 "MCALCFN" 1540859 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-624 1536641 1537164 1537725 "MATSTOR" 1538490 NIL MATSTOR (NIL T) -7 NIL NIL) (-623 1532649 1536016 1536263 "MATRIX" 1536426 NIL MATRIX (NIL T) -8 NIL NIL) (-622 1528419 1529122 1529858 "MATLIN" 1532006 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-621 1518616 1521754 1521831 "MATCAT" 1526669 NIL MATCAT (NIL T T T) -9 NIL 1528086) (-620 1514981 1515994 1517349 "MATCAT-" 1517354 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-619 1513583 1513736 1514067 "MATCAT2" 1514816 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1511695 1512019 1512403 "MAPPKG3" 1513258 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-617 1510676 1510849 1511071 "MAPPKG2" 1511519 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-616 1509175 1509459 1509786 "MAPPKG1" 1510382 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-615 1508786 1508844 1508967 "MAPHACK3" 1509111 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-614 1508378 1508439 1508553 "MAPHACK2" 1508718 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-613 1507816 1507919 1508061 "MAPHACK1" 1508269 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-612 1505924 1506518 1506821 "MAGMA" 1507545 NIL MAGMA (NIL T) -8 NIL NIL) (-611 1502398 1504168 1504628 "M3D" 1505497 NIL M3D (NIL T) -8 NIL NIL) (-610 1496553 1500768 1500810 "LZSTAGG" 1501592 NIL LZSTAGG (NIL T) -9 NIL 1501887) (-609 1492526 1493684 1495141 "LZSTAGG-" 1495146 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-608 1489642 1490419 1490905 "LWORD" 1492072 NIL LWORD (NIL T) -8 NIL NIL) (-607 1482802 1489413 1489547 "LSQM" 1489552 NIL LSQM (NIL NIL T) -8 NIL NIL) (-606 1482026 1482165 1482393 "LSPP" 1482657 NIL LSPP (NIL T T T T) -7 NIL NIL) (-605 1479838 1480139 1480595 "LSMP" 1481715 NIL LSMP (NIL T T T T) -7 NIL NIL) (-604 1476617 1477291 1478021 "LSMP1" 1479140 NIL LSMP1 (NIL T) -7 NIL NIL) (-603 1470543 1475785 1475827 "LSAGG" 1475889 NIL LSAGG (NIL T) -9 NIL 1475967) (-602 1467238 1468162 1469375 "LSAGG-" 1469380 NIL LSAGG- (NIL T T) -8 NIL NIL) (-601 1464864 1466382 1466631 "LPOLY" 1467033 NIL LPOLY (NIL T T) -8 NIL NIL) (-600 1464446 1464531 1464654 "LPEFRAC" 1464773 NIL LPEFRAC (NIL T) -7 NIL NIL) (-599 1462793 1463540 1463793 "LO" 1464278 NIL LO (NIL T T T) -8 NIL NIL) (-598 1462446 1462558 1462587 "LOGIC" 1462698 T LOGIC (NIL) -9 NIL 1462778) (-597 1462308 1462331 1462402 "LOGIC-" 1462407 NIL LOGIC- (NIL T) -8 NIL NIL) (-596 1461501 1461641 1461834 "LODOOPS" 1462164 NIL LODOOPS (NIL T T) -7 NIL NIL) (-595 1458919 1461418 1461483 "LODO" 1461488 NIL LODO (NIL T NIL) -8 NIL NIL) (-594 1457465 1457700 1458051 "LODOF" 1458666 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1453884 1456320 1456361 "LODOCAT" 1456793 NIL LODOCAT (NIL T) -9 NIL 1457004) (-592 1453618 1453676 1453802 "LODOCAT-" 1453807 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1450932 1453459 1453577 "LODO2" 1453582 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1448361 1450869 1450914 "LODO1" 1450919 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1447224 1447389 1447700 "LODEEF" 1448184 NIL LODEEF (NIL T T T) -7 NIL NIL) (-588 1442510 1445354 1445396 "LNAGG" 1446343 NIL LNAGG (NIL T) -9 NIL 1446787) (-587 1441657 1441871 1442213 "LNAGG-" 1442218 NIL LNAGG- (NIL T T) -8 NIL NIL) (-586 1437822 1438584 1439222 "LMOPS" 1441073 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-585 1437219 1437581 1437622 "LMODULE" 1437682 NIL LMODULE (NIL T) -9 NIL 1437724) (-584 1434465 1436864 1436987 "LMDICT" 1437129 NIL LMDICT (NIL T) -8 NIL NIL) (-583 1427692 1433411 1433709 "LIST" 1434200 NIL LIST (NIL T) -8 NIL NIL) (-582 1427217 1427291 1427430 "LIST3" 1427612 NIL LIST3 (NIL T T T) -7 NIL NIL) (-581 1426224 1426402 1426630 "LIST2" 1427035 NIL LIST2 (NIL T T) -7 NIL NIL) (-580 1424358 1424670 1425069 "LIST2MAP" 1425871 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1423070 1423750 1423791 "LINEXP" 1424044 NIL LINEXP (NIL T) -9 NIL 1424192) (-578 1421717 1421977 1422274 "LINDEP" 1422822 NIL LINDEP (NIL T T) -7 NIL NIL) (-577 1418484 1419203 1419980 "LIMITRF" 1420972 NIL LIMITRF (NIL T) -7 NIL NIL) (-576 1416764 1417059 1417474 "LIMITPS" 1418179 NIL LIMITPS (NIL T T) -7 NIL NIL) (-575 1411219 1416275 1416503 "LIE" 1416585 NIL LIE (NIL T T) -8 NIL NIL) (-574 1410269 1410712 1410753 "LIECAT" 1410893 NIL LIECAT (NIL T) -9 NIL 1411044) (-573 1410110 1410137 1410225 "LIECAT-" 1410230 NIL LIECAT- (NIL T T) -8 NIL NIL) (-572 1402722 1409559 1409724 "LIB" 1409965 T LIB (NIL) -8 NIL NIL) (-571 1398359 1399240 1400175 "LGROBP" 1401839 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-570 1396229 1396502 1396863 "LF" 1398081 NIL LF (NIL T T) -7 NIL NIL) (-569 1395069 1395760 1395789 "LFCAT" 1395996 T LFCAT (NIL) -9 NIL 1396135) (-568 1391981 1392607 1393293 "LEXTRIPK" 1394435 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-567 1388687 1389551 1390054 "LEXP" 1391561 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-566 1387085 1387398 1387799 "LEADCDET" 1388369 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-565 1386281 1386355 1386582 "LAZM3PK" 1387006 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-564 1381197 1384360 1384897 "LAUPOL" 1385794 NIL LAUPOL (NIL T T) -8 NIL NIL) (-563 1380764 1380808 1380975 "LAPLACE" 1381147 NIL LAPLACE (NIL T T) -7 NIL NIL) (-562 1378692 1379865 1380116 "LA" 1380597 NIL LA (NIL T T T) -8 NIL NIL) (-561 1377754 1378348 1378389 "LALG" 1378450 NIL LALG (NIL T) -9 NIL 1378508) (-560 1377469 1377528 1377663 "LALG-" 1377668 NIL LALG- (NIL T T) -8 NIL NIL) (-559 1376379 1376566 1376863 "KOVACIC" 1377269 NIL KOVACIC (NIL T T) -7 NIL NIL) (-558 1376213 1376237 1376279 "KONVERT" 1376341 NIL KONVERT (NIL T) -9 NIL NIL) (-557 1376047 1376071 1376113 "KOERCE" 1376175 NIL KOERCE (NIL T) -9 NIL NIL) (-556 1373781 1374541 1374934 "KERNEL" 1375686 NIL KERNEL (NIL T) -8 NIL NIL) (-555 1373283 1373364 1373494 "KERNEL2" 1373695 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-554 1367134 1371822 1371877 "KDAGG" 1372254 NIL KDAGG (NIL T T) -9 NIL 1372460) (-553 1366663 1366787 1366992 "KDAGG-" 1366997 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-552 1359838 1366324 1366479 "KAFILE" 1366541 NIL KAFILE (NIL T) -8 NIL NIL) (-551 1354293 1359349 1359577 "JORDAN" 1359659 NIL JORDAN (NIL T T) -8 NIL NIL) (-550 1350592 1352498 1352553 "IXAGG" 1353482 NIL IXAGG (NIL T T) -9 NIL 1353941) (-549 1349511 1349817 1350236 "IXAGG-" 1350241 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-548 1345096 1349433 1349492 "IVECTOR" 1349497 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-547 1343862 1344099 1344365 "ITUPLE" 1344863 NIL ITUPLE (NIL T) -8 NIL NIL) (-546 1342298 1342475 1342781 "ITRIGMNP" 1343684 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-545 1341043 1341247 1341530 "ITFUN3" 1342074 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-544 1340675 1340732 1340841 "ITFUN2" 1340980 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-543 1338477 1339548 1339845 "ITAYLOR" 1340410 NIL ITAYLOR (NIL T) -8 NIL NIL) (-542 1327468 1332663 1333822 "ISUPS" 1337350 NIL ISUPS (NIL T) -8 NIL NIL) (-541 1326572 1326712 1326948 "ISUMP" 1327315 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-540 1321836 1326373 1326452 "ISTRING" 1326525 NIL ISTRING (NIL NIL) -8 NIL NIL) (-539 1321049 1321130 1321345 "IRURPK" 1321750 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-538 1319985 1320186 1320426 "IRSN" 1320829 T IRSN (NIL) -7 NIL NIL) (-537 1318020 1318375 1318810 "IRRF2F" 1319623 NIL IRRF2F (NIL T) -7 NIL NIL) (-536 1317767 1317805 1317881 "IRREDFFX" 1317976 NIL IRREDFFX (NIL T) -7 NIL NIL) (-535 1316382 1316641 1316940 "IROOT" 1317500 NIL IROOT (NIL T) -7 NIL NIL) (-534 1313020 1314071 1314761 "IR" 1315724 NIL IR (NIL T) -8 NIL NIL) (-533 1310633 1311128 1311694 "IR2" 1312498 NIL IR2 (NIL T T) -7 NIL NIL) (-532 1309709 1309822 1310042 "IR2F" 1310516 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1309500 1309534 1309594 "IPRNTPK" 1309669 T IPRNTPK (NIL) -7 NIL NIL) (-530 1306054 1309389 1309458 "IPF" 1309463 NIL IPF (NIL NIL) -8 NIL NIL) (-529 1304371 1305979 1306036 "IPADIC" 1306041 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-528 1303870 1303928 1304117 "INVLAPLA" 1304307 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-527 1293519 1295872 1298258 "INTTR" 1301534 NIL INTTR (NIL T T) -7 NIL NIL) (-526 1289867 1290608 1291471 "INTTOOLS" 1292705 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-525 1289453 1289544 1289661 "INTSLPE" 1289770 T INTSLPE (NIL) -7 NIL NIL) (-524 1287403 1289376 1289435 "INTRVL" 1289440 NIL INTRVL (NIL T) -8 NIL NIL) (-523 1285010 1285522 1286096 "INTRF" 1286888 NIL INTRF (NIL T) -7 NIL NIL) (-522 1284425 1284522 1284663 "INTRET" 1284908 NIL INTRET (NIL T) -7 NIL NIL) (-521 1282427 1282816 1283285 "INTRAT" 1284033 NIL INTRAT (NIL T T) -7 NIL NIL) (-520 1279660 1280243 1280868 "INTPM" 1281912 NIL INTPM (NIL T T) -7 NIL NIL) (-519 1276369 1276968 1277712 "INTPAF" 1279046 NIL INTPAF (NIL T T T) -7 NIL NIL) (-518 1271620 1272564 1273597 "INTPACK" 1275356 T INTPACK (NIL) -7 NIL NIL) (-517 1268474 1271349 1271476 "INT" 1271513 T INT (NIL) -8 NIL NIL) (-516 1267726 1267878 1268086 "INTHERTR" 1268316 NIL INTHERTR (NIL T T) -7 NIL NIL) (-515 1267165 1267245 1267433 "INTHERAL" 1267640 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-514 1265011 1265454 1265911 "INTHEORY" 1266728 T INTHEORY (NIL) -7 NIL NIL) (-513 1256334 1257954 1259732 "INTG0" 1263363 NIL INTG0 (NIL T T T) -7 NIL NIL) (-512 1236907 1241697 1246507 "INTFTBL" 1251544 T INTFTBL (NIL) -8 NIL NIL) (-511 1236156 1236294 1236467 "INTFACT" 1236766 NIL INTFACT (NIL T) -7 NIL NIL) (-510 1233547 1233993 1234556 "INTEF" 1235710 NIL INTEF (NIL T T) -7 NIL NIL) (-509 1232008 1232757 1232786 "INTDOM" 1233087 T INTDOM (NIL) -9 NIL 1233294) (-508 1231377 1231551 1231793 "INTDOM-" 1231798 NIL INTDOM- (NIL T) -8 NIL NIL) (-507 1227869 1229801 1229856 "INTCAT" 1230655 NIL INTCAT (NIL T) -9 NIL 1230974) (-506 1227342 1227444 1227572 "INTBIT" 1227761 T INTBIT (NIL) -7 NIL NIL) (-505 1226017 1226171 1226484 "INTALG" 1227187 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-504 1225474 1225564 1225734 "INTAF" 1225921 NIL INTAF (NIL T T) -7 NIL NIL) (-503 1218928 1225284 1225424 "INTABL" 1225429 NIL INTABL (NIL T T T) -8 NIL NIL) (-502 1213878 1216607 1216636 "INS" 1217604 T INS (NIL) -9 NIL 1218285) (-501 1211118 1211889 1212863 "INS-" 1212936 NIL INS- (NIL T) -8 NIL NIL) (-500 1209897 1210124 1210421 "INPSIGN" 1210871 NIL INPSIGN (NIL T T) -7 NIL NIL) (-499 1209015 1209132 1209329 "INPRODPF" 1209777 NIL INPRODPF (NIL T T) -7 NIL NIL) (-498 1207909 1208026 1208263 "INPRODFF" 1208895 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-497 1206909 1207061 1207321 "INNMFACT" 1207745 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-496 1206106 1206203 1206391 "INMODGCD" 1206808 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-495 1204615 1204859 1205183 "INFSP" 1205851 NIL INFSP (NIL T T T) -7 NIL NIL) (-494 1203799 1203916 1204099 "INFPROD0" 1204495 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-493 1200809 1201968 1202459 "INFORM" 1203316 T INFORM (NIL) -8 NIL NIL) (-492 1200419 1200479 1200577 "INFORM1" 1200744 NIL INFORM1 (NIL T) -7 NIL NIL) (-491 1199942 1200031 1200145 "INFINITY" 1200325 T INFINITY (NIL) -7 NIL NIL) (-490 1198560 1198808 1199129 "INEP" 1199690 NIL INEP (NIL T T T) -7 NIL NIL) (-489 1197836 1198457 1198522 "INDE" 1198527 NIL INDE (NIL T) -8 NIL NIL) (-488 1197400 1197468 1197585 "INCRMAPS" 1197763 NIL INCRMAPS (NIL T) -7 NIL NIL) (-487 1192711 1193636 1194580 "INBFF" 1196488 NIL INBFF (NIL T) -7 NIL NIL) (-486 1189206 1192556 1192659 "IMATRIX" 1192664 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-485 1187918 1188041 1188356 "IMATQF" 1189062 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-484 1186138 1186365 1186702 "IMATLIN" 1187674 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-483 1180764 1186062 1186120 "ILIST" 1186125 NIL ILIST (NIL T NIL) -8 NIL NIL) (-482 1178717 1180624 1180737 "IIARRAY2" 1180742 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-481 1174085 1178628 1178692 "IFF" 1178697 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-480 1169128 1173377 1173565 "IFARRAY" 1173942 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-479 1168335 1169032 1169105 "IFAMON" 1169110 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-478 1167918 1167983 1168038 "IEVALAB" 1168245 NIL IEVALAB (NIL T T) -9 NIL NIL) (-477 1167593 1167661 1167821 "IEVALAB-" 1167826 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-476 1167251 1167507 1167570 "IDPO" 1167575 NIL IDPO (NIL T T) -8 NIL NIL) (-475 1166528 1167140 1167215 "IDPOAMS" 1167220 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-474 1165862 1166417 1166492 "IDPOAM" 1166497 NIL IDPOAM (NIL T T) -8 NIL NIL) (-473 1164947 1165197 1165251 "IDPC" 1165664 NIL IDPC (NIL T T) -9 NIL 1165813) (-472 1164443 1164839 1164912 "IDPAM" 1164917 NIL IDPAM (NIL T T) -8 NIL NIL) (-471 1163846 1164335 1164408 "IDPAG" 1164413 NIL IDPAG (NIL T T) -8 NIL NIL) (-470 1160101 1160949 1161844 "IDECOMP" 1163003 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-469 1152975 1154024 1155071 "IDEAL" 1159137 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-468 1152139 1152251 1152450 "ICDEN" 1152859 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-467 1151238 1151619 1151766 "ICARD" 1152012 T ICARD (NIL) -8 NIL NIL) (-466 1149310 1149623 1150026 "IBPTOOLS" 1150915 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-465 1144924 1148930 1149043 "IBITS" 1149229 NIL IBITS (NIL NIL) -8 NIL NIL) (-464 1141647 1142223 1142918 "IBATOOL" 1144341 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-463 1139427 1139888 1140421 "IBACHIN" 1141182 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-462 1137304 1139273 1139376 "IARRAY2" 1139381 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-461 1133457 1137230 1137287 "IARRAY1" 1137292 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-460 1127396 1131875 1132353 "IAN" 1132999 T IAN (NIL) -8 NIL NIL) (-459 1126907 1126964 1127137 "IALGFACT" 1127333 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-458 1126434 1126547 1126576 "HYPCAT" 1126783 T HYPCAT (NIL) -9 NIL NIL) (-457 1125972 1126089 1126275 "HYPCAT-" 1126280 NIL HYPCAT- (NIL T) -8 NIL NIL) (-456 1122651 1123982 1124024 "HOAGG" 1125005 NIL HOAGG (NIL T) -9 NIL 1125684) (-455 1121245 1121644 1122170 "HOAGG-" 1122175 NIL HOAGG- (NIL T T) -8 NIL NIL) (-454 1115076 1120686 1120852 "HEXADEC" 1121099 T HEXADEC (NIL) -8 NIL NIL) (-453 1113824 1114046 1114309 "HEUGCD" 1114853 NIL HEUGCD (NIL T) -7 NIL NIL) (-452 1112927 1113661 1113791 "HELLFDIV" 1113796 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-451 1111155 1112704 1112792 "HEAP" 1112871 NIL HEAP (NIL T) -8 NIL NIL) (-450 1105022 1111070 1111132 "HDP" 1111137 NIL HDP (NIL NIL T) -8 NIL NIL) (-449 1098734 1104659 1104810 "HDMP" 1104923 NIL HDMP (NIL NIL T) -8 NIL NIL) (-448 1098059 1098198 1098362 "HB" 1098590 T HB (NIL) -7 NIL NIL) (-447 1091556 1097905 1098009 "HASHTBL" 1098014 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-446 1089309 1091184 1091363 "HACKPI" 1091397 T HACKPI (NIL) -8 NIL NIL) (-445 1085005 1089163 1089275 "GTSET" 1089280 NIL GTSET (NIL T T T T) -8 NIL NIL) (-444 1078531 1084883 1084981 "GSTBL" 1084986 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-443 1070767 1077567 1077831 "GSERIES" 1078322 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-442 1069789 1070242 1070271 "GROUP" 1070532 T GROUP (NIL) -9 NIL 1070691) (-441 1068905 1069128 1069472 "GROUP-" 1069477 NIL GROUP- (NIL T) -8 NIL NIL) (-440 1067274 1067593 1067980 "GROEBSOL" 1068582 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-439 1066214 1066476 1066528 "GRMOD" 1067057 NIL GRMOD (NIL T T) -9 NIL 1067225) (-438 1065982 1066018 1066146 "GRMOD-" 1066151 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-437 1061310 1062336 1063336 "GRIMAGE" 1065002 T GRIMAGE (NIL) -8 NIL NIL) (-436 1059777 1060037 1060361 "GRDEF" 1061006 T GRDEF (NIL) -7 NIL NIL) (-435 1059221 1059337 1059478 "GRAY" 1059656 T GRAY (NIL) -7 NIL NIL) (-434 1058454 1058834 1058886 "GRALG" 1059039 NIL GRALG (NIL T T) -9 NIL 1059131) (-433 1058115 1058188 1058351 "GRALG-" 1058356 NIL GRALG- (NIL T T T) -8 NIL NIL) (-432 1054923 1057704 1057880 "GPOLSET" 1058022 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-431 1054279 1054336 1054593 "GOSPER" 1054860 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-430 1050038 1050717 1051243 "GMODPOL" 1053978 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-429 1049043 1049227 1049465 "GHENSEL" 1049850 NIL GHENSEL (NIL T T) -7 NIL NIL) (-428 1043109 1043952 1044978 "GENUPS" 1048127 NIL GENUPS (NIL T T) -7 NIL NIL) (-427 1042806 1042857 1042946 "GENUFACT" 1043052 NIL GENUFACT (NIL T) -7 NIL NIL) (-426 1042218 1042295 1042460 "GENPGCD" 1042724 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-425 1041692 1041727 1041940 "GENMFACT" 1042177 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-424 1040260 1040515 1040822 "GENEEZ" 1041435 NIL GENEEZ (NIL T T) -7 NIL NIL) (-423 1034134 1039873 1040034 "GDMP" 1040183 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-422 1023516 1027905 1029011 "GCNAALG" 1033117 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-421 1021937 1022809 1022838 "GCDDOM" 1023093 T GCDDOM (NIL) -9 NIL 1023250) (-420 1021407 1021534 1021749 "GCDDOM-" 1021754 NIL GCDDOM- (NIL T) -8 NIL NIL) (-419 1020079 1020264 1020568 "GB" 1021186 NIL GB (NIL T T T T) -7 NIL NIL) (-418 1008699 1011025 1013417 "GBINTERN" 1017770 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-417 1006536 1006828 1007249 "GBF" 1008374 NIL GBF (NIL T T T T) -7 NIL NIL) (-416 1005317 1005482 1005749 "GBEUCLID" 1006352 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-415 1004666 1004791 1004940 "GAUSSFAC" 1005188 T GAUSSFAC (NIL) -7 NIL NIL) (-414 1003043 1003345 1003658 "GALUTIL" 1004385 NIL GALUTIL (NIL T) -7 NIL NIL) (-413 1001360 1001634 1001957 "GALPOLYU" 1002770 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-412 998749 999039 999444 "GALFACTU" 1001057 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-411 990555 992054 993662 "GALFACT" 997181 NIL GALFACT (NIL T) -7 NIL NIL) (-410 987942 988600 988629 "FVFUN" 989785 T FVFUN (NIL) -9 NIL 990505) (-409 987207 987389 987418 "FVC" 987709 T FVC (NIL) -9 NIL 987892) (-408 986849 987004 987085 "FUNCTION" 987159 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-407 984519 985070 985559 "FT" 986380 T FT (NIL) -8 NIL NIL) (-406 983337 983820 984023 "FTEM" 984336 T FTEM (NIL) -8 NIL NIL) (-405 981602 981890 982292 "FSUPFACT" 983029 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-404 979999 980288 980620 "FST" 981290 T FST (NIL) -8 NIL NIL) (-403 979174 979280 979474 "FSRED" 979881 NIL FSRED (NIL T T) -7 NIL NIL) (-402 977853 978108 978462 "FSPRMELT" 978889 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-401 974938 975376 975875 "FSPECF" 977416 NIL FSPECF (NIL T T) -7 NIL NIL) (-400 957311 965868 965909 "FS" 969747 NIL FS (NIL T) -9 NIL 972029) (-399 945961 948951 953007 "FS-" 953304 NIL FS- (NIL T T) -8 NIL NIL) (-398 945477 945531 945707 "FSINT" 945902 NIL FSINT (NIL T T) -7 NIL NIL) (-397 943758 944470 944773 "FSERIES" 945256 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 942776 942892 943122 "FSCINT" 943638 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 939010 941720 941762 "FSAGG" 942132 NIL FSAGG (NIL T) -9 NIL 942391) (-394 936772 937373 938169 "FSAGG-" 938264 NIL FSAGG- (NIL T T) -8 NIL NIL) (-393 935814 935957 936184 "FSAGG2" 936625 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-392 933473 933752 934305 "FS2UPS" 935532 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 933059 933102 933255 "FS2" 933424 NIL FS2 (NIL T T T T) -7 NIL NIL) (-390 931919 932090 932398 "FS2EXPXP" 932884 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-389 931345 931460 931612 "FRUTIL" 931799 NIL FRUTIL (NIL T) -7 NIL NIL) (-388 922766 926844 928200 "FR" 930021 NIL FR (NIL T) -8 NIL NIL) (-387 917842 920485 920526 "FRNAALG" 921922 NIL FRNAALG (NIL T) -9 NIL 922529) (-386 913521 914591 915866 "FRNAALG-" 916616 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-385 913159 913202 913329 "FRNAAF2" 913472 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-384 911524 912016 912310 "FRMOD" 912972 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-383 909247 909915 910231 "FRIDEAL" 911315 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-382 908446 908533 908820 "FRIDEAL2" 909154 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 907703 908111 908153 "FRETRCT" 908158 NIL FRETRCT (NIL T) -9 NIL 908329) (-380 906815 907046 907397 "FRETRCT-" 907402 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-379 904024 905244 905304 "FRAMALG" 906186 NIL FRAMALG (NIL T T) -9 NIL 906478) (-378 902157 902613 903243 "FRAMALG-" 903466 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-377 896059 901632 901908 "FRAC" 901913 NIL FRAC (NIL T) -8 NIL NIL) (-376 895695 895752 895859 "FRAC2" 895996 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 895331 895388 895495 "FR2" 895632 NIL FR2 (NIL T T) -7 NIL NIL) (-374 890004 892917 892946 "FPS" 894065 T FPS (NIL) -9 NIL 894621) (-373 889453 889562 889726 "FPS-" 889872 NIL FPS- (NIL T) -8 NIL NIL) (-372 886901 888598 888627 "FPC" 888852 T FPC (NIL) -9 NIL 888994) (-371 886694 886734 886831 "FPC-" 886836 NIL FPC- (NIL T) -8 NIL NIL) (-370 885572 886182 886224 "FPATMAB" 886229 NIL FPATMAB (NIL T) -9 NIL 886381) (-369 883272 883748 884174 "FPARFRAC" 885209 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-368 878667 879164 879846 "FORTRAN" 882704 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-367 876383 876883 877422 "FORT" 878148 T FORT (NIL) -7 NIL NIL) (-366 874058 874620 874649 "FORTFN" 875709 T FORTFN (NIL) -9 NIL 876333) (-365 873821 873871 873900 "FORTCAT" 873959 T FORTCAT (NIL) -9 NIL 874021) (-364 871881 872364 872763 "FORMULA" 873442 T FORMULA (NIL) -8 NIL NIL) (-363 871669 871699 871768 "FORMULA1" 871845 NIL FORMULA1 (NIL T) -7 NIL NIL) (-362 871192 871244 871417 "FORDER" 871611 NIL FORDER (NIL T T T T) -7 NIL NIL) (-361 870288 870452 870645 "FOP" 871019 T FOP (NIL) -7 NIL NIL) (-360 868896 869568 869742 "FNLA" 870170 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-359 867564 867953 867982 "FNCAT" 868554 T FNCAT (NIL) -9 NIL 868847) (-358 867130 867523 867551 "FNAME" 867556 T FNAME (NIL) -8 NIL NIL) (-357 865789 866762 866791 "FMTC" 866796 T FMTC (NIL) -9 NIL 866831) (-356 862107 863314 863942 "FMONOID" 865194 NIL FMONOID (NIL T) -8 NIL NIL) (-355 861327 861850 861998 "FM" 862003 NIL FM (NIL T T) -8 NIL NIL) (-354 858750 859396 859425 "FMFUN" 860569 T FMFUN (NIL) -9 NIL 861277) (-353 858018 858199 858228 "FMC" 858518 T FMC (NIL) -9 NIL 858700) (-352 855247 856081 856135 "FMCAT" 857317 NIL FMCAT (NIL T T) -9 NIL 857811) (-351 854142 855015 855114 "FM1" 855192 NIL FM1 (NIL T T) -8 NIL NIL) (-350 851916 852332 852826 "FLOATRP" 853693 NIL FLOATRP (NIL T) -7 NIL NIL) (-349 845402 849572 850202 "FLOAT" 851306 T FLOAT (NIL) -8 NIL NIL) (-348 842840 843340 843918 "FLOATCP" 844869 NIL FLOATCP (NIL T) -7 NIL NIL) (-347 841628 842476 842517 "FLINEXP" 842522 NIL FLINEXP (NIL T) -9 NIL 842615) (-346 840783 841018 841345 "FLINEXP-" 841350 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-345 839859 840003 840227 "FLASORT" 840635 NIL FLASORT (NIL T T) -7 NIL NIL) (-344 837077 837919 837972 "FLALG" 839199 NIL FLALG (NIL T T) -9 NIL 839666) (-343 830861 834563 834605 "FLAGG" 835867 NIL FLAGG (NIL T) -9 NIL 836519) (-342 829587 829926 830416 "FLAGG-" 830421 NIL FLAGG- (NIL T T) -8 NIL NIL) (-341 828629 828772 828999 "FLAGG2" 829440 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 825601 826619 826679 "FINRALG" 827807 NIL FINRALG (NIL T T) -9 NIL 828315) (-339 824761 824990 825329 "FINRALG-" 825334 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-338 824167 824380 824409 "FINITE" 824605 T FINITE (NIL) -9 NIL 824712) (-337 816626 818787 818828 "FINAALG" 822495 NIL FINAALG (NIL T) -9 NIL 823948) (-336 811967 813008 814152 "FINAALG-" 815531 NIL FINAALG- (NIL T T) -8 NIL NIL) (-335 811362 811722 811825 "FILE" 811897 NIL FILE (NIL T) -8 NIL NIL) (-334 810046 810358 810413 "FILECAT" 811097 NIL FILECAT (NIL T T) -9 NIL 811313) (-333 807908 809464 809493 "FIELD" 809533 T FIELD (NIL) -9 NIL 809613) (-332 806528 806913 807424 "FIELD-" 807429 NIL FIELD- (NIL T) -8 NIL NIL) (-331 804343 805165 805511 "FGROUP" 806215 NIL FGROUP (NIL T) -8 NIL NIL) (-330 803433 803597 803817 "FGLMICPK" 804175 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-329 799235 803358 803415 "FFX" 803420 NIL FFX (NIL T NIL) -8 NIL NIL) (-328 798836 798897 799032 "FFSLPE" 799168 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-327 794831 795608 796404 "FFPOLY" 798072 NIL FFPOLY (NIL T) -7 NIL NIL) (-326 794335 794371 794580 "FFPOLY2" 794789 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-325 790157 794254 794317 "FFP" 794322 NIL FFP (NIL T NIL) -8 NIL NIL) (-324 785525 790068 790132 "FF" 790137 NIL FF (NIL NIL NIL) -8 NIL NIL) (-323 780621 784868 785058 "FFNBX" 785379 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-322 775531 779756 780014 "FFNBP" 780475 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-321 770134 774815 775026 "FFNB" 775364 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-320 768966 769164 769479 "FFINTBAS" 769931 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-319 765189 767429 767458 "FFIELDC" 768078 T FFIELDC (NIL) -9 NIL 768454) (-318 763852 764222 764719 "FFIELDC-" 764724 NIL FFIELDC- (NIL T) -8 NIL NIL) (-317 763422 763467 763591 "FFHOM" 763794 NIL FFHOM (NIL T T T) -7 NIL NIL) (-316 761120 761604 762121 "FFF" 762937 NIL FFF (NIL T) -7 NIL NIL) (-315 756708 760862 760963 "FFCGX" 761063 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-314 752310 756440 756547 "FFCGP" 756651 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-313 747463 752037 752145 "FFCG" 752246 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-312 729408 738531 738618 "FFCAT" 743783 NIL FFCAT (NIL T T T) -9 NIL 745270) (-311 724606 725653 726967 "FFCAT-" 728197 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-310 724017 724060 724295 "FFCAT2" 724557 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-309 713217 717007 718224 "FEXPR" 722872 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-308 712216 712651 712693 "FEVALAB" 712777 NIL FEVALAB (NIL T) -9 NIL 713038) (-307 711375 711585 711923 "FEVALAB-" 711928 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-306 709968 710758 710961 "FDIV" 711274 NIL FDIV (NIL T T T T) -8 NIL NIL) (-305 707034 707749 707865 "FDIVCAT" 709433 NIL FDIVCAT (NIL T T T T) -9 NIL 709870) (-304 706796 706823 706993 "FDIVCAT-" 706998 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-303 706016 706103 706380 "FDIV2" 706703 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-302 704709 704966 705253 "FCPAK1" 705749 T FCPAK1 (NIL) -7 NIL NIL) (-301 703837 704209 704350 "FCOMP" 704600 NIL FCOMP (NIL T) -8 NIL NIL) (-300 687477 690889 694449 "FC" 700297 T FC (NIL) -8 NIL NIL) (-299 680072 684118 684159 "FAXF" 685961 NIL FAXF (NIL T) -9 NIL 686652) (-298 677351 678006 678831 "FAXF-" 679296 NIL FAXF- (NIL T T) -8 NIL NIL) (-297 672451 676727 676903 "FARRAY" 677208 NIL FARRAY (NIL T) -8 NIL NIL) (-296 667841 669912 669965 "FAMR" 670977 NIL FAMR (NIL T T) -9 NIL 671437) (-295 666732 667034 667468 "FAMR-" 667473 NIL FAMR- (NIL T T T) -8 NIL NIL) (-294 665928 666654 666707 "FAMONOID" 666712 NIL FAMONOID (NIL T) -8 NIL NIL) (-293 663760 664444 664498 "FAMONC" 665439 NIL FAMONC (NIL T T) -9 NIL 665824) (-292 662452 663514 663651 "FAGROUP" 663656 NIL FAGROUP (NIL T) -8 NIL NIL) (-291 660255 660574 660976 "FACUTIL" 662133 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-290 659354 659539 659761 "FACTFUNC" 660065 NIL FACTFUNC (NIL T) -7 NIL NIL) (-289 651677 658605 658817 "EXPUPXS" 659210 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-288 649160 649700 650286 "EXPRTUBE" 651111 T EXPRTUBE (NIL) -7 NIL NIL) (-287 645354 645946 646683 "EXPRODE" 648499 NIL EXPRODE (NIL T T) -7 NIL NIL) (-286 630516 644013 644439 "EXPR" 644960 NIL EXPR (NIL T) -8 NIL NIL) (-285 624944 625531 626343 "EXPR2UPS" 629814 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-284 624580 624637 624744 "EXPR2" 624881 NIL EXPR2 (NIL T T) -7 NIL NIL) (-283 615934 623717 624012 "EXPEXPAN" 624418 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-282 615761 615891 615920 "EXIT" 615925 T EXIT (NIL) -8 NIL NIL) (-281 615388 615450 615563 "EVALCYC" 615693 NIL EVALCYC (NIL T) -7 NIL NIL) (-280 614928 615046 615088 "EVALAB" 615258 NIL EVALAB (NIL T) -9 NIL 615362) (-279 614409 614531 614752 "EVALAB-" 614757 NIL EVALAB- (NIL T T) -8 NIL NIL) (-278 611871 613183 613212 "EUCDOM" 613767 T EUCDOM (NIL) -9 NIL 614117) (-277 610276 610718 611308 "EUCDOM-" 611313 NIL EUCDOM- (NIL T) -8 NIL NIL) (-276 597854 600602 603342 "ESTOOLS" 607556 T ESTOOLS (NIL) -7 NIL NIL) (-275 597490 597547 597654 "ESTOOLS2" 597791 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-274 597241 597283 597363 "ESTOOLS1" 597442 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-273 591178 592902 592931 "ES" 595695 T ES (NIL) -9 NIL 597101) (-272 586126 587412 589229 "ES-" 589393 NIL ES- (NIL T) -8 NIL NIL) (-271 582501 583261 584041 "ESCONT" 585366 T ESCONT (NIL) -7 NIL NIL) (-270 582246 582278 582360 "ESCONT1" 582463 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-269 581921 581971 582071 "ES2" 582190 NIL ES2 (NIL T T) -7 NIL NIL) (-268 581551 581609 581718 "ES1" 581857 NIL ES1 (NIL T T) -7 NIL NIL) (-267 580767 580896 581072 "ERROR" 581395 T ERROR (NIL) -7 NIL NIL) (-266 574270 580626 580717 "EQTBL" 580722 NIL EQTBL (NIL T T) -8 NIL NIL) (-265 566707 569588 571035 "EQ" 572856 NIL -3213 (NIL T) -8 NIL NIL) (-264 566339 566396 566505 "EQ2" 566644 NIL EQ2 (NIL T T) -7 NIL NIL) (-263 561631 562677 563770 "EP" 565278 NIL EP (NIL T) -7 NIL NIL) (-262 560790 561354 561383 "ENTIRER" 561388 T ENTIRER (NIL) -9 NIL 561433) (-261 557246 558745 559115 "EMR" 560589 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-260 556389 556574 556629 "ELTAGG" 557009 NIL ELTAGG (NIL T T) -9 NIL 557220) (-259 556108 556170 556311 "ELTAGG-" 556316 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-258 555896 555925 555980 "ELTAB" 556064 NIL ELTAB (NIL T T) -9 NIL NIL) (-257 555022 555168 555367 "ELFUTS" 555747 NIL ELFUTS (NIL T T) -7 NIL NIL) (-256 554763 554819 554848 "ELEMFUN" 554953 T ELEMFUN (NIL) -9 NIL NIL) (-255 554633 554654 554722 "ELEMFUN-" 554727 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-254 549524 552733 552775 "ELAGG" 553715 NIL ELAGG (NIL T) -9 NIL 554178) (-253 547809 548243 548906 "ELAGG-" 548911 NIL ELAGG- (NIL T T) -8 NIL NIL) (-252 540677 542476 543303 "EFUPXS" 547085 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-251 534127 535928 536738 "EFULS" 539953 NIL EFULS (NIL T T T) -8 NIL NIL) (-250 531558 531916 532394 "EFSTRUC" 533759 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-249 520630 522195 523755 "EF" 530073 NIL EF (NIL T T) -7 NIL NIL) (-248 519731 520115 520264 "EAB" 520501 T EAB (NIL) -8 NIL NIL) (-247 518944 519690 519718 "E04UCFA" 519723 T E04UCFA (NIL) -8 NIL NIL) (-246 518157 518903 518931 "E04NAFA" 518936 T E04NAFA (NIL) -8 NIL NIL) (-245 517370 518116 518144 "E04MBFA" 518149 T E04MBFA (NIL) -8 NIL NIL) (-244 516583 517329 517357 "E04JAFA" 517362 T E04JAFA (NIL) -8 NIL NIL) (-243 515798 516542 516570 "E04GCFA" 516575 T E04GCFA (NIL) -8 NIL NIL) (-242 515013 515757 515785 "E04FDFA" 515790 T E04FDFA (NIL) -8 NIL NIL) (-241 514226 514972 515000 "E04DGFA" 515005 T E04DGFA (NIL) -8 NIL NIL) (-240 508411 509756 511118 "E04AGNT" 512884 T E04AGNT (NIL) -7 NIL NIL) (-239 507137 507617 507658 "DVARCAT" 508133 NIL DVARCAT (NIL T) -9 NIL 508331) (-238 506341 506553 506867 "DVARCAT-" 506872 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-237 499203 506143 506270 "DSMP" 506275 NIL DSMP (NIL T T T) -8 NIL NIL) (-236 494013 495148 496216 "DROPT" 498155 T DROPT (NIL) -8 NIL NIL) (-235 493678 493737 493835 "DROPT1" 493948 NIL DROPT1 (NIL T) -7 NIL NIL) (-234 488793 489919 491056 "DROPT0" 492561 T DROPT0 (NIL) -7 NIL NIL) (-233 487138 487463 487849 "DRAWPT" 488427 T DRAWPT (NIL) -7 NIL NIL) (-232 481813 482712 483767 "DRAW" 486136 NIL DRAW (NIL T) -7 NIL NIL) (-231 481454 481505 481621 "DRAWHACK" 481756 NIL DRAWHACK (NIL T) -7 NIL NIL) (-230 480185 480454 480745 "DRAWCX" 481183 T DRAWCX (NIL) -7 NIL NIL) (-229 479703 479771 479921 "DRAWCURV" 480111 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-228 470175 472133 474248 "DRAWCFUN" 477608 T DRAWCFUN (NIL) -7 NIL NIL) (-227 466988 468870 468912 "DQAGG" 469541 NIL DQAGG (NIL T) -9 NIL 469814) (-226 455494 462232 462315 "DPOLCAT" 464153 NIL DPOLCAT (NIL T T T T) -9 NIL 464697) (-225 450334 451680 453637 "DPOLCAT-" 453642 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-224 444418 450196 450293 "DPMO" 450298 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-223 438405 444199 444365 "DPMM" 444370 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-222 438038 438114 438212 "DOMAIN" 438327 T DOMAIN (NIL) -8 NIL NIL) (-221 431750 437675 437826 "DMP" 437939 NIL DMP (NIL NIL T) -8 NIL NIL) (-220 431350 431406 431550 "DLP" 431688 NIL DLP (NIL T) -7 NIL NIL) (-219 424994 430451 430678 "DLIST" 431155 NIL DLIST (NIL T) -8 NIL NIL) (-218 421840 423849 423891 "DLAGG" 424441 NIL DLAGG (NIL T) -9 NIL 424670) (-217 420549 421241 421270 "DIVRING" 421420 T DIVRING (NIL) -9 NIL 421528) (-216 419537 419790 420183 "DIVRING-" 420188 NIL DIVRING- (NIL T) -8 NIL NIL) (-215 417639 417996 418402 "DISPLAY" 419151 T DISPLAY (NIL) -7 NIL NIL) (-214 411528 417553 417616 "DIRPROD" 417621 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-213 410376 410579 410844 "DIRPROD2" 411321 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 400006 406011 406065 "DIRPCAT" 406473 NIL DIRPCAT (NIL NIL T) -9 NIL 407300) (-211 397332 397974 398855 "DIRPCAT-" 399192 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-210 396619 396779 396965 "DIOSP" 397166 T DIOSP (NIL) -7 NIL NIL) (-209 393321 395531 395573 "DIOPS" 396007 NIL DIOPS (NIL T) -9 NIL 396236) (-208 392870 392984 393175 "DIOPS-" 393180 NIL DIOPS- (NIL T T) -8 NIL NIL) (-207 391741 392379 392408 "DIFRING" 392595 T DIFRING (NIL) -9 NIL 392704) (-206 391387 391464 391616 "DIFRING-" 391621 NIL DIFRING- (NIL T) -8 NIL NIL) (-205 389176 390458 390499 "DIFEXT" 390858 NIL DIFEXT (NIL T) -9 NIL 391151) (-204 387462 387890 388555 "DIFEXT-" 388560 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-203 384784 386994 387036 "DIAGG" 387041 NIL DIAGG (NIL T) -9 NIL 387061) (-202 384168 384325 384577 "DIAGG-" 384582 NIL DIAGG- (NIL T T) -8 NIL NIL) (-201 379633 383127 383404 "DHMATRIX" 383937 NIL DHMATRIX (NIL T) -8 NIL NIL) (-200 375245 376154 377164 "DFSFUN" 378643 T DFSFUN (NIL) -7 NIL NIL) (-199 370031 373959 374324 "DFLOAT" 374900 T DFLOAT (NIL) -8 NIL NIL) (-198 368264 368545 368940 "DFINTTLS" 369739 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 365297 366299 366697 "DERHAM" 367931 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363146 365072 365161 "DEQUEUE" 365241 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 362364 362497 362692 "DEGRED" 363008 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 358780 359521 360369 "DEFINTRF" 361596 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 356319 356786 357382 "DEFINTEF" 358301 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350150 355760 355926 "DECIMAL" 356173 T DECIMAL (NIL) -8 NIL NIL) (-191 347662 348120 348626 "DDFACT" 349694 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 347258 347301 347452 "DBLRESP" 347613 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 344968 345302 345671 "DBASE" 347016 NIL DBASE (NIL T) -8 NIL NIL) (-188 344103 344927 344955 "D03FAFA" 344960 T D03FAFA (NIL) -8 NIL NIL) (-187 343239 344062 344090 "D03EEFA" 344095 T D03EEFA (NIL) -8 NIL NIL) (-186 341189 341655 342144 "D03AGNT" 342770 T D03AGNT (NIL) -7 NIL NIL) (-185 340507 341148 341176 "D02EJFA" 341181 T D02EJFA (NIL) -8 NIL NIL) (-184 339825 340466 340494 "D02CJFA" 340499 T D02CJFA (NIL) -8 NIL NIL) (-183 339143 339784 339812 "D02BHFA" 339817 T D02BHFA (NIL) -8 NIL NIL) (-182 338461 339102 339130 "D02BBFA" 339135 T D02BBFA (NIL) -8 NIL NIL) (-181 331659 333247 334853 "D02AGNT" 336875 T D02AGNT (NIL) -7 NIL NIL) (-180 329428 329950 330496 "D01WGTS" 331133 T D01WGTS (NIL) -7 NIL NIL) (-179 328531 329387 329415 "D01TRNS" 329420 T D01TRNS (NIL) -8 NIL NIL) (-178 327634 328490 328518 "D01GBFA" 328523 T D01GBFA (NIL) -8 NIL NIL) (-177 326737 327593 327621 "D01FCFA" 327626 T D01FCFA (NIL) -8 NIL NIL) (-176 325840 326696 326724 "D01ASFA" 326729 T D01ASFA (NIL) -8 NIL NIL) (-175 324943 325799 325827 "D01AQFA" 325832 T D01AQFA (NIL) -8 NIL NIL) (-174 324046 324902 324930 "D01APFA" 324935 T D01APFA (NIL) -8 NIL NIL) (-173 323149 324005 324033 "D01ANFA" 324038 T D01ANFA (NIL) -8 NIL NIL) (-172 322252 323108 323136 "D01AMFA" 323141 T D01AMFA (NIL) -8 NIL NIL) (-171 321355 322211 322239 "D01ALFA" 322244 T D01ALFA (NIL) -8 NIL NIL) (-170 320458 321314 321342 "D01AKFA" 321347 T D01AKFA (NIL) -8 NIL NIL) (-169 319561 320417 320445 "D01AJFA" 320450 T D01AJFA (NIL) -8 NIL NIL) (-168 312865 314414 315973 "D01AGNT" 318022 T D01AGNT (NIL) -7 NIL NIL) (-167 312202 312330 312482 "CYCLOTOM" 312733 T CYCLOTOM (NIL) -7 NIL NIL) (-166 308937 309650 310377 "CYCLES" 311495 T CYCLES (NIL) -7 NIL NIL) (-165 308249 308383 308554 "CVMP" 308798 NIL CVMP (NIL T) -7 NIL NIL) (-164 306031 306288 306663 "CTRIGMNP" 307977 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 305405 305504 305657 "CSTTOOLS" 305928 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 301204 301861 302619 "CRFP" 304717 NIL CRFP (NIL T T) -7 NIL NIL) (-161 300251 300436 300664 "CRAPACK" 301008 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 299635 299736 299940 "CPMATCH" 300127 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 299360 299388 299494 "CPIMA" 299601 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 295724 296396 297114 "COORDSYS" 298695 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 291585 293727 294219 "CONTFRAC" 295264 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 290738 291302 291331 "COMRING" 291336 T COMRING (NIL) -9 NIL 291387) (-155 289819 290096 290280 "COMPPROP" 290574 T COMPPROP (NIL) -8 NIL NIL) (-154 289480 289515 289643 "COMPLPAT" 289778 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 279461 289289 289398 "COMPLEX" 289403 NIL COMPLEX (NIL T) -8 NIL NIL) (-152 279097 279154 279261 "COMPLEX2" 279398 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-151 278815 278850 278948 "COMPFACT" 279056 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263149 273443 273484 "COMPCAT" 274486 NIL COMPCAT (NIL T) -9 NIL 275879) (-149 252664 255588 259215 "COMPCAT-" 259571 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 252395 252423 252525 "COMMUPC" 252630 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 252190 252223 252282 "COMMONOP" 252356 T COMMONOP (NIL) -7 NIL NIL) (-146 251773 251941 252028 "COMM" 252123 T COMM (NIL) -8 NIL NIL) (-145 251027 251219 251248 "COMBOPC" 251584 T COMBOPC (NIL) -9 NIL 251757) (-144 249923 250133 250375 "COMBINAT" 250817 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246129 246700 247338 "COMBF" 249347 NIL COMBF (NIL T T) -7 NIL NIL) (-142 244915 245245 245480 "COLOR" 245914 T COLOR (NIL) -8 NIL NIL) (-141 244555 244602 244727 "CMPLXRT" 244862 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240057 241085 242165 "CLIP" 243495 T CLIP (NIL) -7 NIL NIL) (-139 238395 239165 239403 "CLIF" 239885 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 234617 236541 236583 "CLAGG" 237512 NIL CLAGG (NIL T) -9 NIL 238048) (-137 233039 233496 234079 "CLAGG-" 234084 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 232583 232668 232808 "CINTSLPE" 232948 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230084 230555 231103 "CHVAR" 232111 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 229306 229870 229899 "CHARZ" 229904 T CHARZ (NIL) -9 NIL 229918) (-133 229060 229100 229178 "CHARPOL" 229260 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 228166 228763 228792 "CHARNZ" 228839 T CHARNZ (NIL) -9 NIL 228894) (-131 226189 226856 227191 "CHAR" 227851 T CHAR (NIL) -8 NIL NIL) (-130 225914 225975 226004 "CFCAT" 226115 T CFCAT (NIL) -9 NIL NIL) (-129 225159 225270 225452 "CDEN" 225798 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 221151 224312 224592 "CCLASS" 224899 T CCLASS (NIL) -8 NIL NIL) (-127 216204 217180 217933 "CARTEN" 220454 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-126 215312 215460 215681 "CARTEN2" 216051 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-125 213609 214464 214720 "CARD" 215076 T CARD (NIL) -8 NIL NIL) (-124 212981 213309 213338 "CACHSET" 213470 T CACHSET (NIL) -9 NIL 213547) (-123 212477 212773 212802 "CABMON" 212852 T CABMON (NIL) -9 NIL 212908) (-122 210034 212169 212276 "BTREE" 212403 NIL BTREE (NIL T) -8 NIL NIL) (-121 207532 209682 209804 "BTOURN" 209944 NIL BTOURN (NIL T) -8 NIL NIL) (-120 204950 207003 207045 "BTCAT" 207113 NIL BTCAT (NIL T) -9 NIL 207190) (-119 204617 204697 204846 "BTCAT-" 204851 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 199837 203708 203737 "BTAGG" 203993 T BTAGG (NIL) -9 NIL 204172) (-117 199260 199404 199634 "BTAGG-" 199639 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 196304 198538 198753 "BSTREE" 199077 NIL BSTREE (NIL T) -8 NIL NIL) (-115 195442 195568 195752 "BRILL" 196160 NIL BRILL (NIL T) -7 NIL NIL) (-114 192143 194170 194212 "BRAGG" 194861 NIL BRAGG (NIL T) -9 NIL 195118) (-113 190672 191078 191633 "BRAGG-" 191638 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 183880 190018 190202 "BPADICRT" 190520 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 182184 183817 183862 "BPADIC" 183867 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 181884 181914 182027 "BOUNDZRO" 182148 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-109 177399 178490 179357 "BOP" 181037 T BOP (NIL) -8 NIL NIL) (-108 175020 175464 175984 "BOP1" 176912 NIL BOP1 (NIL T) -7 NIL NIL) (-107 173639 174350 174573 "BOOLEAN" 174817 T BOOLEAN (NIL) -8 NIL NIL) (-106 173005 173383 173436 "BMODULE" 173441 NIL BMODULE (NIL T T) -9 NIL 173505) (-105 168815 172803 172876 "BITS" 172952 T BITS (NIL) -8 NIL NIL) (-104 167912 168347 168499 "BINFILE" 168683 T BINFILE (NIL) -8 NIL NIL) (-103 161747 167356 167521 "BINARY" 167767 T BINARY (NIL) -8 NIL NIL) (-102 159574 161002 161044 "BGAGG" 161304 NIL BGAGG (NIL T) -9 NIL 161441) (-101 159405 159437 159528 "BGAGG-" 159533 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158503 158789 158994 "BFUNCT" 159220 T BFUNCT (NIL) -8 NIL NIL) (-99 157204 157382 157667 "BEZOUT" 158327 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 153729 156064 156392 "BBTREE" 156907 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153466 153519 153546 "BASTYPE" 153663 T BASTYPE (NIL) -9 NIL NIL) (-96 153321 153350 153420 "BASTYPE-" 153425 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 152759 152835 152985 "BALFACT" 153232 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151581 152178 152363 "AUTOMOR" 152604 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151306 151311 151338 "ATTREG" 151343 T ATTREG (NIL) -9 NIL NIL) (-92 149585 150003 150355 "ATTRBUT" 150972 T ATTRBUT (NIL) -8 NIL NIL) (-91 149120 149233 149260 "ATRIG" 149461 T ATRIG (NIL) -9 NIL NIL) (-90 148929 148970 149057 "ATRIG-" 149062 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147126 148705 148793 "ASTACK" 148872 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145631 145928 146293 "ASSOCEQ" 146808 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144663 145290 145414 "ASP9" 145538 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144427 144611 144650 "ASP8" 144655 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143297 144032 144174 "ASP80" 144316 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142196 142932 143064 "ASP7" 143196 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141152 141873 141991 "ASP78" 142109 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140123 140832 140949 "ASP77" 141066 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139038 139761 139892 "ASP74" 140023 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 137939 138673 138805 "ASP73" 138937 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 136894 137616 137734 "ASP6" 137852 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 135843 136571 136689 "ASP55" 136807 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 134793 135517 135636 "ASP50" 135755 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 133881 134494 134604 "ASP4" 134714 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 132969 133582 133692 "ASP49" 133802 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 131754 132508 132676 "ASP42" 132858 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130532 131287 131457 "ASP41" 131641 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129484 130209 130327 "ASP35" 130445 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129249 129432 129471 "ASP34" 129476 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 128986 129053 129129 "ASP33" 129204 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 127882 128621 128753 "ASP31" 128885 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127647 127830 127869 "ASP30" 127874 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127382 127451 127527 "ASP29" 127602 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127147 127330 127369 "ASP28" 127374 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 126912 127095 127134 "ASP27" 127139 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 125996 126610 126721 "ASP24" 126832 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 124913 125637 125767 "ASP20" 125897 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124001 124614 124724 "ASP1" 124834 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 122945 123675 123794 "ASP19" 123913 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122682 122749 122825 "ASP12" 122900 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121535 122281 122425 "ASP10" 122569 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119434 121379 121470 "ARRAY2" 121475 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115250 119082 119196 "ARRAY1" 119351 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114282 114455 114676 "ARRAY12" 115073 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108641 110512 110588 "ARR2CAT" 113218 NIL ARR2CAT (NIL T T T) -9 NIL 113976) (-54 106075 106819 107773 "ARR2CAT-" 107778 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 104835 104985 105288 "APPRULE" 105913 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104488 104536 104654 "APPLYORE" 104781 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103462 103753 103948 "ANY" 104311 T ANY (NIL) -8 NIL NIL) (-50 102740 102863 103020 "ANY1" 103336 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100272 101190 101515 "ANTISYM" 102465 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100099 100231 100258 "ANON" 100263 T ANON (NIL) -8 NIL NIL) (-47 94176 98644 99095 "AN" 99666 T AN (NIL) -8 NIL NIL) (-46 90529 91927 91978 "AMR" 92717 NIL AMR (NIL T T) -9 NIL 93316) (-45 89642 89863 90225 "AMR-" 90230 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74192 89559 89620 "ALIST" 89625 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71029 73786 73955 "ALGSC" 74110 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67585 68139 68746 "ALGPKG" 70469 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66862 66963 67147 "ALGMFACT" 67471 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62612 63292 63946 "ALGMANIP" 66386 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53931 62238 62388 "ALGFF" 62545 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53127 53258 53437 "ALGFACT" 53789 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52117 52727 52766 "ALGEBRA" 52826 NIL ALGEBRA (NIL T) -9 NIL 52884) (-36 51835 51894 52026 "ALGEBRA-" 52031 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34095 49838 49891 "ALAGG" 50027 NIL ALAGG (NIL T T) -9 NIL 50188) (-34 33630 33743 33770 "AHYP" 33971 T AHYP (NIL) -9 NIL NIL) (-33 32560 32808 32835 "AGG" 33334 T AGG (NIL) -9 NIL 33613) (-32 31994 32156 32370 "AGG-" 32375 NIL AGG- (NIL T) -8 NIL NIL) (-31 29681 30099 30516 "AF" 31637 NIL AF (NIL T T) -7 NIL NIL) (-30 28950 29208 29364 "ACPLOT" 29543 T ACPLOT (NIL) -8 NIL NIL) (-29 18416 26362 26414 "ACFS" 27125 NIL ACFS (NIL T) -9 NIL 27364) (-28 16430 16920 17695 "ACFS-" 17700 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14653 14680 "ACF" 15559 T ACF (NIL) -9 NIL 15971) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11195 "ABELSG" 11287 T ABELSG (NIL) -9 NIL 11352) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10523 "ABELMON" 10693 T ABELMON (NIL) -9 NIL 10805) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9606 "ABELGRP" 9731 T ABELGRP (NIL) -9 NIL 9813) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8075 "A1AGG" 8080 NIL A1AGG (NIL T) -9 NIL 8120) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 14519fd0..7c106a3d 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,1389 +1,1181 @@ -(721991 . 3409435992) -(((*1 *2 *3 *3 *4 *3 *4 *4 *4 *5 *5 *5 *5 *4 *4 *6 *7) - (-12 (-5 *4 (-517)) (-5 *5 (-623 (-199))) - (-5 *6 (-3 (|:| |fn| (-358)) (|:| |fp| (-82 FCNF)))) - (-5 *7 (-3 (|:| |fn| (-358)) (|:| |fp| (-83 FCNG)))) (-5 *3 (-199)) - (-5 *2 (-952)) (-5 *1 (-682))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-866 (-199))) (-5 *2 (-1162)) (-5 *1 (-437))))) +(722241 . 3409486834) +(((*1 *2 *3 *4 *5 *6) + (|partial| -12 (-5 *4 (-1 *8 *8)) + (-5 *5 + (-1 (-3 (-2 (|:| -2791 *7) (|:| |coeff| *7)) "failed") *7)) + (-5 *6 (-583 (-377 *8))) (-4 *7 (-333)) (-4 *8 (-1134 *7)) + (-5 *3 (-377 *8)) + (-5 *2 + (-2 + (|:| |answer| + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-583 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (|:| |a0| *7))) + (-5 *1 (-527 *7 *8))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4196)) (-4 *1 (-114 *2)) (-4 *2 (-1112))))) +(((*1 *1 *1) + (-12 (-5 *1 (-542 *2)) (-4 *2 (-37 (-377 (-517)))) (-4 *2 (-964))))) +(((*1 *1 *1) + (-12 (-4 *1 (-296 *2 *3)) (-4 *2 (-964)) (-4 *3 (-724)) + (-4 *2 (-421)))) + ((*1 *1 *1) + (-12 (-4 *1 (-312 *2 *3 *4)) (-4 *2 (-1116)) (-4 *3 (-1134 *2)) + (-4 *4 (-1134 (-377 *3))))) + ((*1 *1 *1) (-12 (-4 *1 (-781 *2)) (-4 *2 (-964)) (-4 *2 (-421)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-873 *3 *4 *2)) (-4 *3 (-964)) (-4 *4 (-725)) + (-4 *2 (-779)) (-4 *3 (-421)))) + ((*1 *1 *1) + (-12 (-4 *1 (-873 *2 *3 *4)) (-4 *2 (-964)) (-4 *3 (-725)) + (-4 *4 (-779)) (-4 *2 (-421)))) + ((*1 *2 *2 *3) + (-12 (-4 *3 (-278)) (-4 *3 (-509)) (-5 *1 (-1065 *3 *2)) + (-4 *2 (-1134 *3))))) +(((*1 *2) (-12 (-5 *2 (-1060)) (-5 *1 (-215))))) (((*1 *1 *2) - (-12 (-5 *2 (-844)) (-4 *1 (-212 *3 *4)) (-4 *4 (-963)) - (-4 *4 (-1111)))) - ((*1 *1 *2) - (-12 (-14 *3 (-583 (-1076))) (-4 *4 (-156)) - (-4 *5 (-212 (-3535 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continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1057 (-199))) + (-3 (|:| |str| (-1058 (-199))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2758 + (|:| -3177 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -13292,668 +13510,701 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-512))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-583 (-286 (-199)))) (-5 *4 (-703)) - (-5 *2 (-623 (-199))) (-5 *1 (-240))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-779) (-509))) (-5 *1 (-249 *3 *2)) + (-4 *2 (-13 (-400 *3) (-921)))))) (((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-844)) (-5 *2 (-703)) (-5 *1 (-1006 *4 *5)) (-14 *4 *3) + (-12 (-5 *3 (-845)) (-5 *2 (-703)) (-5 *1 (-1007 *4 *5)) (-14 *4 *3) (-14 *5 *3)))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-583 *1)) (-5 *3 (-583 *7)) (-4 *1 (-982 *4 *5 *6 *7)) - (-4 *4 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\ No newline at end of file diff --git a/src/testsuite/interpreter/1849734.input b/src/testsuite/interpreter/1849734.input new file mode 100644 index 00000000..ca1eb28f --- /dev/null +++ b/src/testsuite/interpreter/1849734.input @@ -0,0 +1,6 @@ +++ Contributed by Gabriel Dos Reis +-- Issue: the interpreter should allow overload of logical operators. +a := 2::OutputForm +b := 4::OutputForm +a and b + |